Radar device

More than one reissue application has been filed for the reissue of U.S. Pat. No. 10,371,796, issued Aug. 6, 2019: application Ser. No. 17/394,286, filed Aug. 4, 2021, which is an application for reissue of U.S. Pat. No. 10,371,796; and this application, application Ser. No. 18/217,419, filed Jun. 30, 2023, which is a continuation reissue of application Ser. No. 17/394,286.

1. Technical Field

The present disclosure relates to a radar device.

2. Description of the Related Art

In recent years, studies are being made of a radar device using radar transmission signals with short wavelengths including microwaves and millimeter waves by which high resolution can be obtained. Moreover, there is a demand for development of a radar device (wide-angle radar device) which detects objects (targets) including not only vehicles but also pedestrians in a wide angular range to improve safety outdoors.

For example, a pulse radar device which repeatedly transmits pulse waves is known as the radar device. A reception signal of a wide-angle pulse radar which detects vehicles and pedestrians in a wide angular range is a signal in which multiple reflected waves from a target (for example, a vehicle) existing in a close distance and a target (for example, a pedestrian) existing in a far distance are mixed. Accordingly, the radar device requires (1) a radar transmitter having a configuration which transmits pulse waves or pulse modulated waves having autocorrelation characteristics achieving low range side lobes (hereafter, referred to as low range side lobe characteristics) and (2) a radar receiver having a configuration with a wide reception dynamic range.

The following two configurations can be given as examples of the configuration of the wide-range radar device.

The first configuration is a configuration in which radar waves being pulse waves or modulated waves are transmitted by performing mechanical or electronic scanning using a directional beam with a narrow angle (with a beam width of about several degrees), and reflected waves are received by using the directional beam with the narrow-angle. In this configuration, scanning needs to be performed many times to obtain high resolution. Accordingly, a tracking performance for a target moving at high speed is poor.

The second configuration is a configuration in which reflected waves are received by an array antenna formed of multiple antennas (antenna elements) and which uses a method of estimating an arrival angle of each reflected wave by using a signal processing algorithm based on a reception phase difference corresponding to a space between the antennas (direction of arrival (DOA) estimation). In this configuration, estimation of the arrival angle in a reception branch can be performed even when some of scan intervals of transmission beams are omitted in a transmission branch. Accordingly, the scanning time is reduced and the tracking performance is improved compared to the first configuration. Examples of the direction-of-arrival estimation method include: Fourier conversion based on matrix operations; a Capon method and a linear prediction (LP) method based on inverted matrix operations; and multiple signal classification (MUSIC) and estimation of signal parameters via rotational invariance techniques (ESPRIT) based on unique value operations.

Moreover, there is proposed a configuration (hereafter, referred also to as MIMO radar) of the radar device which includes multiple antennas (array antennas) in the transmission branch in addition to the reception branch and performs the beam scanning by performing signal processing using transmission and reception array antennas (for example, see Jian Li, Petre Stoica, “MIMO Radar with Colocated Antennas,” Signal Processing Magazine, IEEE Vol. 24, Issue: 5, pp. 106-114, 2007).

In the MIMO radar, by arranging the antenna elements in the transmission and reception array antennas in a certain way, virtual reception array antennas (hereafter, referred to as virtual reception array) can be formed as many as the product of the number of the transmission antenna elements and the number of the reception antenna elements at maximum. This has an effect of increasing an effective aperture length of the array antennas with few elements.

Moreover, the MIMO radar can be applied not only to one-dimensional scanning in a vertical or horizontal direction but also to two-dimensional beam scanning in the vertical and horizontal directions.

However, when the number of antennas in the transmission and reception branch is restricted to achieve cost and size reduction of the MIMO radar (for example, when the number of transmission antennas is about four and the number of reception antennas is about four), the aperture lengths in the vertical and horizontal directions are restricted in the planar virtual reception array formed by the MIMO radar.

One non-limiting and exemplary embodiment provides a radar device which can increase the aperture length in the virtual reception array as much as possible.

In one general aspect, the techniques disclosed here feature a radar device including: a radar transmitter which, in operation, transmits a plurality of radar signals at predetermined transmission cycles from a plurality of transmission antennas; and a radar receiver which, in operation, receives a plurality of reflected wave signals being the plurality of radar signals reflected on a target, by using a plurality of reception antennas, wherein the plurality of transmission antennas include Nt1 transmission antennas arranged in a first direction and Nt2 transmission antennas arranged in a second direction orthogonal to the first direction, the plurality of reception antennas include Na1 reception antennas arranged in the first direction and Na2 reception antennas arranged in the second direction, in the first direction, an inter-element space between any two of the Nt1 transmission antennas and an inter-element space between any two of the Na1 reception antennas equal to a product of the first space and an integer and are different from each other, and in the second direction, an inter-element space between any two of the Nt2 transmission antennas and an inter-element space between any two of the Na2 reception antennas equal to a product of a second space and an integer and are different from each other.

In the one aspect of the present disclosure, the aperture length in the virtual reception array can be increased as much as possible.

It should be noted that general or specific embodiments may be implemented as a system, a method, an integrated circuit, a computer program, a storage medium, or any selective combination thereof.

Additional benefits and advantages of the disclosed embodiments will become apparent from the specification and drawings. The benefits and/or advantages may be individually obtained by the various embodiments and features of the specification and drawings, which need not all be provided in order to obtain one or more of such benefits and/or advantages.

1 FIG.A 1 FIG.B illustrates an antenna arrangement of a transmission array antenna including four transmission antennas (Tx#1 to Tx#4), andillustrates a reception array antenna including four reception antennas (Rx#1 to Rx#4).

1 1 FIGS.A andB 1 FIG.A H V H V In, ddenotes an inter-element space between the reception antennas in a horizontal direction, and ddenotes an inter-element space between the reception antennas in a vertical direction. Meanwhile, in, inter-element spaces among the transmission antennas in the horizontal direction and the vertical direction are 2dand 2d, respectively.

1 FIG.C 1 1 FIGS.A andB illustrates a virtual reception array including the transmission and reception array antennas in the antenna arrangements illustrated in.

1 FIG.C As illustrated in, the virtual reception array includes 16 virtual reception antennas (VA#1 to VA#16) which are planarly arranged in a pattern of four antennas in the horizontal direction and four antennas in the vertical direction.

1 FIG.C H V H V H V In, inter-element spaces among the virtual reception antennas in the horizontal direction and the vertical direction are dand d, respectively. In other words, the aperture lengths Dand Dof the virtual reception array in the horizontal direction and the vertical direction are 3dand 3d, respectively.

H V H V For example, the beam width (Fourier beam width) BW of a Fourier beam which has an equal amplitude weight and which is formed by using a virtual reception array with inter-element spaces of d=d=dand an aperture length of D=D=Dis expressed by the following formula:BW≈0.7λ/D [rad]where λ is a wavelength of a carrier frequency of a radio signal (RF signal) transmitted from a transmission branch.

1 FIG.C In the virtual reception array (D=3d) illustrated in, Fourier beam width BW≈0.7λ/3d [rad].

For example, in the case of d=0.5λ, Fourier beam width BW≈0.7/1.5 [rad]≈30°. Meanwhile, in the case of d=0.7λ, Fourier beam width BW≈0.7/2.1 [rad]≈19°.

Further increasing the inter-element space d can reduce the Fourier beam width BW. However, increasing the inter-element space d generates grating lobes at angles relatively close to a main beam and erroneous detection increases.

2 FIG.A 2 FIG.B 2 2 FIGS.A andB For example,illustrates a directional pattern in the case of inter-element space d=0.5λ, andillustrates a directional pattern in the case of inter-element space d=1.3λ. Note that, in, the main beam is formed in the 0° direction.

2 FIG.A 2 FIG.A As illustrated in, in the case of inter-element space d=0.5λ, the Fourier beam width BW of the main beam is about 30° and is relatively large. Moreover, in, no grating lobes are generated in a range of −90° to +90°.

2 FIG.B Meanwhile, as illustrated in, in the case of inter-element space d=1.3λ, the Fourier beam width BW of the main beam is about 10° and is relatively small. However, grating lobes are generated at angles away from the main beam (0° direction) by −50° and +50°.

2 FIG.B For example, in, when the detection angle of a wide-angle radar is equal to or larger than a range of about −25° to +25°, the grating lobes are generated in the angular detection range and the erroneous detection thereby increases.

As described above, in the reduction of the Fourier beam width BW, there is a restriction that the inter-element space d can be increased only to a certain degree. Instead of increasing the inter-element space d, the aperture length D can be increased by increasing the number of antenna element. However, in consideration of cost reduction, there are restrictions on the aperture length D of the virtual reception array.

When, for example, the MUSIC, the Capon method, or the like is used as the DOA estimation algorithm to achieve angular resolution of about 10° under the restrictions described above, a computation amount for performing eigenvalue decomposition or an inverse matrix operation increases. Moreover, when the DOA estimation algorithm achieving high resolution is applied, it is difficult to obtain high angular separation performance unless the signal to noise ratio (SNR) is sufficiently high.

In one aspect of the present disclosure, when beam scanning is performed two-dimensionally in the vertical direction and the horizontal direction by using a MIMO radar, the aperture lengths of the virtual reception array in the vertical direction and the horizontal direction are increased as much as possible. Using such a virtual reception array can improve the angular resolution with few antenna elements, and the size and cost of the radar device are reduced.

An embodiment of one aspect of the present disclosure is described below in detail with reference to the drawings. Note that, in the embodiment, the same configuration elements are denoted by the same reference numerals and description thereof is omitted to avoid overlapping description.

Description is given below of a radar device configured such that different transmission signals subjected to code division multiplexing are transmitted from multiple transmission antennas in a transmission branch and reception processing is performed by separating the transmission signals in a reception branch. However, the configuration of the radar device is not limited to this and can be such that different transmission signals subjected to frequency division multiplexing are transmitted from multiple transmission antennas in the transmission branch and reception processing is performed by separating the transmission signals in the reception branch. Moreover, similarly, the configuration of the radar device can be such that transmission signals subjected to time division multiplexing are transmitted from multiple transmission antennas in the transmission branch and reception processing is performed by separating the transmission signals in the reception branch.

3 FIG. 10 is a block diagram illustrating a configuration of a radar devicein the embodiment.

10 100 200 300 The radar deviceincludes a radar transmitter (transmission branch), a radar receiver (reception branch), and a reference signal generator.

100 300 100 106 1 106 The radar transmittergenerates high-frequency (radio frequency) radar signals (radar transmission signals), based on a reference signal received from the reference signal generator. Then, the radar transmittertransmits the radar transmission signals at certain transmission cycles by using a transmission array antenna including multiple transmission antennas-to-Nt.

200 202 1 202 200 300 200 202 10 The radar receiverreceives reflected wave signals which are the radar transmission signals reflected on a target (not illustrated), by using a reception array antenna including multiple reception antennas-to-Na. The radar receiverperforms the following processing operations in synchronization with the radar transmitter by using the reference signal received from the reference signal generator. Specifically, the radar receiverperforms signal processing on the reflected wave signals received by the reception antennasand performs at least detection of presence or absence of a target and estimation of a direction of the target. Note that the target is an object to be detected by the radar deviceand includes, for example, vehicles (including four-wheel and two-wheel vehicles) and humans.

300 100 200 300 100 200 100 200 The reference signal generatoris connected to the radar transmitterand the radar receiver. The reference signal generatorprovides the radar transmitterand the radar receiverwith the reference signal serving as a signal for reference, to synchronize the processing of the radar transmitterand the processing of the radar receiver.

100 [Configuration of Radar Transmitter]

100 101 1 101 105 1 105 106 1 106 100 106 106 101 105 The radar transmitterincludes radar transmission signal generators-to-Nt, transmission radio units-to-Nt, and the transmission antennas-to-Nt. Specifically, the radar transmitterincludes Nt transmission antennas, and each of the transmission antennasare connected to a corresponding one of the radar transmission signal generatorsand a corresponding one of the transmission radio units.

101 300 101 106 z z z Each of the radar transmission signal generatorsgenerates timing clocks by multiplying the reference signal received from the reference signal generatorby a certain number, and generates the radar transmission signals based on the generated timing clocks. Then, the radar transmission signal generatorrepeatedly outputs the radar transmission signals at certain radar transmission cycles (Tr). The radar transmission signals are expressed by r(k, M)=I(k, M)+j Q(k, M). In this formula, z is the number corresponding to each of the transmission antennasand z=1, . . . , Nt. Moreover, j is an imaginary unit, k is a discrete time, and M is an ordinal number of the radar transmission cycle.

101 102 103 104 101 106 Each of the radar transmission signal generatorsincludes a code generator, a modulator, and a low pass filter (LPF). Description is given below of components of the radar transmission signal generator-z corresponding to the z-th (z=1, . . . , Nt) transmission antenna.

102 102 1 102 n n Specifically, the code generatorgenerates a code a(z)(n=1, . . . , L) (pulse code) of a code sequence with a code length L, every radar transmission cycle Tr. Codes with low correlation or no correlation are used as the codes a(z)(z=1, . . . , Nt) generated in the respective code generators-to-Nt. Examples of the code sequence include a Walsh-Hadamard code, an M-sequence code, a Gold code, and the like.

103 102 104 n The modulatorperforms pulse modulation (amplitude modulation, amplitude shift keying (ASK), or pulse shift keying) or phase modulation (phase shift keying) on each code a(z)received from the code generator, and outputs the modulated signal to the LPF.

104 103 105 The LPFoutputs a signal component in the modulated signal received from the modulatorwhich is equal to or lower than a certain limit band, as a baseband radar transmission signal to the transmission radio unit.

105 101 106 The z-th (z=1, . . . , Nt) transmission radio unitgenerates a radar transmission signal of a carrier frequency (radio frequency: RF) band by performing frequency conversion on the baseband radar transmission signal outputted from the z-th radar transmission signal generator, amplifies the generated radar transmission signal to certain transmission power P [dB] by using a transmission amplifier, and outputs the amplified radar transmission signal to the z-th transmission antenna.

106 105 The z-th (z=1, . . . , Nt) transmission antennaemits the radar transmission signal outputted from the z-th transmission radio unit, to a space.

4 FIG. 106 100 103 n illustrates the radar transmission signals transmitted from the Nt transmission antennasin the radar transmitter. The pulse code sequence of the code length L is included in a code transmission duration Tw. In each radar transmission cycle Tr, the pulse code sequence is transmitted within the code transmission duration Tw, and the remaining duration (Tr−Tw) is a no-signal duration. Pulse modulation using No samples is performed for each pulse code (a(z)), and Nr (=No×L) sample signals are thereby included in each code transmission duration Tw. In other words, the sampling rate in the modulatoris (No×L)/Tw. Meanwhile, Nu samples are included in the no-signal duration (Tr−Tw).

100 101 101 101 102 103 104 111 112 111 102 112 111 5 FIG. 3 FIG. 3 FIG. The radar transmittermay include a radar transmission signal generatora illustrated ininstead of the radar transmission signal generator. The radar transmission signal generatora does not include the code generator, the modulator, and the LPFwhich are illustrated in, and includes instead a code storageand a DA convertor. The code storagestores in advance the code sequences generated in the code generator() and the stored code sequences are read one by one in cycle. The DA convertorconverts the code sequences (digital signals) outputted from the code storageto analog signals.

200 [Configuration of Radar Receiver]

3 FIG. 200 202 200 201 1 201 214 In, the radar receiverincludes Na reception antennasand forms the array antenna. Moreover, the radar receiverincludes Na antenna system processors-to-Na and a direction estimator.

202 201 Each of the reception antennasreceives the reflected wave signal which is the radar transmission signal reflected on the target (object), and outputs the received reflected wave signal as a reception signal to a corresponding one of the antenna system processors.

201 203 207 Each of the antenna system processorsincludes a reception radio unitand a signal processor.

203 204 205 206 203 300 204 202 205 206 The reception radio unitincludes an amplifier, a frequency convertor, and a quadrature detector. The reception radio unitgenerates timing clocks by multiplying the reference signal received from the reference signal generatorby a certain number, and operates based on the generated timing clocks. Specifically, the amplifieramplifies the reception signal received from the reception antennato a certain level, the frequency convertorperforms frequency conversion to a baseband on a high-frequency band reception signal, and the quadrature detectorconverts the base-band reception signal to baseband reception signals including an I signal and a Q signal.

207 208 209 210 1 210 The signal processorincludes AD convertorsandand separators-to-Nt.

208 206 209 206 208 209 The I signal is inputted into the AD convertorfrom the quadrature detector, and the Q signal is inputted into the AD convertorfrom the quadrature detector. The AD convertorperforms sampling at discrete time on the base-band signal including the I signal to convert the I signal into digital data. The AD convertorperforms sampling at discrete time on the baseband signal including the Q signal to convert the Q signal into digital data.

208 209 In the sampling by the AD convertorsand, Ns discrete samples are obtained per time Tp (=Tw/L) of one sub-pulse in the radar transmission signal. In other words, the number of over samples per one sub-pulse is Ns.

208 209 207 In the following description, by using an I signal Ir(k, M) and a Q signal Qr(k, M), a baseband reception signal which is the outputs of the AD convertorsandat the discrete time k in the M-th radar transmission cycle Tr [M] is expressed as complex number signal x(k, M)=Ir(k, M)+j Qr(k, M). Moreover, in the following description, the discrete time k is based (k=1) on a timing at which the radar transmission cycle (Tr) starts, and the signal processorperiodically operates up to k=(Nr+Nu)Ns/No which is a sampling point before the end of the radar transmission cycle Tr. In other words, k=1, (Nr+Nu)Ns/No. In this case, j is an imaginary unit.

207 210 106 210 211 212 213 210 The signal processorincludes Nt separatorswhose number is equal to the number of the systems for the respective transmission antennas. Each of the separatorsincludes a correlation calculator, an adder, and a Doppler frequency analyzer. Description is given below of a configuration of the z-th (z=1, . . . , Nt) separator.

211 208 209 100 211 n n (z) The correlation calculatorcalculates a correlation between discrete sample values x(k, M) including discrete sample values Ir (k, M) and Qr (k, M) which are sent from the AD convertorsandevery radar transmission cycle Tr and the pulse codes a(z)(where z=1, . . . , Nt, and n=1, . . . , L) with the code length of L which are transmitted from the radar transmitter. For example, the correlation calculatorperforms sliding correlation calculation of the discrete sample values x(k, M) and the pulse codes a(z). For example, a correlation calculation value AC(k, M) of the sliding correlation calculation at the discrete time k in the M-th radar transmission cycle Tr [M] is calculated based on the following formula:

In the above formula, the asterisk (*) represents a complex conjugate operator.

211 For example, the correlation calculatorperforms the correlation calculation during a period of k=1, (Nr+Nu)Ns/No, according to the formula (1).

211 10 211 10 211 10 6 FIG. Note that the correlation calculatoris not limited to one performing the correlation calculation in the period of k=1, . . . , (Nr+Nu)Ns/No. A measurement range (that is, the range of k) can be limited depending on a range in which the target to be measured by the radar deviceexists. This can reduce the computation processing amount of the correlation calculatorin the radar device. For example, in the correlation calculator, the measurement range can be limited to k=Ns(L+1), . . . , (Nr+Nu)Ns/No−NsL. In this case, as illustrated in, the radar devicedoes not perform measurement in a time duration corresponding to the code transmission duration Tw.

200 211 10 212 213 214 200 Thus, when direct loop-back of a radar transmission signal to the radar receiveroccurs, since no processing by the correlation calculatoris performed in a period of the loop-back of the radar transmission signal (at least in a period less than τ1), the radar devicecan perform measurement with effects of the loop-back being eliminated. Moreover, in the case of limiting the measurement range (range of k), processing in which the measurement range (range of k) is similarly limited is applied as processing by the adder, the Doppler frequency analyzer, and the direction estimatorto be described later. This can reduce the processing amount in each component and reduce the power consumption of the radar receiver.

212 211 (z) (z) The adderuses correlation calculation values AC(k, M) received from the correlation calculatorevery discrete time k in the M-th radar transmission cycle Tr, and adds up (performs coherent integration of) the correlation calculation values AC(k, M) during a period (Tr×Np) which is equal to a certain number (Np) of the radar transmission cycles Tr. The addition (coherent integration) processing performed Np times (addition number) during the period (Tr×Np) is expressed by the following formula:

(z) 212 In this formula, Cl(k, m) is the added value of the correlation calculation values (hereafter referred to as correlation added value), Np is an integer of 1 or more, and m is an integer of 1 or more which indicates the ordinal number of the addition number when the addition number Np in the adderis set as a unit. Moreover, z=1, . . . , Nt.

212 211 212 212 200 (z) (z) (z) The adderperforms addition Np times, in a unit of outputs of the correlation calculatorobtained in each radar transmission cycle Tr. Specifically, the addercalculates the correlation value Cl(k, m) every discrete time k, by adding up the correlation calculation values AC(k, Np(m−1)+1) to AC(k, Np×m) as an unit with the timing of the discrete time k being aligned. The addercan thereby improve the SNR of the reflected wave signal in a range where the reflected wave signal from the target has a high correlation, by using the effect of addition of the correlation calculation values performed Np times. Accordingly, the radar receivercan improve a measurement performance relating to estimation of an arrival distance of the target.

212 In order to obtain an ideal addition gain, a condition under which phase components of the correlation calculation values are aligned to some extent needs to be satisfied in the addition duration in which the addition of the correlation calculation values is performed Np times. In other words, the addition number Np is preferably set based on an assumed maximum movement speed of the target to be measured. In this case, as the assumed maximum movement speed of the target increases, the variation of the Doppler frequency included in the reflection wave from the target increases and the time period with a high correlation thus becomes shorter. Accordingly, the addition number Np takes a small value, and the effect of the gain improvement by the addition in the adderbecomes small.

213 212 213 (z) (z) The Doppler frequency analyzerperforms coherent integration, in a unit of Cl(k, Nc(w−1)+1) to Cl(k, Nc×w) being Nc outputs of the adderobtained every discrete time k, with the timings of the discrete time k being aligned. For example, as depicted in the following formula, the Doppler frequency analyzercorrects phase fluctuation φ(fs)=2πfs(Tr×Np)Δφ corresponding to 2Nf different Doppler frequencies fsΔφ, and then performs the coherent integration:

(z) Nant 213 201 In this formula, FT_Cl(k, fs, w) is the w-th output of the Doppler frequency analyzer, and indicates a coherent integration result of the Doppler frequency fsΔφ at the discrete time k in the Nant-th antenna system processor. Note that Nant=1 to Na, fs=Nf+1, . . . , 0, . . . , Nf, k=1, . . . , (Nr+Nu)Ns/No, w is an integer of 1 or more, and Δφ is a phase rotation unit.

201 (z) (z) Nant Nant Each of the antenna system processorsthereby obtains FT_Cl(k, −Nf+1, w), . . . , FT_Cl(k, Nf−1, w) which are the coherent integration results corresponding to the 2Nf Doppler frequency components at every discrete time k, every period (Tr×Np×Nc) which is Np×Nc radar transmission cycles Tr. Note that j is an imaginary unit, and z=1, . . . , Nt.

213 212 In the case of Δφ=1/Nc, the aforementioned processing of the Doppler frequency analyzeris equivalent to performing discrete Fourier transform (DFT) processing on the outputs of the adderat a sampling interval of Tm=(Tr×Np) and a sampling frequency of fm=1/Tm.

213 (z) Moreover, fast Fourier transform (FFT) processing can be used in the Doppler frequency analyzerby setting Nf to an exponent of two. This can reduce the computation processing amount. Note that, in the case of Nf>Nc, the FFT processing can be similarly used by performing zero padding processing of Cl(k, Nc(w−1)+q)=0 in a region of q>Nc, to reduce the computation processing amount.

213 213 212 s r p (z) Furthermore, in the Doppler frequency analyzer, processing of performing a multiply-add operation depicted in the formula (3) can be performed as needed instead of the FFT processing. Specifically, the Doppler frequency analyzercan generate a coefficient exp[−j2πfTNqΔφ] corresponding to fs=−Nf+1, . . . , 0, Nf−1 for Cl(k, Nc(w−1)+q+1) which are Nc outputs of the adderobtained every discrete time k, and perform the multiply-add operation processing as necessary. In this case, q=0 to Nc−1.

(z) (z) (z) 1 2 Na 201 202 In the following description, the w-th outputs FT_Cl(k, fs, w), FT_Cl(k, fs, w), . . . , FT_Cl(k, fs, w) obtained by performing similar processing respectively in the Na antenna system processorsare described as an virtual reception array correlation vector h(k, fs, w) as in the following formula. The virtual reception array correlation vector h(k, fs, w) includes Nt×Na elements, Nt×Na being a product of the number Nt of the transmission antennas and the number Na of the reception antennas. The virtual reception array correlation vector h(k, fs, w) is used to describe processing in which direction estimation is performed based on the phase differences among the reflected wave signals from the target which are received by the respective reception antennasto be described later. In this case, z=1, . . . , Nt and b=1, . . . , Na:

207 Processing in the components of the signal processorhas been described.

214 201 213 201 1 201 —after _ cal [y] —after _ cal The direction estimatorcalculates a virtual reception array correlation vector h(k, fs, w) which is obtained by correcting a phase deviation and an amplitude deviation among the antenna system processorsby using an array correction value h_cal, for the w-th virtual reception array correlation vector h(k, fs, w) of the Doppler frequency analyzersoutputted from the antenna system processors-to-Na. The virtual reception array correlation vector h(k, fs, w) is expressed by the following formula. Note that y=1, . . . , (Nt×Na):

—after _ cal —after _ cal 1 Na×Nr The virtual reception array correlation vector h(k, fs, w) in which the deviations among the antennas are corrected is a column vector including Na×Nr elements. In the following description, the elements of the virtual reception array correlation vector h(k, fs, w) are described as h(k, fs, w), . . . , h(k, fs, w) and are used in the description of the direction estimation processing.

10 [Antenna Arrangement in Radar Device]

106 202 10 Description is given of an arrangement of the Nt transmission antennasand the Na reception antennasin the radar devicehaving the configuration described above.

106 202 The Nt transmission antennasand the Na reception antennasare arranged with uneven spaces in the horizontal direction and the vertical direction.

TH RH H 106 202 Specifically, inter-element spaces among N(also expressed as Nt1 in some cases) transmission antennasarranged on a straight line in the horizontal direction and inter-element spaces among N(also expressed as Na1 in some cases) reception antennasarranged on a straight line in the horizontal direction each satisfy a relationship of being a product of a predetermined value dand an integer (corresponding to a first predetermined value), and are all values different from one another.

TV RV V 106 202 Similarly, inter-element spaces among N(also expressed as Nt2 in some cases) transmission antennasarranged on a straight line in the vertical direction and inter-element spaces among N(also expressed as Na2 in some cases) reception antennasarranged on a straight line in the vertical direction each satisfy a relationship of being a product of a predetermined value dand an integer (corresponding to a second predetermined value), and are all values different from one another.

106 202 Moreover, the arrangement of the transmission antennasand the reception antennasin the embodiment is assumed to satisfy the following restriction conditions.

106 202 TH 1 H 2 H NTH-1 H RH 1 H 2 H NRH-1 H The number of the transmission antennasarranged on a straight line in the horizontal direction is Nand the inter-element spaces among these antennas are α×d, α×d, . . . , α×d, respectively. Meanwhile, the number of the reception antennasarranged on a straight line in the horizontal direction is Nand the inter-element spaces among these antennas are β×d, β×d, . . . , βλd, respectively.

106 202 TV 1 V 2 V NTV-1 V RV 1 V 2 V NRV-1 V Moreover, the number of the transmission antennasarranged on a straight line in the vertical direction is Nand the inter-element spaces among these antennas are γ×d, γ×d, . . . , γ×d, respectively. Meanwhile, the number of the reception antennasarranged on a straight line in the vertical direction is Nand the inter-element spaces among these antennas are η×d, η×d, . . . , η×d, respectively.

<Condition A-1>

202 202 106 1 2 1 2 The sum (aperture length of the reception antennasin the horizontal direction) of the inter-element spaces among the reception antennasarranged on a straight line in the horizontal direction is smaller than the smallest value of the inter-element spaces among the transmission antennasarranged on a straight line in the horizontal direction:min(α,α, . . . )>(β+β+ . . . ).

106 106 202 1 2 1 2 Alternatively, the sum (aperture length of the transmission antennasin the horizontal direction) of the inter-element spaces among the transmission antennasarranged on a straight line in the horizontal direction is smaller than the smallest value of the inter-element spaces among the reception antennasarranged on a straight line in the horizontal direction:min(β,β, . . . >(α+α+ . . . ).

106 202 In other words, in the horizontal direction, the sum of the inter-element spaces among the transmission antennasor the sum of the inter-element spaces among the reception antennasis smaller than the smallest value of the inter-element spaces among the other antennas.

TH RH TH RH 1 1 2 {0, β, β+β, 1 1 1 1 1 2 α, α+β, α+β+β, 2 2 1 2 1 2 H α, α+β, α+β+β}×d<Condition A-2> When the condition A-1 is satisfied, N×Nhorizontal linear array elements are included in the virtual reception array. For example, in the case of N=N=3, the horizontal linear array elements are formed of elements arranged at the following positions:

nth nrh TH RH H H H The inter-element spaces αand βare set such that inter-element spaces each between any two of the N×Nhorizontal linear array elements arranged on a straight line in the horizontal direction out of the Nt×Na elements in virtual reception array increase in increments of d, from 1×dto n×d(n is an integer of 2 or more). In this case, the certain number described above is the largest natural number satisfying the following formula:

<Condition B-1>

202 202 106 1 2 1 2 The sum (aperture length of the reception antennasin the vertical direction) of the inter-element spaces among the reception antennasarranged on a straight line in the vertical direction is smaller than the smallest value of the inter-element spaces among the transmission antennasarranged on a straight line in the vertical direction:min(γ,γ, . . . )>(η+η+ . . . )

106 106 202 1 2 1 2 Alternatively, the sum (aperture length of the transmission antennasin the vertical direction) of the inter-element spaces among the transmission antennasarranged on a straight line in the vertical direction is smaller than the smallest value of the inter-element spaces among the reception antennasarranged on a straight line in the vertical direction:min(η,η, . . . )>(γ+γ+ . . . )

106 202 In other words, in the vertical direction, the sum of the inter-element spaces among the transmission antennasor the sum of the inter-element spaces among the reception antennasis smaller than the smallest value of the inter-element spaces among the other antennas.

TV RV TV RV 1 1 2 {0, η, η+n, 1 1 1 1 1 2 γ, γ+η, γ+η+η, 2 2 1 2 1 2 V γ, γ+η, γ+η+η}×d<Condition B-2> When the condition B-1 is satisfied, N×Nvertical linear array elements are included in the virtual reception array. For example, in the case of N=N=3, the vertical linear array elements are formed of elements arranged at the following positions:

ntv nrv TV RV V V V The inter-element spaces γand ηare set such that an inter-element spaces each between any two of the N×Nvertical linear array elements arranged on a straight line in the vertical direction out of the Nt×Na elements in the virtual reception array increase in increments of d, from 1×dto n×d(n is an integer of 2 or more). In this case, the certain number described above is the largest natural number satisfying the following formula:

The conditions A-1, A-2, B-1, and B-2 have been described above.

H V The virtual reception array satisfying the conditions A-1, A-2, B-1, and B-2 achieves an array arrangement which minimizes redundancy of the inter-element spaces each between any two array elements in the non-uniform linear array longest in the horizontal direction and in the non-uniform linear array longest in the vertical direction (Minimum Redundancy Array. See, for example, A. Moffet, “Minimum-redundancy linear arrays”, Antennas and Propagation, IEEE Transactions on, vol. 16, no. 2, (1968), pp. 172-175). This can increase an array aperture of the radar device and thereby improve the angular resolution thereof. Moreover, since spatial sampling by the array elements can be performed in basic units (for example, d, d: about 0.5λ) in which no grating lobes are generated within the detection range, it is possible to suppress grating lobes and side lobes.

7 FIG.A 7 FIG.B 7 FIG.A 106 202 Next,illustrates an antenna arrangement example of the transmission antennasand the reception antennas.illustrates elements arrangement of a virtual reception array obtained from the antenna arrangement illustrated in.

106 202 106 202 In this example, the number Nt of the transmission antennasis four and the number Na of the reception antennasis four. Moreover, the four transmission antennasare denoted respectively by Tx#1 to Tx#4, and the four reception antennasare denoted respectively by Rx#1 to Rx#4.

7 FIG.A In, the transmission antennas Tx#1 to Tx#4 are arranged such that one antenna is arranged on the right side of the transmission antenna Tx#1 in the horizontal direction (L shape turned +90°), the transmission antenna Tx#1 being a base point and being the top antenna out of three antennas arranged in the vertical direction. Meanwhile, the reception antennas Rx#1 to Rx#4 are arranged such that one antenna is arranged above the reception antenna Rx#3 in the vertical direction (L shape turned −90°), the reception antenna Rx#3 being a base point and being the rightmost antenna out of three antennas arranged in the horizontal direction.

7 7 FIGS.A andB 7 FIG.A 7 FIG.A H V H V V H H V 106 106 202 202 Moreover, in, ddenotes a basic unit of the inter-element spaces in the horizontal direction and ddenotes a basic unit of the inter-element spaces in the vertical direction. In, the inter-element space between the transmission antennasin the horizontal direction is 7dand the inter-element spaces among the transmission antennasin the vertical direction are dand 2d. Moreover, in, the inter-element spaces among the reception antennasin the horizontal direction are 2dand dand the inter-element space between the reception antennasin the vertical direction is 7d.

7 FIG.A 7 FIG.A 7 FIG.A H H V V 202 106 106 202 In, the sum (3d) of the inter-element spaces among the reception antennasin the horizontal direction is smaller than the smallest value (7d) of the inter-element space between the transmission antennasin the horizontal direction. Moreover, in, the sum (3d) of the inter-element spaces among the transmission antennasin the vertical direction is smaller than the smallest value (7d) of the inter-element space between the reception antennasin the vertical direction. In other words, the antenna arrangement ofsatisfies the conditions A-1 and B-1 described above.

7 FIG.A 7 FIG.A H TH RH H V TV RV V 106 106 202 202 202 106 202 106 Furthermore, in, the largest value (7d) of the inter-element space between the transmission antennaswhich are the antennas fewer in number out of the Ntransmission antennasand the Nreception antennasarranged in the horizontal direction is greater than the largest value (2d) of the inter-element spaces among the reception antennaswhich are the antennas more in number. Similarly, in, the largest value (7d) of the inter-element space between the reception antennaswhich are the antennas fewer in number out of the Ntransmission antennasand the Nreception antennasarranged in the vertical direction is greater than the largest value (2d) of the inter-element spaces among the transmission antennaswhich are the antennas more in number.

106 202 106 202 106 202 TH TV RH RV TH TV RH RV 7 FIG.A Moreover, it is preferable that the Nt transmission antennasare arranged such that N×Ntakes the largest value and the Na reception antennasare arranged such that N×Ntakes the largest value. For example, in, the Nt (=four) transmission antennasare arranged such that (N×N)=(2×3), and the Na (=four) reception antennasare arranged such that (N×N)=(3×2). This can maximize the aperture surface of the virtual reception array formed by the Nt transmission antennasand the Na reception antennas.

7 FIG.B 7 FIG.A The elements arrangement of the virtual reception array illustrated inand provided by the antenna arrangement illustrated indescribed above has the following characteristics.

(1) Horizontal Direction

H H H H H H H H 7 FIG.A 7 FIG.B 7 FIG.B Due to horizontal positional relationships among the two transmission antennas Tx#1 and Tx#4 arranged with an inter-element space 7din the horizontal direction and the three reception antennas Rx#1, Rx#2, and Rx#3 arranged with inter-element spaces 2dand din the horizontal direction in, the virtual reception array illustrated inincludes a virtual horizontal linear array antenna HLA including six elements arranged on a straight line with inter-element spaces 2d, d, 4d, 2d, and din the horizontal direction (VA#1, VA#5, VA#9, VA#4, VA#8, and VA#12 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 H H H H H When the horizontal position of VA#1 is a reference, the horizontal coordinates (x, x, x, x, x, x) of the six elements (VA#1, VA#5, VA#9, VA#4, VA#8, VA#12) forming the virtual horizontal linear array antenna HLA are such that (x, x, x, x, x, x)=[0, 2d, 3d, 7d, 9d, 10d].

A B H H The inter-element spaces |x−x| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual horizontal linear array antenna HLA are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}×d. By using the virtual horizontal linear array antenna HLA including six elements, it is possible to perform direction-of-arrival estimation in which an uniform linear array including 11 elements arranged with inter-element spaces of the basic unit din the horizontal direction are virtually assumed to be used.

H H 10 10 10 For example, by setting dto 0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the horizontal direction. Moreover, since the array aperture length of the radar deviceis 10d=5λ, the beam width BW thereof is about 8° and the radar devicecan achieve high angular resolution of BW=10° or less.

214 The specific direction estimation processing in the horizontal direction in the direction estimatoris performed as follows.

H 7 FIG.B H Inter-element Space of 1×d: Combination of VA#5 and VA#9 H Inter-element Space of 2×d: Combination of VA#4 and VA#8 H Inter-element Space of 3×d: Combination of VA#1 and VA#9 H Inter-element Space of 4×d: Combination of VA#9 and VA#4 H Inter-element Space of 5×d: Combination of VA#5 and VA#4 H Inter-element Space of 6×d: Combination of VA#9 and VA#8 H Inter-element Space of 7×d: Combination of VA#1 and VA#4 H Inter-element Space of 8×d: Combination of VA#5 and VA#12 H Inter-element Space of 9×d: Combination of VA#1 and VA#8 H Inter-element Space of 10×d: Combination of VA#1 and VA#12. First, each of the inter-element spaces between two elements which is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}×ddescribed above incan be obtained, for example, from one of the following combinations of the virtual antenna elements (VA) elements of the virtual reception array in the horizontal direction:

TH RH H H H 7 FIG.A Specifically, each of the inter-element spaces between any two of the N×Nvirtual antenna elements (VA) arranged on a straight line in the horizontal direction is a product of dand an integer of 1 or more, the any two virtual antenna elements are elements the inter-element space between which is a product of the space dand an integer, and the inter-element spaces are values including products of dand all integers from 1 to a predetermined value. In other words, the antenna arrangement ofsatisfies the condition A-2 described above.

When there are multiple combinations of elements the inter-element spaces among which are the same, it is possible to select one of the combinations or perform averaging processing for the multiple combinations (an example in which one combination is selected is described herein).

—after _ cal 1 —after _ cal The element numbers (numbers of VA#) of the virtual reception array correspond to the element numbers of the column vector of the virtual reception array correlation vector h(k, fs, w) which is illustrated in the formula (6) and in which the deviations among the antennas are corrected. For example, VA#1 corresponds to the first element h(k, fs, w) out of the column vector elements of h(k, fs, w). The same applies to the other elements VA#2 to VA#16.

214 VAH H VAH VAH VAH VAH 7 FIG.B The direction estimatorgenerates a correlation vector h(k, fs, w) of the uniform linear array including 11 elements arranged with the inter-element spaces of the basic unit din the horizontal direction, based on combinations of the inter-element spaces and the virtual antenna elements (VA) described above. The correlation vector h(k, fs, w) of the uniform linear array is expressed by the following formula. Note that the number of elements in the correlation vector h(k, fs, w) of the uniform linear array in the horizontal direction is expressed as N(N=11 in):

214 H In horizontal direction-of-arrival estimation, the direction estimatorcalculates a spatial profile with an azimuth direction θ in a direction estimation evaluation function value P(θ, k, fs, w) being variable within a certain angular range, extracts a certain number of maximum peaks in the calculated spatial profile in the descending order, and outputs the azimuth directions of the maximum peaks as direction-of-arrival estimation values.

H Note that the evaluation function value P(θ, k, fs, w) can be calculated by various methods by using a direction-of-arrival estimation algorithm. For example, an estimation method using an array antenna which is disclosed in Direction-of-arrival estimation using signal subspace modeling Cadzow, J. A.; Aerospace and Electronic Systems, IEEE Transactions on Volume: 28, Issue: 1 Publication Year: 1992, Page(s): 64-79 can be used. Moreover, in the case where multiple waves with a high correlation arrive, it is possible to apply a spatial smoothing method for correlation suppression after applying various direction-of-arrival estimation algorithms. This can be similarly applied also to the direction-of-arrival estimation processing to be described below.

For example a beamformer method can be expressed by the following formulae. Alternatively, other methods such as the Capon and the MUSIC can be similarly applied:

H u u In these formulae, subscript H is the Hermitian transpose operator. Moreover, a(θ) is a direction vector of the virtual reception array for a wave arriving from the azimuth direction θ.

u 1 u u 1 1 Furthermore, the azimuth direction θis a vector changed at certain direction intervals βwithin an azimuth range in which the direction-of-arrival estimation is performed. For example, θis set as follows:θ=θ min+uβ,u=0, . . . ,NUNU=floor[(θ max−θ min)/β]+1where, floor(x) is a function which returns the largest integer not exceeding a real number x.

8 FIG. 8 FIG. 8 FIG. 10 H illustrates a direction estimation result (calculator simulation result) obtained by using the configuration described above. In, simulation conditions are such that the beamformer method is used and a target direction is set to 0°. Moreover, the direction estimation result illustrated inis a result of the direction-of-arrival estimation performed while virtually assuming that the radar devicehas the uniform linear array including 11 elements arranged with the inter-element spaces of the basic unit din the horizontal direction.

8 FIG. As illustrated in, it is found that the beam width BW of the beam in the target direction 0° is about 8°, the side lobe level of 13 dB or lower is obtained, and the no grating lobes are generated.

(2) Vertical Direction

V V V V V V V V 7 FIG.A 7 FIG.B 7 FIG.B Due to vertical positional relationships among the three transmission antennas Tx#1, Tx#2, and Tx#3 arranged with inter-element spaces dand 2din the vertical direction and the two reception antennas Rx#3 and Rx#4 arranged with an inter-element space 7din the vertical direction in, the virtual reception array illustrated inform a virtual vertical linear array antenna VLA including six elements arranged on a straight line with inter-element spaces 2d, d, 4d, 2d, and din the vertical direction (VA#11, VA#10, VA#9, VA#15, VA#14, and VA#13 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 V V V V V When the vertical position of VA#11 is a reference, the vertical coordinates (y, y, y, y, y, y) of the six elements (VA#11, VA#10, VA#9, VA#15, VA#14, VA#13) forming the virtual vertical linear array antenna VLA are such that (y, y, y, y, y, y)=[0, 2d, 3d, 7d, 9d, 10d].

A B V V 10 The inter-element spaces |y−y| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual vertical linear array antenna VLA are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}×d. By using the virtual vertical linear array antenna VLA including six elements, the radar devicecan be virtually assumed to have a uniform linear array including 11 elements arranged with inter-element spaces of the basic unit din the vertical direction, and perform the direction-of-arrival estimation with high angular resolution.

V V 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the vertical direction. Moreover, since the array aperture length of the radar deviceis 10d=5λ, the beam width BW thereof is about 8° and the radar devicecan achieve high angular resolution of BW=10° or less.

214 The specific direction estimation processing in the vertical direction in the direction estimatoris performed as follows.

V 7 FIG.B V Inter-element Space of 1×d: Combination of VA#10 and VA#9 V Inter-element Space of 2×d: Combination of VA#11 and VA#10 V Inter-element Space of 3×d: Combination of VA#11 and VA#9 V Inter-element Space of 4×d: Combination of VA#9 and VA#15 V Inter-element Space of 5×d: Combination of VA#10 and VA#15 V Inter-element Space of 6×d: Combination of VA#9 and VA#14 V Inter-element Space of 7×d: Combination of VA#10 and VA#14 V Inter-element Space of 8×d: Combination of VA#10 and VA#13 V Inter-element Space of 9×d: Combination of VA#11 and VA#14 V Inter-element Space of 10×d: Combination of VA#11 and VA#13. First, each of the inter-element spaces between two elements which is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}×ddescribed above incan be obtained, for example, from one of the following combinations of the virtual reception array of virtual antenna elements (VA) in the vertical direction:

TV RV V V V 7 FIG.A Specifically, each of the inter-element spaces between any two of the N×Nvirtual antenna elements (VA) arranged on a straight line in the vertical direction is a product of dand an integer of 1 or more, the any two virtual antenna elements are elements the inter-element space between which is a product of the space dand an integer, and the inter-element spaces are values including products of dand all integers from 1 to a predetermined value. In other words, the antenna arrangement ofsatisfies the condition B-2 described above.

When there are multiple combinations of elements the inter-element spaces among which are the same, it is possible to select one of the combinations or perform averaging processing for the multiple combinations (an example in which one combination is selected is described herein).

—after _ cal 1 —after _ cal The element numbers (numbers of VA#) of the virtual antenna elements (VA) correspond to the element numbers of the column vector of the virtual reception array correlation vector h(k, fs, w) which is illustrated in the formula (6) and in which the deviations among the antennas are corrected. For example, VA#1 corresponds to the first element h(k, fs, w) out of the column vector elements of h(k, fs, w). The same applies to the other elements VA#2 to VA#16.

214 VAV V VAV VAV The direction estimatorgenerates a correlation vector h(k, fs, w) of the uniform linear array including 11 elements arranged with the inter-element spaces of the basic unit din the vertical direction, based on combinations of the inter-element spaces and the virtual antenna elements (VA) described above. The correlation vector h(k, fs, w) of the uniform linear array is expressed by the following formula. Note that the number of elements in the correlation vector h(k, fs, w) of the uniform linear array in the vertical direction is expressed as

214 V In vertical direction-of-arrival estimation, the direction estimatorcalculates a spatial profile with an elevation direction φ in a direction estimation evaluation function value P(φ, k, fs, w) being variable within a certain angular range, extracts a certain number of maximum peaks in the calculated spatial profile in the descending order, and outputs the elevation directions of the maximum peaks as direction-of-arrival estimation values.

V Note that the evaluation function value P(φ, k, fs, w) can be calculated by various methods by using a direction-of-arrival estimation algorithm. For example, an estimation method using an array antenna which is disclosed in Direction-of-arrival estimation using signal subspace modeling Cadzow, J. A.; Aerospace and Electronic Systems, IEEE Transactions on Volume: 28, Issue: 1 Publication Year: 1992, Page(s): 64-79 can be used. Moreover, in the case where multiple waves with a high correlation arrive, it is possible to apply a spatial smoothing method for correlation suppression after applying various direction-of-arrival estimation algorithms. This can be similarly applied also to the direction-of-arrival estimation processing to be described below.

For example a beamformer method can be expressed by the following formulae. Alternatively, other methods such as the Capon and the MUSIC can be similarly applied:

V v v In these formulae, subscript H is the Hermitian transpose operator. Moreover, a(φ) is a direction vector of the virtual reception array for a wave arriving from the elevation direction φ.

v 2 v v 2 2 Furthermore, φis a vector changed at certain direction intervals βwithin an elevation range in which the direction-of-arrival estimation is performed. For example, φis set as follows:φ=φ min+vβ,v=0, . . . ,NVNV=floor[(φ max−φ min)/β]+1

7 FIG.B The characteristics of the virtual antenna elements arrangement of the virtual reception array illustrated inhave been described.

Note that, in the embodiment, the direction vector of the virtual reception array is assumed to be calculated in advance based on the virtual antenna elements arrangement VA#1, . . . , VA#(Nt×Na) of the virtual reception array to be described later.

Moreover, the time information k described above can be converted to distance information and then outputted. In the case of converting the time information k to distance information R(k), the following formula can be used:

w 0 where Tis the code transmission duration, L is the pulse code length, and Cis a light speed

d s Moreover, Doppler frequency information (fsΔφ) may be converted to a relative speed component and then outputted. The Doppler frequency information fsΔφ can be converted to the relative speed component v(f) by using the following formula:

105 where λ is the wavelength of the carrier frequency of the RF signal outputted from the transmission radio unit.

7 FIG.B 7 FIG.A As described above, in the radar device with relatively few antenna elements of four transmission antennas and four reception antennas, the aperture surface formed of the virtual reception array illustrated incan be maximized in the horizontal direction and the vertical direction by using the antennas arrangement illustrated in.

10 In other words, in the embodiment, in the radar device, when the beam scanning is two-dimensionally performed in the vertical direction and the horizontal direction by using the MIMO radar, the aperture lengths of the virtual reception array in the vertical direction and the horizontal direction can be increased as much as possible.

10 202 10 H V Moreover, in the radar device, it is possible to set the inter-element spaces (d, d) among the reception antennasin both of the horizontal direction and the vertical direction to, for example, 0.5λ, and achieve high resolution of Fourier beam width BW=about 8° in Fourier beam scanning with equal amplitude weight. In other words, the radar devicecan achieve high resolution in the horizontal direction and the vertical direction without using a direction-of-arrival estimation algorithm capable of achieving high resolution, which leads to a low computation amount.

10 As described above, in the embodiment, it is possible to improve the angular resolution with few antennas by using the virtual reception array described above and thereby reduce the size and cost of the radar device.

7 FIG.A Note that a space between the set of transmission antennas Tx#1 to Tx#4 and the set of reception antennas Rx#1 to Rx#4 indoes not affect the virtual antenna elements arrangement of the virtual reception array. However, arranging the set transmission antennas Tx#1 to Tx#4 and the set of reception antennas Rx#1 to Rx#4 close to each other increases the degree of coupling among the transmission and reception antennas. Accordingly, the set of transmission antennas Tx#1 to Tx#4 and the set of reception antennas Rx#1 to Rx#4 are preferably arranged away from each other as much as possible within an allowable antenna size. The same applies to the other antenna arrangements to be described below.

7 FIG.A 7 FIG.B 7 FIG.A 7 FIG.A Moreover,illustrates an example of the antenna arrangement for four transmission antennas and four reception antennas. However, a configuration similar to the virtual antenna elements arrangement of the virtual reception array illustrated inis obtained also when the reception antennas are arranged in the transmission antenna arrangement ofand the transmission antennas are arranged in the reception antenna arrangement of, and similar effects can be obtained also in this case. The same applies to the other antenna arrangements to be described below.

(Variation 1 of Embodiment 1)

106 202 106 202 7 FIG.A 9 FIG.A 9 FIG.B 9 FIG.A The antenna arrangement for the four transmission antennasand the four reception antennasis not limited to the antenna arrangement illustrated in. For example,illustrates another antenna arrangement example for the four transmission antennasand the four reception antennas.illustrates a virtual antenna elements arrangement of virtual reception array obtained from the antenna arrangement illustrated in.

9 FIG.A 7 FIG.A 9 FIG.A illustrates an arrangement pattern of the transmission antennas Tx#1 to Tx#4 in which one antenna is arranged on the right side of the transmission antenna Tx#1 in the horizontal direction as in, the transmission antenna Tx#1 being a base point and being the top antenna out of three antennas arranged in the vertical direction. Meanwhile, in, the reception antennas Rx#1 to Rx#4 are arranged such that one antenna is arranged above the reception antenna Rx#2 in the vertical direction (T-shape turned 180°), the reception antenna Rx#2 being a base point and being the middle antenna out of three antennas arranged in the horizontal direction.

9 FIG.B 9 FIG.A 7 FIG.B 9 9 FIGS.A toB The virtual antenna elements arrangement of the virtual reception array illustrated inwhich is provided by the antenna arrangement illustrated inhas the characteristics (1) and (2) described above as in. The characteristics are specifically described below by using.

(1) Horizontal Direction

H H H H H H H H 9 FIG.A 9 FIG.B 9 FIG.B Due to horizontal positional relationships among the two transmission antennas Tx#1 and Tx#4 arranged with an inter-element space 7din the horizontal direction and the three reception antennas Rx#1, Rx#2, and Rx#3 arranged with the inter-element spaces 2dand din the horizontal direction in, the virtual reception array illustrated inincludes a virtual horizontal linear array antenna HLA including six elements arranged on a straight line with inter-element spaces 2d, d, 4d, 2d, and din the horizontal direction (VA#1, VA#5, VA#9, VA#4, VA#8, and VA#12 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 H H H H H When the horizontal position of VA#1 is a reference, the horizontal coordinates (x, x, x, x, x, x) of the six elements (VA#1, VA#5, VA#9, VA#4, VA#8, VA#12) forming the virtual horizontal linear array antenna HLA are such that (x, x, x, x, x, x)=[0, 2d, 3d, 7d, 9d, 10d].

A B H H 10 The inter-element spaces |x−x| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual horizontal linear array antenna HLA are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}×d. By using the virtual horizontal linear array antenna HLA including six elements, the radar devicecan be virtually assumed to have an uniform linear array including 11 elements arranged with inter-element spaces of the basic unit din the horizontal direction, and perform the direction-of-arrival estimation with high angular resolution.

H H 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the horizontal direction. Moreover, since the array aperture length of the radar deviceis 10d=5λ, the beam width BW thereof is about 8° and the radar devicecan achieve high angular resolution of BW=10° or less.

(2) Vertical Direction

V V V V V V V V 9 FIG.A 9 FIG.B 9 FIG.B Due to vertical positional relationships among the three transmission antennas Tx#1, Tx#2, and Tx#3 arranged with inter-element spaces dand 2din the vertical direction and the two reception antennas Rx#2 and Rx#4 arranged with an inter-element space 7din the vertical direction in, the virtual reception array illustrated inincludes a virtual vertical linear array antenna VLA including six elements arranged on a straight line with inter-element spaces 2d, d, 4d, 2d, and din the vertical direction (VA#7, VA#6, VA#5, VA#15, VA#14, and VA#13 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 V V V V V When the vertical position of VA#7 is a reference, the vertical coordinates (y, y, y, y, y, y) of the six elements (VA#7, VA#6, VA#5, VA#15, VA#14, VA#13) forming the virtual vertical linear array antenna VLA are such that (y, y, y, y, y, y)=[0, 2d, 3d, 7d, 9d, 10d].

A d V V 10 The inter-element spaces |y−y| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual vertical linear array antenna VLA are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}×d. By using the virtual vertical linear array antenna VLA including six elements, the radar devicecan be virtually assumed to have a uniform linear array including 11 elements arranged with inter-element spaces of the basic unit din the vertical direction, and perform the direction-of-arrival estimation with high angular resolution.

V V 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the vertical direction. Moreover, since the array aperture length of the radar deviceis 10d=5λ, the beam width BW thereof is about 8° and the radar devicecan achieve high angular resolution of BW=10° or less.

(Variation 2 of Embodiment 1)

10 106 202 In Embodiment 1, when high angular resolution of about 10° is unnecessary in Embodiment 1 as the angular resolution in the horizontal direction or the vertical direction, the radar devicemay include only three transmission antennasor three reception antennas.

10 106 202 Description is given below of an example in which no high angular resolution is required as the angular resolution in the vertical direction and the radar deviceincludes three transmission antennasand four reception antennas.

10 FIG.A 10 FIG.B 10 FIG.A 106 202 illustrates antennas arrangement example of the transmission antennasand the reception antennas.illustrates virtual antenna elements arrangement of virtual reception array obtained from the antenna arrangement illustrated in.

10 FIG.A 10 FIG.A 106 202 In, the three transmission antennasare denoted respectively by Tx#1 to Tx#3, and the four reception antennasare denoted respectively by Rx#1 to Rx#4. In, the transmission antennas Tx#1 to Tx#3 are arranged such that one antenna is arranged on the right side of the transmission antenna Tx#1 in the horizontal direction with an inter-element space smaller than an inter-element space in the vertical direction (L shape turned +90°), the transmission antenna Tx#1 being a base point and being the top antenna out of two antennas arranged in the vertical direction. Meanwhile, the reception antennas Rx#1 to Rx#4 are arranged such that one antenna is arranged above the reception antenna Rx#3 in the vertical direction with an inter-element space smaller than an inter-element space in the horizontal direction (L shape turned −90°), the reception antenna Rx#3 being a base point and being the rightmost antenna out of three antennas arranged in the horizontal direction.

106 202 Moreover, the arrangement of the transmission antennasand the reception antennasin this variation is assumed to satisfy the restriction conditions A-1, A-2, B-1, and B-2 described in Embodiment 1.

10 FIG.B 10 FIG.A The virtual antenna elements arrangement of the virtual reception array illustrated inand provided by the antenna arrangement illustrated inhas the following characteristics.

(1) Horizontal Direction

H H H H H H H H 10 FIG.A 10 FIG.B 10 FIG.B Due to horizontal positional relationships among the two transmission antennas Tx#1 and Tx#3 arranged with an inter-element space 5din the horizontal direction and the three reception antennas Rx#1, Rx#2, and Rx#3 arranged with inter-element spaces dand 2din the horizontal direction in, the virtual reception array illustrated inincludes a virtual horizontal linear array antenna HLA including six elements arranged on a straight line with inter-element spaces d, 2d, 2d, d, and 2din the horizontal direction (VA#1, VA#4, VA#7, VA#3, VA#6, and VA#9 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 H H H H H When the horizontal position of VA#1 is a reference, the horizontal coordinates (x, x, x, x, x, x) of the six elements (VA#1, VA#4, VA#7, VA#3, VA#6, VA#9) forming the virtual horizontal linear array antenna HLA are such that (x, x, x, x, x, x)=[0, d, 3d, 5d, 6d, 8d].

A B H H 10 The inter-element spaces |x−x| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual horizontal linear array antenna HLA are {1, 2, 3, 4, 5, 6, 7, 8}×d. By using the virtual horizontal linear array antenna HLA including six elements, the radar devicecan be virtually assumed to have an uniform linear array including nine elements arranged with inter-element spaces of the basic unit din the horizontal direction, and perform the direction-of-arrival estimation with high angular resolution.

H H 10 10 10 For example, by setting dto 0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the horizontal direction. Moreover, since the array aperture length of the radar deviceis 8d=4λ, the beam width BW thereof is about 10° and the radar devicecan achieve high angular resolution of BW=10° or less.

(2) Vertical Direction

V V V V V 10 FIG.A 10 FIG.B 10 FIG.B Due to vertical positional relationships among the two transmission antennas Tx#1 and Tx#2 arranged with an inter-element space din the vertical direction and the two reception antennas Rx#3 and Rx#4 arranged with an inter-element space 3din the vertical direction in, the virtual reception array illustrated inincludes a virtual vertical linear array antenna VLA including four elements arranged on a straight line with inter-element spaces d, 2d, and din the vertical direction (VA#8, VA#7, VA#11, and VA#10 surrounded by the broken line illustrated in).

1 2 3 4 1 2 3 4 V V V When the vertical position of VA#8 is a reference, the vertical coordinates (y, y, y, y) of the four elements (VA#8, VA#7, VA#11, VA#10) forming the virtual vertical linear array antenna VLA are such that (y, y, y, y)=[0, d, 3d, 4d].

A B V V 10 The inter-element spaces |y−y| (where A and B are each one of integers from one to four, and A≠B) each between any two different elements included in the virtual vertical linear array antenna VLA are {1, 2, 3, 4}×d. By using the virtual vertical linear array antenna VLA including four elements, the radar devicecan be virtually assumed to have a uniform linear array including five elements arranged with inter-element spaces of the basic unit din the vertical direction, and perform the direction-of-arrival estimation with high angular resolution.

V V 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the vertical direction. Meanwhile, since the array aperture length of the radar deviceis 4d=2λ, the beam width BW thereof is about 20°.

(Variation 3 of Embodiment 1)

10 202 106 10 106 202 In Embodiment 1, the radar deviceusing five or more reception antennasmay include three transmission antennas. Alternatively, the radar deviceusing five or more transmission antennasmay include three reception antennas.

10 106 202 Description is given below of an example of the radar devicewhich includes three transmission antennasand five reception antennas.

11 FIG.A 11 FIG.B 11 FIG.A 106 202 illustrates an arrangement example of the transmission antennasand the reception antennas.illustrates an arrangement of virtual reception array obtained from the antenna arrangement illustrated in.

11 FIG.A 11 FIG.A 24 24 FIGS.A toF 106 202 In, the three transmission antennasare denoted respectively by Tx#1 to Tx#3, and the five reception antennasare denoted respectively by Rx#1 to Rx#5. In, the transmission antennas Tx#1 to Tx#3 are arranged such that one antenna is arranged on the right side of the transmission antenna Tx#1 in the horizontal direction (L shape turned +90°), the transmission antenna Tx#1 being a base point and being the top antenna out of two antennas arranged in the vertical direction. Meanwhile, the reception antennas Rx#1 to Rx#5 are arranged such that one antenna is arranged on each of the upper and lower sides of the reception antenna Rx#3 in the vertical direction, the reception antenna Rx#3 being a base point and being the middle antenna out of three antennas arranged in the horizontal direction (cross shape). Note that the arrangement of the reception antennas Rx#1 to Rx#5 are not limited to the cross-shaped arrangement, and may be a L-shaped arrangement or a T-shaped arrangement (see, for example,to be described later).

106 202 Moreover, the arrangement of the transmission antennasand the reception antennasin this variation is an arrangement satisfying the restriction conditions A-1, A-2, B-1, and B-2 described in Embodiment 1.

11 FIG.B 11 FIG.A The virtual antenna elements arrangement of the virtual reception array illustrated inand provided by the antenna arrangement illustrated inhas the following characteristics.

(1) Horizontal Direction

H H H H H H H H 11 FIG.A 11 FIG.B 11 FIG.B Due to horizontal positional relationships among the two transmission antennas Tx#1 and Tx#3 arranged with an inter-element space 7din the horizontal direction and the three reception antennas Rx#2, Rx#3, and Rx#4 arranged with inter-element spaces 2dand din the horizontal direction in, the virtual reception array illustrated inincludes a virtual horizontal linear array antenna HLA including six elements arranged on a straight line with inter-element spaces 2d, d, 4d, 2d, and din the horizontal direction (VA#4, VA#7, VA#10, VA#6, VA#9, and VA#12 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 H H H H H When the horizontal position of VA#4 is a reference, the horizontal coordinates (x, x, x, x, x, x) of the six elements (VA#4, VA#7, VA#10, VA#6, VA#9, VA#12) forming the virtual horizontal linear array antenna HLA are such that (x, x, x, x, x, x)=[0, 2d, 3d, 7d, 9d, 10d].

A B H H 10 The inter-element spaces |x−x| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual horizontal linear array antenna HLA are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}×d. By using the virtual horizontal linear array antenna HLA including six elements, the radar devicecan be virtually assumed to have an uniform linear array including 11 elements arranged with inter-element spaces of the basic unit din the horizontal direction, and perform the direction-of-arrival estimation with high angular resolution.

H H 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the horizontal direction. Moreover, since the array aperture length of the radar deviceis 10d=5λ, the beam width BW thereof is about 8° and the radar devicecan achieve high angular resolution of BW=10° or less.

(2) Vertical Direction

V V V V V V V V 11 FIG.A 11 FIG.B 11 FIG.B Due to vertical positional relationships among the two transmission antennas Tx#1 and Tx#2 arranged with an inter-element space 7din the vertical direction and the three reception antennas Rx#1, Rx#3, and Rx#5 arranged with inter-element spaces dand 2din the vertical direction in, the virtual reception array illustrated inincludes a virtual vertical linear array antenna VLA including six elements arranged on a straight line with inter-element spaces d, 2d, 4d, d, and 2din the vertical direction (VA#2, VA#8, VA#14, VA#1, VA#7, and VA#13 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 V V V V V When the vertical position of VA#2 is a reference, the vertical coordinates (y, y, y, y, y, y) of the six elements (VA#2, VA#8, VA#14, VA#1, VA#7, VA#13) forming the virtual vertical linear array antenna VLA are such that (y, y, y, y, y, y)=[0, d, 3d, 7d, 8d, 10d].

A B V V V 10 The inter-element spaces |y−y| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual vertical linear array antenna VLA are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}×d. By using the virtual vertical linear array antenna VLA including six elements, the radar devicecan be virtually assumed to have a uniform linear array including 11 elements arranged with inter-element spaces of the basic unit din the vertical direction, and perform the direction-of-arrival estimation with high angular resolution. Note that the uniform linear array includes no inter-element spaces other than the inter-element spaces of the basic unit d.

V V 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the vertical direction. Moreover, since the array aperture length of the radar deviceis 10d=5λ, the beam width BW thereof is about 8° and the radar devicecan achieve high angular resolution of BW=10° or less.

In some cases, a radar device uses sub-array antennas in which array elements forming an array antenna each include multiple antenna elements (sub-arrayed antenna elements), to improve a directional gain of the array antenna.

12 FIG. 13 FIG.A 12 FIG. V For example,illustrates an example in which sub-arrayed antenna element is applied to the configuration ofwhen the radar detection range of the radar device can be reduced in the vertical direction and the smallest inter-element space in the vertical direction is 2d. In, using the sub-arrayed antenna elements are formed by stacking two antenna elements in the vertical direction can narrow the directivity in the vertical direction and reduce radiation in an unnecessary direction, thereby improving the array element gain.

Regarding the inter-element spaces of the array antenna, antenna elements are difficult to arrange with inter-element spaces smaller than the size of the antenna elements. For example, stacking the antenna elements of the sub-arrayed antenna elements in the vertical direction increases the size of the sub-arrayed antenna elements to about one wavelength, and this restricts the arrangement of the array antenna in the radar device. Specifically, in the radar device having the sub-array antenna configuration, the smallest inter-element space in the antenna arrangement in the vertical direction is restricted to be equal to or more than a certain value.

As described above, when the sub-array antenna configuration is used in the radar device, the size of each sub-arrayed antenna element is large, and the space between any two of the sub-arrayed antenna elements needs to be increased. As a result, grating lobes may be generated on a directional pattern of the array antenna.

In view of this, in the embodiment, description is given of an antenna arrangement which achieves high resolution in the vertical/horizontal direction and which can perform the direction-of-arrival estimation with the generation of grating lobes suppressed in a wide range when the sub-array antennas are used.

10 3 FIG. Note that, since the radar device of the embodiment has the same basic configuration as the radar deviceof Embodiment 1, description is given with reference to.

10 10 Moreover, the radar devicein which the antenna elements are stacked in the vertical direction to form sub-arrayed antenna elements is described below as an example. Note that the antenna elements are not stacked in the horizontal direction to form sub-arrayed antenna elements and the radar devicehas the same characteristics as that in Embodiment 1.

106 202 As in Embodiment 1, Nt transmission antennasand Na reception antennasare arranged with uneven inter-element spaces in the horizontal direction and the vertical direction.

106 202 106 202 106 202 TV RV V V Moreover, the transmission antennasand the reception antennasin the embodiment are arranged in the vertical direction (direction in which the antenna elements are formed) such that there is one or more combinations of the inter-element spaces among the Ntransmission antennasand the inter-element spaces among the Nreception antennasin which the difference between the inter-element spaces is the basic unit dof the inter-element spaces in the vertical direction. Moreover, the basic unit dof the inter-element spaces in the vertical direction is set to be less than 1λ (for example, 0.5λ). Specifically, the transmission antennasand the reception antennasare arranged to include at least one arrangement satisfying the following formula (hereafter referred to as condition B-3).

V <Condition B-3>(inter-element space between transmission antennas 106 in vertical direction)−(inter-element space between reception antennas 202 in vertical direction)|=d≈0.5λ<1λ.

10 106 202 Moreover, the radar devicehaving the arrangement of the transmission antennasand the reception antennasof the embodiment satisfies the restriction conditions described in Embodiment 1 except for B-1, that is the restriction conditions A-1, A-2, and B-2.

13 FIG.A 13 FIG.B 13 FIG.A 106 202 illustrates an arrangement example of the transmission antennasand the reception antennas.illustrates a virtual antenna element arrangement of a virtual reception array obtained from the antenna arrangement illustrated in.

106 202 106 202 In this example, the number Nt of the transmission antennasis four and the number Na of the reception antennasis four. Moreover, the four transmission antennasare denoted respectively by Tx#1 to Tx#4, and the four reception antennasare denoted respectively by Rx#1 to Rx#4.

13 FIG.A In, the transmission antennas Tx#1 to Tx#4 are arranged in a pattern in which one antenna is arranged on the right side of the transmission antenna Tx#1 in the horizontal direction (L shape turned +90°), the transmission antenna Tx#1 being a base point and being the top antenna out of three antennas arranged in the vertical direction. Meanwhile, the reception antennas Rx#1 to Rx#4 are arranged in a pattern in which one antenna is arranged above the reception antenna Rx#2 in the vertical direction (T-shape turned 180°), the reception antenna Rx#2 being a base point and being the middle antenna out of three antennas arranged in the horizontal direction.

13 FIG.B 13 FIG.A The virtual antenna elements arrangement of the virtual reception array illustrated inand provided by the antenna arrangement illustrated inhas the following characteristics.

(1) Horizontal Direction

H H H H H H H H 13 FIG.A 13 FIG.B 13 FIG.B Due to horizontal positional relationships among the two transmission antennas Tx#1 and Tx#4 arranged with an inter-element space 7din the horizontal direction and the three reception antennas Rx#1, Rx#2, and Rx#3 arranged with inter-element spaces 2dand din the horizontal direction in, the virtual reception array illustrated inincludes a virtual horizontal linear array antenna HLA including six elements arranged on a straight line with inter-element spaces 2d, d, 4d, 2d, and din the horizontal direction (VA#1, VA#5, VA#9, VA#4, VA#8, and VA#12 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 H H H H H When the horizontal position of VA#1 is a reference, the horizontal coordinates (x, x, x, x, x, x) of the six elements (VA#1, VA#5, VA#9, VA#4, VA#8, VA#12) forming the virtual horizontal linear array antenna HLA are such that (x, x, x, x, x, x)=[0, 2d, 3d, 7d, 9d, 10d].

A B H H 10 The inter-element spaces |x−x| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual horizontal linear array antenna HLA are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}×d. By using the virtual horizontal linear array antenna HLA including six elements, the radar devicecan be virtually assumed to have an uniform linear array including 11 elements arranged with inter-element spaces of the basic unit din the horizontal direction, and perform the direction-of-arrival estimation with high angular resolution.

H H 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the horizontal direction. Moreover, since the array aperture length of the radar deviceis 10d=5λ, the beam width BW thereof is about 8° and the radar devicecan achieve high angular resolution of BW=10° or less.

(2) Vertical Direction

V V V V V V V V 13 FIG.A 13 FIG.B 13 FIG.B Due to vertical positional relationships among the three transmission antennas Tx#1, Tx#2, and Tx#3 arranged with inter-element spaces 2dand 4din the vertical direction and the two reception antennas Rx#2 and Rx#4 arranged with an inter-element space 5din the vertical direction in, the virtual reception array illustrated inincludes a virtual vertical linear array antenna VLA including six elements arranged on a straight line with inter-element spaces 4d, d, d, 3d, and 2din the vertical direction (VA#7, VA#6, VA#15, VA#5, VA#14, and VA#13 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 V V V V V When the vertical position of VA#7 is a reference, the vertical coordinates (y, y, y, y, y, y) of the six elements (VA#7, VA#6, VA#15, VA#5, VA#14, VA#13) forming the virtual vertical linear array antenna VLA are such that (y, y, y, y, y, y)=[0, 4d, 5d, 6d, 9d, 11d].

A B V V V 10 The inter-element space |y−y| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual vertical linear array antenna VLA are {1, 2, 3, 4, 5, 6, 7, 9, 11}×d. By using combinations of elements out of the six elements in the virtual vertical linear array antenna VLA whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7}×d, the radar devicecan be virtually assumed to have an uniform linear array including eight elements arranged with inter-element spaces of the basic unit din the vertical direction, and perform the direction-of-arrival estimation with high angular resolution.

V V V V 10 10 10 Meanwhile, by using combinations whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7, 9, 11}×d, the radar devicecan be virtually assumed to have a linear array including 10 elements arranged with inter-element spaces 2dwhich are twice the basic unit din the vertical direction, and perform the direction-of-arrival estimation. In this case, in the radar deviceassumed to have the linear array including 10 elements, the spatial side robe slightly increases but the aperture length is further increased compared to the radar deviceassumed to have the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit d. Accordingly, the angular resolution can be improved.

V V V V V 10 10 10 10 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the vertical direction. Moreover, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit d, the array aperture length of the radar deviceis 7d=3.5λ, and the beam width BW thereof is thus about 11°. Meanwhile, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the linear array including 10 elements arranged with the inter-element spaces 2d, the array aperture length of the radar deviceis 11d=5.5λ. Accordingly, the beam width BW of the radar deviceis about 7° and the radar devicecan achieve high angular resolution of BW=10° or less.

10 10 V V V V V 13 FIG.A 13 FIG.B 13 FIG.B 13 FIG.A As described above, in the radar device, in the case of d=0.5λ, in, |(inter-element space 4dbetween Tx#2 and Tx#3 in vertical direction)−(inter-element space 5dbetween Rx#2 and Rx#4 in vertical direction)|=d≈0.5λ <1λ, and the condition B-3 is satisfied. Thus, in, the arrangement of the virtual reception array in the vertical direction includes one or more inter-element spaces (≈0.5λ) which are 1λ or smaller (inter-element space between VA#6 and VA#15 and inter-element space between VA#15 and VA#5 illustrated in). The radar deviceusing the arrangement illustrated incan be virtually assumed to have a uniform linear array including multiple elements arranged with inter-element spaces of the basic unit din the vertical direction and perform the direction-of-arrival estimation with high angular resolution, also in the sub-array antenna configuration.

14 FIG. 14 FIG. 14 FIG. 14 FIG. 8 10 10 10 V V illustrates a direction estimation result (calculator simulation result) obtained by using the configuration described above. In, simulation conditions are such that the beamformer method is used and a target direction is set to 0°. Moreover, the direction estimation result (element DOA) illustrated by the solid line inis a result of the direction-of-arrival estimation performed while virtually assuming that the radar devicehas the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit din the vertical direction. Meanwhile, the direction estimation result (element DOA) illustrated by the dotted line inis a result of the direction-of-arrival estimation performed while virtually assuming that the radar devicehas the linear array including 10 elements arranged with the inter-element spaces twice the basic unit din the vertical direction.

14 FIG. 14 FIG. 14 FIG. 10 10 10 As illustrated in, it is found that, in the radar devicevirtually assumed to have the uniform linear array including eight elements, the beam width BW of the beam in the target direction θ° is about 11° and the side lobe level of 13 dB or lower is obtained. Meanwhile, as illustrated in, it is found that, in the radar devicevirtually assumed to have the linear array including 10 elements, the side lobes increases but the beam width BW of the beam in the target direction 0° decreases compared to those in the radar devicevirtually assumed to have the uniform linear array including eight elements (solid line). Moreover, as illustrated in, it is found that no grating lobes are generated in both cases.

10 10 10 As described above, in the embodiment, in the radar devicewhich has the sub-array antenna configuration and which performs beam scanning two-dimensionally in the vertical direction and the horizontal direction by using the MIMO radar, the aperture lengths of the virtual reception array in the vertical direction and the horizontal direction can be increased as much as possible. Accordingly, in the embodiment, it is possible to improve the angular resolution of the radar devicewith few antennas by using this virtual reception array and thereby reduce the size and cost of the radar device.

(Variation 1 of Embodiment 2)

13 FIG.A V The antenna arrangement in the MIMO radar ofdescribed above can be applied as long as the size of a sub-arrayed antenna element which is formed by stacking elements in the vertical direction is smaller than 2d.

13 FIG.A 15 FIG.A 15 FIG.A V V In the arrangement of, the smallest inter-element space in the vertical direction is the inter-element space between Tx#1 and Tx#2 and is 2d. Meanwhile, in the arrangement of, the smallest inter-element space in the vertical direction is the inter-element space between Rx#2 and Rx#4 and is 3d. Accordingly, a sub-arrayed antenna element which is larger in size in the vertical direction can be used in the arrangement of. Using the sub-arrayed antenna element which is larger in size in the vertical direction can improve the gain in the vertical direction and also narrow the directivity in the vertical direction.

V V 15 FIG.C Meanwhile, when the size of a sub-arrayed antenna element which is formed by stacking elements in the vertical direction is larger than 2din the vertical direction, for example, when a sub-array antenna element which is formed by stacking three antenna elements in the vertical direction as illustrated inis used, the antenna arrangement to be described below can be used. Description is given below of an antenna arrangement example applicable as long as the size of a sub-array antenna element which is formed by stacking elements in the vertical direction is 3dor smaller in the vertical direction.

15 FIG.A 15 FIG.B 15 FIG.A 106 202 illustrates an arrangement example of the transmission antennasand the reception antennas.illustrates an arrangement of a virtual reception array obtained from the antenna arrangement illustrated in.

106 202 106 202 In this example, the number Nt of the transmission antennasis four and the number Na of the reception antennasis four. Moreover, the four transmission antennasare denoted respectively by Tx#1 to Tx#4, and the four reception antennasare denoted respectively by Rx#1 to Rx#4.

15 FIG.A In, the transmission antennas Tx#1 to Tx#4 are arranged such that one antenna is arranged on the right side of the transmission antenna Tx#1 in the horizontal direction (L shape turned +90°), the transmission antenna Tx#1 being a base point and being the top antenna out of three antennas arranged in the vertical direction. Meanwhile, the reception antennas Rx#1 to Rx#4 are arranged such that one antenna is arranged above the reception antenna Rx#2 in the vertical direction (T-shape turned 180°), the reception antenna Rx#2 being a base point and being the middle antenna out of three antennas arranged in the horizontal direction.

15 FIG.B 15 FIG.A The arrangement of the virtual reception array illustrated inand provided by the antenna arrangement illustrated inhas the following characteristics.

(1) Horizontal Direction

H H H H H H H H 15 FIG.A 15 FIG.B 15 FIG.B Due to horizontal positional relationships among the two transmission antennas Tx#1 and Tx#4 arranged with an inter-element space 7din the horizontal direction and the three reception antennas Rx#1, Rx#2, and Rx#3 arranged with inter-element spaces 2dand din the horizontal direction in, the virtual reception array illustrated inincludes a virtual horizontal linear array antenna HLA including six elements arranged on a straight line with inter-element spaces 2d, d, 4d, 2d, and din the horizontal direction (VA#1, VA#5, VA#9, VA#4, VA#8, and VA#12 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 H H H H H When the horizontal position of VA#1 is a reference, the horizontal coordinates (x, x, x, x, x, x) of the six elements (VA#1, VA#5, VA#9, VA#4, VA#8, VA#12) forming the virtual horizontal linear array antenna HLA are such that (x, x, x, x, x, x)=[0, 2d, 3d, 7d, 9d, 10d].

A B H H 10 The inter-element spaces |x−x| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual horizontal linear array antenna HLA are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}×d. By using the virtual horizontal linear array antenna HLA including six elements, the radar devicecan be virtually assumed to have an uniform linear array including 11 elements arranged with inter-element spaces of the basic unit din the horizontal direction, and perform the direction-of-arrival estimation with high angular resolution.

H H 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the horizontal direction. Moreover, since the array aperture length of the radar deviceis 10d=5λ, the beam width BW thereof is about 8° and the radar devicecan achieve high angular resolution of BW=10° or less.

(2) Vertical Direction

V V V V V V V V 15 FIG.A 15 FIG.B 15 FIG.B Due to vertical positional relationships among the three transmission antennas Tx#1, Tx#2, and Tx#3 arranged with inter-element spaces 4dand 5din the vertical direction and the two reception antennas Rx#2 and Rx#4 arranged with an inter-element space 3din the vertical direction in, the virtual reception array illustrated inincludes a virtual vertical linear array antenna VLA including six elements arranged on a straight line with inter-element spaces 3d, 2d, 3d, 1d, and 3din the vertical direction (VA#7, VA#15, VA#6, VA#14, VA#5, and VA#13 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 V V V V V When the vertical position of VA#7 is a reference, the vertical coordinates (y, y, y, y, y, y) of the six elements (VA#7, VA#15, VA#6, VA#14, VA#5, VA#13) forming the virtual vertical linear array antenna VLA are such that (y, y, y, y, y, y)=[0, 3d, 5d, 8d, 9d, 12d].

A B V V V 10 The inter-element spaces |y−y| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual vertical linear array antenna VLA are {1, 2, 3, 4, 5, 6, 7, 8, 9, 12}×d. By using combinations of elements out of the six elements in the virtual vertical linear array antenna VLA whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7, 8, 9}×d, the radar devicecan be virtually assumed to have an uniform linear array including 10 elements arranged with inter-element spaces of the basic unit din the vertical direction, and perform the direction-of-arrival estimation with high angular resolution.

V V V V 10 10 10 Meanwhile, by using combinations whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7, 8, 9, 12}×d, the radar devicecan be virtually assumed to have a linear array including 11 elements arranged with an inter-element space 3dwhich is three times the basic unit din the vertical direction, and perform the direction-of-arrival estimation. In this case, in the radar deviceassumed to have the linear array including 11 elements, the spatial side robe slightly increases but the aperture length is further increased compared to the radar deviceassumed to have the uniform linear array including 10 elements arranged with the inter-element spaces of the basic unit d. Accordingly, the angular resolution can be improved.

V V V V V 10 10 10 10 10 10 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the vertical direction. Moreover, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the uniform linear array including 10 elements arranged with the inter-element spaces of the basic unit d, the array aperture length of the radar deviceis 9d=4.5λ. Accordingly, the beam width BW of the radar deviceis about 9° and the radar devicecan achieve high angular resolution of BW=10° or less. Meanwhile, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the linear array including 11 elements arranged with the inter-element space 3d, the array aperture length of the radar deviceis 12d=6λ. Accordingly, the beam width BW of the radar deviceis about 7° and the radar devicecan achieve high angular resolution of BW=10° or less.

(Variation 2 of Embodiment 2)

16 FIG. 17 FIG.A 16 FIG. 10 H In the embodiment described above, a case where a sub-arrayed antenna element is formed by arranging antenna elements in the vertical direction is described. However, a sub-arrayed antenna element can be formed by arranging antenna elements in the horizontal direction. Specifically,illustrates an example in which a sub-arrayed antenna element is applied towhen the radar detection range of the radar devicecan be reduced in the horizontal direction and the smallest inter-element space in the horizontal direction is 2d. In, forming the sub-arrayed antenna element by stacking two antenna elements in the horizontal direction can narrow the directivity in the horizontal direction and reduce radiation in an unnecessary direction, thereby improving the array element gain.

10 However, as in the case of stacking in the vertical direction described above, stacking the antenna elements in the horizontal direction increases the size of the sub-arrayed antennas element to about one wavelength, and this restricts the arrangement of the array antenna. Specifically, in the radar devicehaving the sub-array antenna configuration, the smallest inter-element space in the array arrangement horizontal direction is restricted to be equal to or more than a certain value.

In view of this, in this variation, description is given of an antenna arrangement which achieves high resolution in the vertical/horizontal direction and which can perform the direction-of-arrival estimation with the generation of grating lobes suppressed in a wide range when the sub-array antenna is used in the horizontal direction.

106 202 As in Embodiment 1, Nt transmission antennasand Na reception antennasare arranged with uneven inter-element spaces in the horizontal direction and the vertical direction.

106 202 106 202 106 202 TV RV H H Moreover, the transmission antennasand the reception antennasin the embodiment are arranged in the horizontal direction (direction in which the sub-array antennas are formed) such that there is one or more combinations of the inter-element spaces among the Ntransmission antennasand the inter-element spaces among the Nreception antennasin which the difference between the inter-element spaces is the basic unit dof the inter-element spaces in the horizontal direction. Moreover, the basic unit dof the inter-element spaces in the horizontal direction is set to be less than 1λ (for example, 0.5λ). Specifically, the transmission antennasand the reception antennasare arranged to include at least one arrangement satisfying the following formula (hereafter referred to as condition A-3).

106 202 H <Condition A-3>(inter-element space between transmission antennasin horizontal direction)−(inter-element space between reception antennasin horizontal direction)|=d≈0.5λ<1λ.

106 202 Moreover, the arrangement of the transmission antennasand the reception antennasof the variation satisfies the restriction conditions described in Embodiment 1 except for A-1, that is A-2, B-1, and B-2.

10 10 10 As a result, also in the radar devicehaving the sub-array antenna configuration in the horizontal direction, the aperture lengths of the virtual reception array in the vertical direction and the horizontal direction can be increased as much as possible. Accordingly, it is possible to improve the angular resolution of the radar devicewith few antennas by using this virtual reception array and thereby reduce the size and cost of the radar device.

(Variation 3 of Embodiment 2)

18 FIG. 17 FIG.A 18 FIG. V H In this variation, description is given of the case where a sub-arrayed antenna element is formed by arranging antenna elements in both the vertical direction and the horizontal direction.illustrates an example in which a sub-arrayed antenna element arranged in a two-by-two matrix pattern is applied towhen the radar detection range can be reduced in both the vertical direction and the horizontal direction and the smallest inter-element spaces in the vertical direction and the horizontal direction are 2dand 2d, respectively. In, forming the sub-arrayed antenna element by stacking antenna elements in the vertical direction and the horizontal direction can narrow the directivity in the vertical direction and the horizontal direction and reduce radiation in an unnecessary direction, thereby improving the array element gain.

10 10 However, stacking the antenna elements in the vertical direction and the horizontal direction increases the size of the sub-arrayed antenna element to one wavelength or more, and this restricts the arrangement of the array antenna in the radar device. Specifically, in the radar device, the smallest inter-element spaces in the array arrangement vertical direction and horizontal direction are each restricted to be equal to or more than a certain value.

In view of this, in this variation, description is given of an antenna arrangement which achieves high resolution in the vertical/horizontal direction and which can perform the direction-of-arrival estimation with the generation of grating lobes suppressed in a wide range when the sub-array antenna is used in both the vertical direction and the horizontal direction.

106 202 As in Embodiment 1, Nt transmission antennasand Na reception antennasare arranged with uneven inter-element spaces in the horizontal direction and the vertical direction.

106 202 106 202 106 202 TV RV V V The transmission antennasand the reception antennasin the embodiment are arranged in the vertical direction such that there is one or more combinations of the inter-element spaces among the Ntransmission antennasand the inter-element spaces among the Nreception antennasin which the difference between the inter-element spaces is the basic unit dof the inter-element spaces in the vertical direction. Moreover, the basic unit dof the inter-element spaces in the vertical direction is set to be less than 1λ (for example, 0.5λ). Specifically, the transmission antennasand the reception antennasare arranged in the vertical direction to include at least one arrangement satisfying the following formula (condition B-3).

106 202 V <Condition B-3>(inter-element space between transmission antennasin vertical direction)−(inter-element space between reception antennasin vertical direction)|=d≈0.5λ<1λ.

106 202 106 202 106 202 TV RV H H Moreover, the transmission antennasand the reception antennasin the embodiment are arranged in the horizontal direction such that there is one or more combinations of the inter-element spaces among the Ntransmission antennasand the inter-element spaces among the Nreception antennasin which the difference between the inter-element spaces is the basic unit dof the inter-element spaces in the horizontal direction. Moreover, the basic unit dof the inter-element spaces in the horizontal direction is set to be less than 1λ (for example, 0.5λ). Specifically, the transmission antennasand the reception antennasare arranged in the horizontal direction to include at least one arrangement satisfying the following formula (condition A-3).

106 202 H <Condition A-3>(inter-element space between transmission antennasin horizontal direction)−(inter-element space between reception antennasin horizontal direction)|=d0.5λ<1λ.

106 202 Moreover, the arrangement of the transmission antennasand the reception antennasof the variation satisfies the restriction conditions described in Embodiment 1 except for A-1 and B-1, that is A-2 and B-2.

17 FIG.A 17 FIG.B 17 FIG.A 106 202 illustrates an arrangement example of the transmission antennasand the reception antennas.illustrates an arrangement of a virtual reception array obtained from the antenna arrangement illustrated in.

106 202 106 202 In this example, the number Nt of the transmission antennasis four and the number Na of the reception antennasis four. Moreover, the four transmission antennasare denoted respectively by Tx#1 to Tx#4, and the four reception antennasare denoted respectively by Rx#1 to Rx#4.

17 FIG.A In, the transmission antennas Tx#1 to Tx#4 are arranged such that one antenna is arranged on the right side of the transmission antenna Tx#1 in the horizontal direction (L shape turned +90°), the transmission antenna Tx#1 being a base point and being the top antenna out of three antennas arranged in the vertical direction. Meanwhile, the reception antennas Rx#1 to Rx#4 are arranged such that one antenna is arranged above the reception antenna Rx#2 in the vertical direction, the reception antenna Rx#2 being a base point and being the middle antenna out of three antennas arranged in the horizontal direction.

17 FIG.B 17 FIG.A 17 FIG.B illustrates the arrangement of the virtual reception array provided by the antenna arrangement illustrated in. The arrangement of the virtual reception array illustrated inhas the following characteristics.

(1) Horizontal Direction

H H H H H H H H 17 FIG.A 17 FIG.B 17 FIG.B Due to horizontal positional relationships among the two transmission antennas Tx#1 and Tx#4 arranged with an inter-element space 5din the horizontal direction and the three reception antennas Rx#1, Rx#2, and Rx#3 arranged with inter-element spaces 4dand 2din the horizontal direction in, the virtual reception array illustrated inincludes a virtual horizontal linear array antenna HLA including six elements arranged on a straight line with inter-element spaces 4d, d, d, 3d, and 2din the horizontal direction (VA#1, VA#5, VA#4, VA#9, VA#8, and VA#12 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 H H H H H When the horizontal position of VA#1 is a reference, the horizontal coordinates (x, x, x, x, x, x) of the six elements (VA#1, VA#5, VA#4, VA#9, VA#8, VA#12) forming the virtual horizontal linear array antenna HLA are such that (x, x, x, x, x, x)=[0, 4d, 5d, 6d, 9d, 11d].

A B H H H 10 The inter-element spaces |x−x| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual horizontal linear array antenna HLA are {1, 2, 3, 4, 5, 6, 7, 9, 11}×d. By using combinations of elements out of the six elements in the virtual horizontal linear array antenna HLA whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7}×d, the radar devicecan be virtually assumed to have an uniform linear array including eight elements arranged with inter-element spaces of the basic unit din the horizontal direction, and perform the direction-of-arrival estimation with high angular resolution.

H H H H 10 10 10 Meanwhile, by using combinations whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7, 9, 11}×d, the radar devicecan be virtually assumed to have a linear array including 10 elements arranged with inter-element spaces 2dwhich are twice the basic unit din the horizontal direction, and perform the direction-of-arrival estimation. In this case, in the radar deviceassumed to have the linear array including 10 elements, the spatial side robe slightly increases but the aperture length is further increased compared to the radar deviceassumed to have the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit d. Accordingly, the angular resolution can be improved.

H H H H H 10 10 10 10 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the horizontal direction. Moreover, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit d, the array aperture length of the radar deviceis 7d=3.5λ, and the beam width BW thereof is thus about 11°. Meanwhile, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the linear array including 10 elements arranged with the inter-element space 2d, the array aperture length of the radar deviceis 11d=5.5λ. Accordingly, the beam width BW of the radar deviceis about 7° and the radar devicecan achieve high angular resolution of BW=10° or less.

H H H H H 17 FIG.A 17 FIG.B 17 FIG.B 17 FIG.A 10 10 As described above, in the case of d=0.5λ, in, the radar devicesatisfies the condition A-3 which is |(inter-element space 5dbetween Tx#1 and Tx#4 in horizontal direction)−(inter-element space 4dbetween Rx#1 and Rx#2 in horizontal direction)|=d≈0.5λ<1λ. Thus, in, the arrangement of the virtual reception array in the horizontal direction includes one or more inter-element spaces which are 1λ or smaller (≈0.5λ) (inter-element space between VA#5 and VA#4 and inter-element space between VA#4 and VA#9 illustrated in). The radar deviceusing the arrangement illustrated incan be virtually assumed to have a linear array including multiple elements arranged with inter-element spaces of the basic unit din the horizontal direction and perform the direction-of-arrival estimation with high angular resolution.

(2) Vertical Direction

V V V V V V V V 17 FIG.A 17 FIG.B 17 FIG.B Due to vertical positional relationships among the three transmission antennas Tx#1, Tx#2, and Tx#3 arranged with inter-element spaces 2dand 4din the vertical direction and the two reception antennas Rx#2 and Rx#4 arranged with the inter-element space 5din the vertical direction in, the virtual reception array illustrated inincludes a virtual vertical linear array antenna VLA including six elements arranged on a straight line with inter-element spaces 4d, d, d, 3d, and 2din the vertical direction (VA#7, VA#6, VA#15, VA#5, VA#14, and VA#13 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 V V V V V When the vertical position of VA#7 is a reference, the vertical coordinates (y, y, y, y, y, y) of the six elements (VA#7, VA#6, VA#15, VA#5, VA#14, VA#13) forming the virtual vertical linear array antenna VLA are such that (y, y, y, y, y, y)=[0, 4d, 5d, 6d, 9d, 11d].

A B V V V 10 The inter-element spaces |y−y| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual vertical linear array antenna VLA are {1, 2, 3, 4, 5, 6, 7, 9, 11}×d. By using combinations of elements out of the six elements in the virtual vertical linear array antenna VLA whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7}×d, the radar devicecan be virtually assumed to have an uniform linear array including eight elements arranged with inter-element spaces of the basic unit din the vertical direction, and perform the direction-of-arrival estimation with high angular resolution.

V V V V 10 10 10 Meanwhile, by using combinations whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7, 9, 11}×d, the radar devicecan be virtually assumed to have a linear array including 10 elements arranged with inter-element spaces 2dwhich are twice the basic unit din the vertical direction, and perform the direction-of-arrival estimation. In this case, in the radar deviceassumed to have the linear array including 10 elements, the spatial side robe slightly increases but the aperture length is further increased compared to the radar deviceassumed to have the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit d. Accordingly, the angular resolution can be improved.

V V V V V 10 10 10 10 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the vertical direction. Moreover, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit d, the array aperture length of the radar deviceis 7d=3.5λ and the beam width BW thereof is thus about 11°. Meanwhile, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the linear array including 10 elements arranged with the inter-element spaces 2d, the array aperture length of the radar deviceis 11d=5.5λ. Accordingly, the beam width BW of the radar deviceis about 7° and the radar devicecan achieve high angular resolution of BW=10° or less.

V V V V V 17 FIG.A 17 FIG.B 17 FIG.B 17 FIG.A 10 10 As described above, in the case of d=0.5λ, in, the radar devicesatisfies the condition B-3 which is |(inter-element space 4dbetween Tx#2 and Tx#3 in vertical direction)−(inter-element space 5dbetween Rx#2 and Rx#4 in vertical direction)|=d≈0.5λ<1λ. Thus, in, the arrangement of the virtual reception array in the vertical direction includes one or more inter-element spaces which are 1λ or smaller (≈0.5λ) (inter-element space between VA#6 and VA#15 and inter-element space between VA#15 and VA#5 illustrated in). The radar deviceusing the arrangement illustrated incan be virtually assumed to have a linear array including multiple elements arranged with inter-element spaces of the basic unit din the vertical direction and perform the direction-of-arrival estimation with high angular resolution.

10 10 10 Accordingly, also in the radar devicewhich has the sub-array antenna configuration in both the vertical direction and the horizontal direction, the aperture lengths of the virtual reception array in the vertical direction and the horizontal direction can be increased as much as possible. Accordingly, it is possible to improve the angular resolution of the radar devicewith few antennas by using this virtual reception array and thereby reduce the size and cost of the radar device.

(Variation 4 of Embodiment 2)

V H The antenna arrangement of the MIMO radar described in Variation 3 can be applied as long as the vertical and horizontal sizes of a sub-arrayed antenna element which is formed by stacking antenna elements in the vertical and horizontal directions are smaller than 2dand 2d, respectively.

10 V H V H 19 FIG. Meanwhile, in the radar device, when the vertical and horizontal sizes of a sub-arrayed antenna element which is formed by stacking antenna elements in the vertical and horizontal directions are larger than 2dand 2d, respectively, for example, when a sub-arrayed antenna element is formed by stacking three antenna elements in each of the vertical direction and the horizontal direction as illustrated inis used, the antenna arrangement to be described below can be used. Description is given below of an antenna arrangement example applicable as long as the vertical size of a sub-arrayed antenna element which is formed by stacking antenna elements in the vertical direction is smaller than 3dand the horizontal size of the sub-arrayed antenna element is formed by stacking the antenna elements in the horizontal direction is smaller than 3d.

20 FIG.A 20 FIG.B 20 FIG.A 106 202 illustrates an arrangement example of the transmission antennasand the reception antennas.illustrates an arrangement of a virtual reception array obtained from the antenna arrangement illustrated in.

106 202 106 202 In this example, the number Nt of the transmission antennasis four and the number Na of the reception antennasis four. Moreover, the four transmission antennasare denoted respectively by Tx#1 to Tx#4, and the four reception antennasare denoted respectively by Rx#1 to Rx#4.

20 FIG.A In, the transmission antennas Tx#1 to Tx#4 are arranged in a pattern in which one antenna is arranged on the right side of the transmission antenna Tx#1 in the horizontal direction with an inter-element space smaller than inter-element spaces in the vertical direction (L shape turned −180°), the transmission antenna Tx#1 being a base point and being the top antenna out of three antennas arranged in the vertical direction. Meanwhile, the reception antennas Rx#1 to Rx#4 are arranged such that one antenna is arranged above the reception antenna Rx#3 in the vertical direction with an inter-element space smaller than inter-element spaces in the horizontal direction (L shape turned −90°), the reception antenna Rx#3 being a base point and being the rightmost antenna out of three antennas arranged in the horizontal direction.

20 FIG.B 20 FIG.A The arrangement of the virtual reception array illustrated inand provided by the antenna arrangement illustrated inhas the following characteristics.

(1) Horizontal Direction

H H H H H H H H 20 FIG.A 20 FIG.B 20 FIG.B Horizontal positional relationships among the two transmission antennas Tx#1 and Tx#4 arranged with an inter-element space 3din the horizontal direction and the three reception antennas Rx#1, Rx#2, and Rx#3 arranged with inter-element spaces 4dand 5din the horizontal direction insatisfy the condition A-3 and, due to this positional relationship, the virtual reception array illustrated inincludes a virtual horizontal linear array antenna HLA including six elements arranged on a straight line with inter-element spaces 3d, d, 3d, 2d, and 3din the horizontal direction (VA#1, VA#4, VA#5, VA#8, VA#9, and VA#12 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 H H H H H When the horizontal position of VA#1 is a reference, the horizontal coordinates (x, x, x, x, x, x) of the six elements (VA#1, VA#4, VA#5, VA#8, VA#9, VA#12) forming the virtual horizontal linear array antenna HLA are such that (x, x, x, x, x, x)=[0, 3d, 4d, 7d, 9d, 12d].

A B H H H 10 The inter-element spaces |x−x| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual horizontal linear array antenna HLA are {1, 2, 3, 4, 5, 6, 7, 8, 9, 12}×d. By using combinations of elements out of the six elements in the virtual horizontal linear array antenna HLA whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7, 8, 9}×d, the radar devicecan be virtually assumed to have an uniform linear array including 10 elements arranged with the inter-element spaces of the basic unit din the horizontal direction, and perform the direction-of-arrival estimation with high angular resolution.

H H H H 10 10 10 Meanwhile, by using combinations whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7, 8, 9, 12}×d, the radar devicecan be virtually assumed to have a linear array including 11 elements arranged with an inter-element space 3dwhich is three times the basic unit din the horizontal direction, and perform the direction-of-arrival estimation. In this case, in the radar deviceassumed to have the linear array including 11 elements, the spatial side robe slightly increases but the aperture length is further increased compared to the radar deviceassumed to have the uniform linear array including 10 elements arranged with the inter-element spaces of the basic unit d. Accordingly, the angular resolution can be improved.

H H H H H 10 10 10 10 10 10 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the horizontal direction. Moreover, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the uniform linear array including 10 elements arranged with the inter-element spaces of the basic unit d, the array aperture length of the radar deviceis 9d=4.5λ. Accordingly, the beam width BW of the radar deviceis about 9° and the radar devicecan achieve high angular resolution of BW=10° or less. Meanwhile, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the linear array including 11 elements arranged with the inter-element space 3d, the array aperture length of the radar deviceis 12d=6λ. Accordingly, the beam width BW of the radar deviceis about 7° and the radar devicecan achieve high angular resolution of BW=10° or less.

(2) Vertical Direction

V V V V V V V V 20 FIG.A 20 FIG.B 20 FIG.B Vertical positional relationships among the three transmission antennas Tx#1, Tx#2, and Tx#3 arranged with inter-element spaces 4dand 5din the vertical direction and the two reception antennas Rx#3 and Rx#4 arranged with an inter-element space 3din the vertical direction insatisfy the condition B-3 and, due to this positional relationship, the virtual reception array illustrated inincludes a virtual vertical linear array antenna VLA including six elements arranged on a straight line with inter-element spaces 3d, 2d, 3d, d, and 3din the vertical direction (VA#11, VA#15, VA#10, VA#14, VA#9, and VA#13 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 V V V V V When the vertical position of VA#11 is a reference, the vertical coordinates (y, y, y, y, y, y) of the six elements (VA#11, VA#15, VA#10, VA#14, VA#9, VA#13) forming the virtual vertical linear array antenna VLA are such that (y, y, y, y, y, y)=[0, 3d, 5d, 8d, 9d, 12d].

A B V V V 10 The inter-element spaces |y−y| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual vertical linear array antenna VLA are {1, 2, 3, 4, 5, 6, 7, 8, 9, 12}×d. By using combinations of elements out of the six elements in the virtual vertical linear array antenna VLA whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7, 8, 9}×d, the radar devicecan be virtually assumed to have an uniform linear array including 10 elements arranged with inter-element spaces of the basic unit din the vertical direction, and perform the direction-of-arrival estimation with high angular resolution.

V V V V 10 10 10 Meanwhile, by using combinations whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7, 8, 9, 12}×d, the radar devicecan be virtually assumed to have a linear array including 11 elements arranged with an inter-element space 3dwhich is three times the basic unit din the vertical direction, and perform the direction-of-arrival estimation. In this case, in the radar deviceassumed to have the linear array including 11 elements, the spatial side robe slightly increases but the aperture length is further increased compared the radar deviceassumed to have to the uniform linear array including 10 elements arranged with the inter-element spaces of the basic unit d. Accordingly, the angular resolution can be improved.

V V V V V 10 10 10 10 10 10 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the vertical direction. Moreover, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the uniform linear array including 10 elements arranged with the inter-element spaces of the basic unit d, the array aperture length of the radar deviceis 9d=4.5λ. Accordingly, the beam width BW of the radar deviceis about 9° and the radar devicecan achieve high angular resolution of BW=10° or less. Meanwhile, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the linear array including 11 elements arranged with the inter-element space 3d, the array aperture length of the radar deviceis 12d=6λ. Accordingly, the beam width BW of the radar deviceis about 7° and the radar devicecan achieve high angular resolution of BW=10° or less.

(Variation 5 of Embodiment 2)

10 106 202 When high angular resolution of about 10° is unnecessary in Embodiment 2 as the angular resolution in the horizontal direction or the vertical direction, the radar devicemay include three transmission antennasor three reception antennas.

10 106 202 Description is given below of an example in which no high angular resolution is required as the angular resolution in the vertical direction and the radar deviceincludes three transmission antennasand four reception antennas.

Moreover, there is used a MIMO array arrangement in which the size of the array element is one wavelength (1λ) or more in the vertical and horizontal directions due to stacking of the antenna elements in the vertical and horizontal directions.

21 FIG.A 21 FIG.B 21 FIG.A 106 202 illustrates an arrangement example of the transmission antennasand the reception antennas.illustrates an arrangement of a virtual reception array obtained from the antenna arrangement illustrated in.

21 FIG.A 21 FIG.A 106 202 In, the three transmission antennasare denoted respectively by Tx#1 to Tx#3, and the four reception antennasare denoted respectively by Rx#1 to Rx#4. In, the transmission antennas Tx#1 to Tx#3 are arranged in a pattern in which one antenna is arranged on the right side of the transmission antenna Tx#1 in the horizontal direction with an inter-element space larger than an inter-element space in the vertical direction (L shape turned +90°), the transmission antenna Tx#1 being a base point and being the top antenna out of two antennas arranged in the vertical direction. Meanwhile, the reception antennas Rx#1 to Rx#4 are arranged such that one antenna is arranged above the reception antenna Rx#2 in the vertical direction with an inter-element space smaller than inter-element spaces in the horizontal direction (T-shape turned 180°), the reception antenna Rx#2 being a base point and being the middle antenna out of three antennas arranged in the horizontal direction.

106 202 Moreover, the arrangement of the transmission antennasand the reception antennasin this variation satisfies the restriction conditions described in Embodiment 1 except for A-1 and B-1, that is A-2 and B-2.

21 FIG.B 21 FIG.A The arrangement of the virtual reception array illustrated inand provided by the antenna arrangement illustrated inhas the following characteristics.

(1) Horizontal Direction

H H H H H H H H 21 FIG.A 21 FIG.B 21 FIG.B Horizontal positional relationships among the two transmission antennas Tx#1 and Tx#3 arranged with an inter-element space 5din the horizontal direction and the three reception antennas Rx#1, Rx#2, and Rx#3 arranged with inter-element spaces 4dand 2din the horizontal direction insatisfy the condition A-3 and, due to this positional relationship, the virtual reception array illustrated inincludes a virtual horizontal linear array antenna HLA including six elements arranged on a straight line with inter-element spaces 4d, d, d, 3d, and 2din the horizontal direction (VA#1, VA#4, VA#3, VA#7, VA#6, and VA#9 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 H H H H H When the horizontal position of VA#1 is a reference, the horizontal coordinates (x, x, x, x, x, x) of the six elements (VA#1, VA#4, VA#3, VA#7, VA#6, VA#9) forming the virtual horizontal linear array antenna HLA are such that (x, x, x, x, x, x)=[0, 4d, 5d, 6d, 9d, 11d].

A B H H H 10 The inter-element spaces |x−x| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual horizontal linear array antenna HLA are {1, 2, 3, 4, 5, 6, 7, 9, 11}×d. By using combinations of elements out of the six elements in the virtual horizontal linear array antenna HLA whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7}×d, the radar devicecan be virtually assumed to have an uniform linear array including eight elements arranged with the inter-element spaces of the basic unit din the horizontal direction, and perform the direction-of-arrival estimation with high angular resolution.

H H H H 10 10 10 Meanwhile, by using combinations whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7, 9, 11}×d, the radar devicecan be virtually assumed to have a linear array including 10 elements arranged with inter-element spaces 2dwhich are twice the basic unit din the horizontal direction, and perform the direction-of-arrival estimation. In this case, in the radar deviceassumed to have the linear array including 10 elements, the spatial side robe slightly increases but the aperture length is further increased compared to the radar deviceassumed to have the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit d. Accordingly, the angular resolution can be improved.

H H H H H 10 10 10 10 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the horizontal direction. Moreover, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit d, the array aperture length of the radar deviceis 7d=3.5λ, and the beam width BW thereof is thus about 11°. Meanwhile, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the linear array including 10 elements arranged with the inter-element spaces 2d, the array aperture length of the radar deviceis 11d=5.5λ. Accordingly, the beam width BW of the radar deviceis about 7° and the radar devicecan achieve high angular resolution of BW=10° or less.

(2) Vertical Direction

V V V V V 21 FIG.A 21 FIG.B 21 FIG.B Vertical positional relationships among the two transmission antennas Tx#1 and Tx#2 arranged with an inter-element space 2din the vertical direction and the two reception antennas Rx#2 and Rx#4 arranged with an inter-element space 3din the vertical direction insatisfy the condition B-3 and, due to this positional relationship, the virtual reception array illustrated inincludes a virtual vertical linear array antenna VLA including four elements arranged on a straight line with inter-element spaces 2d, d, and 2din the vertical direction (VA#5, VA#4, VA#11, and VA#10 surrounded by the broken line illustrated in).

1 2 3 4 1 2 3 4 V V V When the vertical position of VA#5 is a reference, the vertical coordinates (y, y, y, y) of the four elements (VA#5, VA#4, VA#11, VA#10) forming the virtual vertical linear array antenna VLA are such that (y, y, y, y)=[0, 2d, 3d, 5d].

A B V V V 10 The inter-element spaces |y−y| (where A and B are each one of integers from one to four, and A≠B) each between any two different elements included in the virtual vertical linear array antenna VLA are {1, 2, 3, 5}×d. By using combinations of elements out of the four elements in the virtual vertical linear array antenna VLA whose inter-element spaces are {1, 2, 3}×d, the radar devicecan be virtually assumed to have an uniform linear array including four elements arranged with inter-element spaces of the basic unit din the vertical direction, and perform the direction-of-arrival estimation with high angular resolution.

V V V V 10 10 10 Meanwhile, by using combinations whose inter-element spaces are {1, 2, 3, 5}×d, the radar devicecan be virtually assumed to have a linear array including five elements arranged with an inter-element space 2dwhich is twice the basic unit din the vertical direction, and perform the direction-of-arrival estimation. In this case, in the radar deviceassumed to have the linear array including five elements, the spatial side robe slightly increases but the aperture length is further increased compared to the radar deviceassumed to have the uniform linear array including four elements arranged with the inter-element spaces of the basic unit d. Accordingly, the angular resolution can be improved.

V V V 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the vertical direction. Moreover, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the linear array including five elements arranged with the inter-element space 2d, the array aperture length of the radar deviceis 5d=2.5λ, and the beam width BW thereof is thus about 16°.

(Variation 6 of Embodiment 2)

10 202 106 10 106 202 In Embodiment 2, a radar deviceusing five or more reception antennasmay include three transmission antennas. Alternatively, a radar deviceusing five or more transmission antennasmay include three reception antennas.

10 106 202 Description is given below of an example of the radar devicewhich includes three transmission antennasand five reception antennas.

Moreover, there is used a MIMO array arrangement in which the size of the array element is about one wavelength (1λ) in the vertical and horizontal directions due to stacking of the antenna elements in the vertical and horizontal directions.

22 FIG.A 22 FIG.B 22 FIG.A 106 202 illustrates an arrangement example of the transmission antennasand the reception antennas.illustrates an arrangement of a virtual reception array obtained from the antenna arrangement illustrated in.

22 FIG.A 22 FIG.A 24 24 FIGS.A toF 106 202 In, the three transmission antennasare denoted respectively by Tx#1 to Tx#3, and the five reception antennasare denoted respectively by Rx#1 to Rx#5. In, the transmission antennas Tx#1 to Tx#3 are arranged in a pattern in which one antenna is arranged on the right side of the transmission antenna Tx#1 in the horizontal direction (L shape turned +90°), the transmission antenna Tx#1 being the base point and being the top antenna out of two antennas arranged in the vertical direction. Meanwhile, the reception antennas Rx#1 to Rx#5 are arranged such that one antenna is arranged on each of the upper and lower sides of the reception antenna Rx#3 in the vertical direction, the reception antenna Rx#3 being a base point and being the middle antenna out of three antennas arranged in the horizontal direction (cross shape). Note that the arrangement of the reception antennas Rx#1 to Rx#5 are not limited to the cross arrangement, and may be a L-shaped arrangement or a T-shaped arrangement (see, for example,to be described later).

106 202 Moreover, the arrangement of the transmission antennasand the reception antennasin this variation satisfies the restriction conditions described in Embodiment 1 except for A-1 and B-1, that is A-2 and B-2.

22 FIG.B 22 FIG.A The arrangement of the virtual reception array illustrated inand provided by the antenna arrangement illustrated inhas the following characteristics.

(1) Horizontal Direction

H H H H H H H H 22 FIG.A 22 FIG.B 22 FIG.B Horizontal positional relationships among the two transmission antennas Tx#1 and Tx#3 arranged with an inter-element space 5din the horizontal direction and the three reception antennas Rx#2, Rx#3, and Rx#4 arranged with inter-element spaces 4dand 2din the horizontal direction insatisfy the condition A-3 and, due to this positional relationship, the virtual reception array illustrated inincludes a virtual horizontal linear array antenna HLA including six elements arranged on a straight line with inter-element spaces 4d, d, d, 3d, and 2din the horizontal direction (VA#4, VA#7, VA#6, VA#10, VA#9, and VA#12 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 H H H H H When the horizontal position of VA#4 is a reference, the horizontal coordinates (x, x, x, x, x, x) of the six elements (VA#4, VA#7, VA#6, VA#10, VA#9, VA#12) forming the virtual horizontal linear array antenna HLA are such that (x, x, x, x, x, x)=[0, 4d, 5d, 6d, 9d, 11d].

A B H H H 10 The inter-element spaces |x−x| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual horizontal linear array antenna HLA are {1, 2, 3, 4, 5, 6, 7, 9, 11}×d. By using combinations of elements out of the six elements in the virtual horizontal linear array antenna HLA whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7}×d, the radar devicecan be virtually assumed to have an uniform linear array including eight elements arranged with the inter-element spaces of the basic unit din the horizontal direction, and perform the direction-of-arrival estimation with high angular resolution.

H H H H 10 10 10 Meanwhile, by using combinations whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7, 9, 11}×d, the radar devicecan be virtually assumed to have a linear array including 10 elements arranged with inter-element spaces 2dwhich are twice the basic unit din the horizontal direction, and perform the direction-of-arrival estimation. In this case, in the radar deviceassumed to have the linear array including 10 elements, the spatial side robe slightly increases but the aperture length is further increased compared to the radar deviceassumed to have the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit d. Accordingly, the angular resolution can be improved.

H H H H H 10 10 10 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the horizontal direction. Moreover, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit d, the array aperture length of the radar deviceis 7d=3.5λ, and the beam width BW thereof is thus about 11°. Meanwhile, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the linear array including 10 elements arranged with the inter-element spaces 2d, the array aperture length of the radar deviceis 11d=5.5λ. Accordingly, the beam width BW thereof is about 7° and the radar devicecan achieve high angular resolution of BW=10° or less.

(2) Vertical Direction

V V V V V V V V 22 FIG.A 22 FIG.B 22 FIG.B Vertical positional relationships among the two transmission antennas Tx#1 and Tx#2 arranged with an inter-element space 5din the vertical direction and the three reception antennas Rx#1, Rx#3, and Rx#5 arranged with inter-element spaces 2dand 4din the vertical direction insatisfy the condition B-3 and, due to this positional relationship, the virtual reception array illustrated inincludes a virtual vertical linear array antenna VLA including six elements arranged on a straight line with inter-element spaces 2d, 3d, d, d, and 4din the vertical direction (VA#2, VA#8, VA#1, VA#14, VA#7, and VA#13 surrounded by the broken line illustrated in).

1 2 3 4 5 6 1 2 3 4 5 6 V V V V V When the vertical position of VA#2 is a reference, the vertical coordinates (y, y, y, y, y, y) of the six elements (VA#2, VA#8, VA#1, VA#14, VA#7, VA#13) forming the virtual vertical linear array antenna VLA are such that (y, y, y, y, y, y)=[0, 2d, 5d, 6d, 7d, 11d].

A B V V V 10 The inter-element spaces |y−y| (where A and B are each one of integers from one to six, and A≠B) each between any two different elements included in the virtual vertical linear array antenna VLA are {1, 2, 3, 4, 5, 6, 7, 9, 11}×d. By using combinations of elements out of the six elements in the virtual vertical linear array antenna VLA whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7}×d, the radar devicecan be virtually assumed to have an uniform linear array including eight elements arranged with inter-element spaces of the basic unit din the vertical direction, and perform the direction-of-arrival estimation with high angular resolution.

V V V V V 10 10 10 Meanwhile, by using combinations whose inter-element spaces are {1, 2, 3, 4, 5, 6, 7, 9, 11}×d, the radar devicecan be virtually assumed to have a linear array including 10 elements arranged with inter-element spaces of the basic unit dand inter-element spaces 2dwhich are twice the basic unit din the vertical direction, and perform the direction-of-arrival estimation. In this case, in the radar deviceassumed to have the linear array including 10 elements, the spatial side robe slightly increases but the aperture length is further increased compared to the radar deviceassumed to have the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit d. Accordingly, the main beam becomes sharper and the angular resolution can be improved.

V V V V V 10 10 10 10 10 10 10 For example, in the case of d=0.5λ, the radar devicecan perform the direction-of-arrival estimation with the generation of grating lobes being suppressed in a wide range from −90° to +90° in the vertical direction. Moreover, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the uniform linear array including eight elements arranged with the inter-element spaces of the basic unit d, the array aperture length of the radar deviceis 7d=3.5λ, and the beam width BW thereof is thus about 11°. Meanwhile, when the radar deviceperforms the direction-of-arrival estimation while being virtually assumed to have the linear array including 10 elements arranged with the inter-element spaces 2d, the array aperture length of the radar deviceis 11d=5.5λ. Accordingly, the beam width BW of the radar deviceis about 7° and the radar devicecan achieve high angular resolution of BW=10° or less.

The embodiments of one aspect of the present disclosure have been described above.

Operations in the embodiments and variations described above can be carried out while being combined with one another as appropriate.

10 106 202 7 9 13 15 20 FIGS.A,A,A, andA toA (1) The antenna arrangements of the radar deviceincluding four transmission antennasand four reception antennasare not limited to the antenna arrangements illustrated in.

106 202 106 202 For example, the antenna arrangement may be a combination of the arrangement of the transmission antennasand the arrangement of the reception antennaswhich are each any of L-shaped and T-shaped arrangements. This can maximize the aperture surface formed by the virtual reception array extending in the vertical direction and the horizontal direction, as in the embodiments described above. Moreover, the arrangement of the transmission antennasand the arrangement of the reception antennasmay each be an arrangement of an L-shape or a T-shape flipped vertically or horizontally.

23 23 FIGS.A toF 23 23 FIGS.A andF 23 FIG.C 23 FIG.A 23 FIG.D 23 FIG.F 23 FIG.E 23 FIG.B 106 106 106 illustrate examples of the antenna arrangements for four transmission antennasin each of which two transmission antennasare arranged in the horizontal direction and three transmission antennasare arranged in the vertical direction and from which the equivalent effects can be obtained. As illustrated in, the arrangement may be an L-shaped arrangement (), an arrangement of an L-shape flipped vertically (), an arrangement of an L-shape turned 180° (), an arrangement of an L-shape flipped horizontally (), an arrangement of a T-shape turn +90° (), or an arrangement of a T-shape turned −90° ().

106 106 23 23 FIGS.A toF V V V V Moreover, the number of the transmission antennasis not limited to four. Similar effects can be obtained when inter-element spaces α and β among three of the transmission antennaswhich are illustrated in each ofand which are arranged on a straight line in the vertical direction are replaced with each other. Specifically, similar effects can be obtained when the inter-element space αdbetween the element #1 and the element #2 and the inter-element space βdbetween the element #2 and the element #3 are replaced such that the inter-element space between the element #1 and the element #2 is βdand the inter-element space between the element #2 and the element #3 is αd.

24 24 FIGS.A toF 24 24 FIGS.A andF 24 FIG.B 24 FIG.C 24 FIG.E 24 FIG.F 24 FIG.D 24 FIG.A 202 202 202 illustrate examples of the antenna arrangements for four reception antennasin each of which three reception antennasare arranged in the horizontal direction and two reception antennasare arranged in the vertical direction and from which the equivalent effects can be obtained. As illustrated in, the arrangement may be an L-shaped arrangement (), an arrangement of an L-shape flipped horizontally (), an arrangement of an L-shape flipped vertically (), an arrangement of an L-shape turned 180° (), a T-shaped arrangement (), or an arrangement of a T-shape flipped vertically ().

202 202 24 24 FIGS.A toF H H H H Moreover, the number of the reception antennasis not limited to four. Similar effects can be obtained when inter-element spaces α and β among three of the reception antennaswhich are illustrated in each ofand which are arranged on a straight line in the horizontal direction are replaced with each other. Specifically, similar effects can be obtained when the inter-element space αdbetween the element #1 and the element #2 and the inter-element space βdbetween the element #2 and the element #3 are replaced such that the inter-element space between the element #1 and the element #2 is βdand the inter-element space between the element #2 and the element #3 is αd.

10 106 202 10 106 202 202 106 23 23 FIGS.A toF 24 24 FIGS.A toF 24 24 FIGS.A toF 23 23 FIGS.A toF In the radar devicein which the arrangement of the transmission antennasis set to any of the arrangements ofand the arrangement of the reception antennasis set to any of the arrangements of the, the effects similar to those in the embodiments described above can be obtained. Moreover, also in the radar devicein which the arrangement of the transmission antennasis set to any of the arrangements of the reception antennasofand the arrangement of the reception antennasis set to any of the arrangements of the transmission antennasof the, the effects similar to those in the embodiments described above can be obtained.

(2) In the embodiments described above, description is given of the case where a coded pulse radar is used. However, the present disclosure can be applied also to a radar method using pulse waves subjected to frequency modulation such as in a chirp pulse radar.

10 100 200 3 FIG. (3) In the radar deviceillustrated in, the radar transmitterand the radar receivercan be arranged at separate positions physically located away from each other.

10 10 10 (4) For example, the radar deviceincludes, although not illustrated, a central processing unit (CPU), a storage medium such as a read only memory (ROM) storing control programs, and a work memory such as a random access memory (RAM). In this case the functions of the units described above are implemented by the CPU executing the control programs. Note that the hardware configuration of the radar deviceis not limited to the example described above. For example, the function units of the radar devicecan be implemented as an integrated circuit (IC). The function units can be each separately implemented on one chip. Alternatively, some or all of the function units can be implemented on one chip.

214 214 (5) In the embodiments described above, the direction estimatorperforms the direction estimation processing in the horizontal direction by forming the virtual horizontal linear array antenna HLA based on the inter-element spaces each between any two different elements in the horizontal direction. Moreover, the direction estimatorperforms the direction estimation processing in the vertical direction by forming the virtual vertical linear array antenna VLA based on the inter-element spaces each between any two different elements in the vertical direction.

However, the direction estimation processing is not limited to that described above. The two-dimensional direction estimation processing can be performed by forming an array antenna (hereafter, referred to as virtual surface-arranged array antenna) virtually surface-arranged based on the inter-element spaces in the horizontal and vertical directions.

25 FIG. is a diagram illustrating another configuration of the direction estimator.

250 25 FIG. Description is given below of operations of a direction estimatorillustrated in.

250 201 251 252 253 25 FIG. As in the embodiments described above, the direction estimatorillustrated inreceives the virtual reception array correlation vector h(k, fs, w) obtained by performing processing in the Na antenna system processors, and includes a direction vector storage, a correlation vector generator, and an evaluation function calculator.

26 FIG. 26 FIG. 250 T PT is a view illustrating a three-dimensional coordinate system used for the description of the operations of the direction estimator. First, in, the position vector of a physical target Pbased on the original point O is defined as r.

T PT T T T T T T T 106 202 The azimuth angle θ is defined as an angle between a straight line O-P′ and the Z-axis, where PT is a projection point at which a position vector rof the physical target P′ is projected on an XZ plane (when the X coordinate of the physical target Pis a positive value, θ>0). The elevation angle φ is defined as an angle of a line connecting the physical target P, the original point O, and the projection point P′ on a plane including the physical target P, the original point O, and the projection point P′ (when the Y coordinate of the physical target Pis a positive value, φ>0). Note that description is given below of an example in which the transmission antennasand the reception antennasare arranged on a XY plane.

va va va The position vector of the n-th element in the virtual reception array based on the original point O is referred to as Sn. In this case, n=1, Nt×Na.

1 2 va 1 202 1 106 202 202 1 In this case, the position vector Sof the first element in the virtual reception array is determined based on a positional relationship between the physical position of the first reception antenna-and the original point O. The other position vectors S, . . . , Snare determined based on the position vector Sof the first element in the virtual reception array while maintaining the relative arrangement of the virtual reception array determined from the inter-element spaces among the transmission antennasand the reception antennasexisting in the XY plane. Note that the original point O may match the physical position of the first reception antenna-.

200 T PT When the radar receiverreceives a reflected wave from the physical target Pexisting in a far field, a phase difference d (r, 2, 1) of a reception signal at the second element of the virtual reception array from a reception signal at the first element is expressed by the formula (15). In this case, <x, y> is an inner product operator of a vector x and a vector y:

2 1 Moreover, the position vector of the second element of the virtual reception array based on the position vector of the first element is expressed as an inter-element vector D(2, 1) in the formula (16):D(2,1)=S−S  (16).

200 T PT va va va va va va (t) (r) (t) (r) (r) (t) Similarly, when the radar receiverreceives the reflected wave from the physical target Pexisting in the far field, a phase difference d(r, n, n) of a reception signal at the n-th element of the virtual reception array from a reception signal at the n-th element is expressed by the formula (17). In this case, n=1, . . . , Nt×Na, n=Nt×Na:

va va va va (t) (r) (t) (r) Moreover, the position vector of the n-th element of the virtual reception array based on the position vector of the n-th element is expressed as an inter-element vector D(n, n) in the formula (18).

PT va va va va va va PT PT T (t) (r) (t) (r) (t) (r) As depicted in formulae (17) and (18), the phase difference d(r, n, n) of the reception signal at the n-th element of the virtual reception array from the reception signal at the n-th element depends on the inter-element vector D(n, n) and an unit vector (r/|r|) indicating the direction in which the physical target Pexists in the far field.

va va (t) (r) 250 Moreover, when the elements of the virtual reception array exist on the same plane, the inter-element vector D(n, n) exists on the same plane. The direction estimatorforms the virtual surface-arranged array antenna by using all or some of such inter-element vectors while assuming that elements virtually exist at positions indicated by the inter-element vectors, and performs the two-dimensional direction estimation processing.

Note that, when virtual elements are arranged to overlap one another, one of the overlapping elements is fixedly selected in advance. Alternatively, averaging processing can be performed by using reception signals at all or some of the virtual elements overlapping one another.

Description is given below of two-dimensional direction estimation processing using the beamformer method in the case where the virtual surface-arranged array antenna is formed by using Nq inter-element vector groups.

va(nq) va(nq) q (t) (r) In this case, the nq-th inter-element vector forming the virtual surface-arranged array antenna is expressed as D(n, n). In this case, nq=1, . . . , N.

252 VA 1 Na×Nr —after _ cal The correlation vector generatorgenerates a virtual surface-arranged array antenna correlation vector h(k, fs, w) depicted in the formula (19) by using h(k, fs, w), . . . , h(k, fs, w) which are elements of the virtual reception array correlation vector h(k, fs, w):

251 VA The direction vector storagestores a virtual surface-arranged array direction vector a(θu, φv) depicted by the formula (20).

PT PT T PT PT 253 Relationships among the azimuth angle θ, the elevation angle φ, and the unit vector (r/|r|) indicating the direction of the physical target Pin the case where the virtual reception array exists in the XY plane are expressed by the formula (21). The evaluation function calculatorthus calculates r/|r| by using the formula (21) for each of the angular directions θu and φv used to calculate a two-dimensional spatial profile in the vertical and horizontal directions.

253 The evaluation function calculatorperforms the two-dimensional direction estimation processing in the horizontal and vertical directions by using the virtual surface-arranged array antenna correlation vector and the virtual surface-arranged array direction vector.

VA VA VA u VA u VA H 2 In the two-dimensional direction estimation processing using the beamformer method, the two-dimensional spatial profile in the vertical and horizontal directions are calculated from the virtual surface-arranged array antenna correlation vector h(k, fs, w) and the virtual surface-arranged array direction vector a(θu, φv), by using the two-dimensional direction estimation evaluation function depicted in the formula (22), and the azimuth angle and the elevation angle at which the two-dimensional spatial profile takes the largest value are set as a direction-of-arrival estimation value.P(θ,,k,fs,w)=|a(θ,)h(k,fs,w)|  (22)

200 VA VA Note that the radar receivercan use methods other than the beamformer method. For example, a high-resolution direction-of-arrival estimation algorithm such as the Capon method and the MUSIC method can be applied while using the virtual surface-arranged array antenna correlation vector h(k, fs, w) and the virtual surface-arranged array direction vector a(θu, φv). This increases the computation amount but can further improve the angular resolution.

27 FIG. 9 FIG.A 9 FIG.B 27 FIG. 9 FIG.B 27 FIG. va va va va va va va q H V (t) (t) (t) (t) (t) (t) (t) is a view illustrating a virtual surface-arranged array antenna formed by using the antenna arrangement ofand the arrangement of the virtual reception array of. Specifically,illustrates a virtual surface-arranged array antenna formed based on the virtual reception array including 16 (=Nt×Na) elements illustrated in, under the assumption that elements virtually exist at positions indicated by 16 types of inter-element vectors D(n, 1), D(n, 2), . . . , D(n, 16). Since n=1, . . . , 16 (=Nt×Na), the number of virtual elements is 256 (=16×16) if there is no overlapping of the positions indicated by the 16 types of inter-element vectors D(n, 1), D(n, 2), . . . , D(n, 16). However, in, since there is overlapping of the positions, the virtual surface-arranged array antenna is formed of 169 elements. Accordingly, the virtual surface-arranged array antenna is formed by using N=169 inter-element vector groups. Note that setting of D=0.6 wavelength and D=0.68 wavelength is used.

28 FIG.A 28 FIG.B 28 FIG.A 9 FIG.B 28 FIG.B 9 FIG.B va va va (t) (t) (t) is a view illustrating elements virtually arranged at positions indicated by the inter-element vectors D(n, 1). Meanwhile,is a view illustrating elements virtually arranged at positions indicated by the inter-element vectors D(n, 2). In this case, n=1, . . . , 16 (=Nt×Na). Specifically, in, elements are virtually arranged at positions each indicated by an inter-element vector between the element VA#1 inand a corresponding one of the element VA#1, . . . , the element VA#16. In, elements are virtually arranged at positions each indicated by an inter-element vector between the element VA#2 inand a corresponding one of the element VA#1, . . . , the element VA#16.

va va va va va (t) (t) (t) (t) (t) 28 28 FIGS.A andB 27 FIG. Furthermore, elements are virtually arranged at positions indicated by the inter-element vectors D(n, 3), . . . , D(n, 16) as in.illustrates all elements virtually arranged at positions indicated by all inter-element vectors D(n, 1), D(n, 2), . . . , D(n, 16) as the virtual surface-arranged array antenna. In this case, the virtual elements include those overlapping one another. The processing is performed with one of the overlapping elements being fixedly selected in advance.

27 FIG. 200 Using the virtual surface-arranged array antenna illustrated incan virtually increase the number of elements in the radar receiver. It is thus possible to obtain an effect of reducing the grating lobe and side lobe levels in the two-dimensional spatial profile calculated in the two-dimensional direction estimation processing.

29 FIG.A 9 FIG.B 29 FIG.B 9 FIG.B 29 FIG.C 27 FIG. 29 FIG.D 27 FIG. is a view illustrating a result of calculator simulation of the two-dimensional direction estimation processing performed under a condition A by using the virtual reception array illustrated in.is a view illustrating a result of calculator simulation of the two-dimensional direction estimation processing performed under a condition B by using the virtual reception array illustrated in.is a view illustrating a result of calculator simulation of the two-dimensional direction estimation processing performed under the condition A by using the virtual surface-arranged array antenna illustrated in.is a view illustrating a result of calculator simulation of the two-dimensional direction estimation processing performed under the condition B by using the virtual surface-arranged array antenna illustrated in.

29 29 FIGS.A andC display heat maps of the two-dimensional spatial profile in the beamformer method under the condition A which is the case where waves from the physical target arrive from two different directions (θ, φ)=(15°, 5°), (15°, −5°) at the same reception power level. The numerical values at the right ends of the heat maps indicate decibel (dB) values.

29 29 FIGS.B andD display heat maps of the two-dimensional spatial profile in the beamformer method under the condition B which is the case where waves from the physical target arrives from two different directions (θ, φ)=(−20°, 0°), (−10°, 0°) at the same reception power level. The numerical values at the right ends of the heat maps indicate decibel (dB) values.

29 29 FIGS.C andD 29 29 FIGS.A andB 29 29 FIGS.C andD From the calculator simulation results, it is found that regions of heat map display inare smaller than those in, that is, in, it is possible to virtually increase the number of elements by using the virtual surface-arranged array antenna and obtain the effect of reducing the grating lobe and side lobe levels in the two-dimensional spatial profile calculated in the two-dimensional direction estimation processing.

250 250 214 Note that, since the direction estimatorcalculates the two-dimensional spatial profile by using the virtual surface-arranged array antenna, the computation processing amount of the direction estimatoris greater than that of the direction estimator. However, in the case of using the beamformer method, the computation amount can be reduced by using two-dimensional FFT processing.

Although various embodiments have been described above with reference to the drawings, the present disclosure is not limited to the examples described above as a matter of course. It is apparent that those skilled in the art can come up with various changes and modifications within the scope described in the claims. Such changes and modifications are understood to belong to the technical scope of the present disclosure. Moreover, the components in the embodiments described above can be arbitrary combined within the scope not departing from the spirit of the disclosure.

In the embodiments described above, description is given of the examples in which the present disclosure is achieved by using hardware. However, the present disclosure can be achieved by software in collaboration with hardware.

Moreover, the functional blocks used in the description of the aforementioned embodiments are achieved typically as a LSI which is an integrated circuit. The integrated circuit may control the functional blocks used in the description of the aforementioned embodiments and include an input terminal and an output terminal. These functional blocks can be each separately implemented on one chip. Alternatively, some or all of the functional blocks may be implemented on one chip. Although the integrated circuit is described as LSI in this case, the integrated circuit may also be referred to as IC, system LSI, super LSI, or ultra LSI depending on the degree of integration.

The circuit integration method is not limited to a LSI and can be achieved by using a dedicated circuit or a general-purpose processor. It is possible to use a field programmable gate array (FPGA) which is programmable after the manufacturing of the LSI, or a reconfigurable processor in which connection or settings of a circuit cell inside the LSI is reconfigurable.

When a circuit integration technique replacing the LSI appears due to progress in semiconductor technology or advent of another deriving technique, the functional blocks can be integrated by using such a technique as a matter of course. Application of bio-technology and the like is probable.

<Outline of Present Disclosure>

The radar device of the present disclosure includes: a radar transmitter which, in operation, transmits a plurality of radar signals at predetermined transmission cycles from a plurality of transmission antennas; and a radar receiver which, in operation, receives a plurality of reflected wave signals being the plurality of radar signals reflected on a target, by using a plurality of reception antennas, wherein the plurality of transmission antennas include Nt1 transmission antennas arranged in a first direction and Nt2 transmission antennas arranged in a second direction orthogonal to the first direction, the plurality of reception antennas include Na1 reception antennas arranged in the first direction and Na2 reception antennas arranged in the second direction, in the first direction, an inter-element space between any two of the Nt1 transmission antennas and an inter-element space between any two of the Na1 reception antennas equal to a product of the first space and an integer and are different from each other, and in the second direction, an inter-element space between any two of the Nt2 transmission antennas and an inter-element space between any two of the Na2 reception antennas equal to a product of a second space and an integer and are different from each other.

In the radar device of the present disclosure, a sum of the inter-element space between any two of the transmission antennas in the first direction is smaller than a smallest value of the inter-element space between any two of the reception antennas in the first direction, or a sum of the inter-element space between any two of the reception antennas in the first direction is smaller than a smallest value of the inter-element space between any two of the transmission antennas in the first direction.

In the radar device of the present disclosure, in the first direction, a largest value of the inter-element space between any two of the antennas fewer in number out of the Nt1 transmission antennas and the Na1 reception antennas is larger than a largest value of the inter-element space between any two of the antennas more in number, and in the second direction, a largest value of the inter-element space between any two of the antennas fewer in number out of the Nt2 transmission antennas and the Na2 reception antennas is larger than a largest value of the inter-element space between any two of the antennas more in number.

In the radar device of the present disclosure, the radar receiver receives the plurality of reflected wave signals as signals received by using a virtual reception array formed by the plurality of transmission antennas and the plurality of reception antennas and, in the virtual reception array, a plurality of inter-element spaces each between any two virtual antenna elements out of the Nt1×Na1 virtual antenna elements arranged in the first direction are each a product of the first space and an integer of 1 or more, and include products of the first space and all integers from 1 to a first predetermined value.

In the radar device of the present disclosure, the radar receiver receives the plurality of reflected wave signals as signals received by using a virtual reception array formed by the plurality of transmission antennas and the plurality of reception antennas and, in the virtual reception array, a plurality of inter-element spaces each between any two virtual antenna elements out of the Nt2×Na2 virtual antenna elements arranged in the second direction are each a product of the second space and an integer of 1 or more, and include products of the second space and all integers from 1 to a second predetermined value.

In the radar device of the present disclosure, at least the plurality of transmission antennas and the plurality of reception antennas are each formed of a plurality of sub-arrayed antenna elements, there is at least one combination of the inter-element space between any two of the Nt1 transmission antennas and the inter-element space between any two of the Na1 reception antennas in which a difference between any two of the inter-element spaces is smaller than one wavelength, where a size of each of the sub-arrayed antenna elements in the first direction is one wavelength or more, and there is at least one combination of the inter-element space between any two of the Nt2 transmission antennas and the inter-element space between any two of the Na2 reception antennas in which a difference between any two of the inter-element spaces is smaller than one wavelength, where a size of each of the sub-arrayed antenna elements in the second direction is one wavelength or more.

In the radar device of the present disclosure, the radar receiver receives the plurality of reflected wave signals as signals received by using a virtual surface-arranged array antenna in which elements are virtually arranged at positions indicated by inter-element vectors at all of elements in the virtual reception array formed by the plurality of transmission antennas and the plurality of reception antennas and, in the virtual reception array, a plurality of inter-element spaces each between any two of the Nt1×Na1 virtual antenna elements arranged in the first direction are each a product of the first space and an integer of 1 or more, and include products of the first space and all integers from 1 to a first predetermined value.

In the radar device of the present disclosure, the radar receiver receives the plurality of reflected wave signals as signals received by using the virtual surface-arranged array antenna in which elements are virtually arranged at positions indicated by the inter-element vectors at all of elements in the virtual reception array formed by the plurality of transmission antennas and the plurality of reception antennas and, in the virtual reception array, a plurality of inter-element spaces each between any two of the Nt2×Na2 virtual antenna elements arranged in the second direction are each a product of the second space and an integer of 1 or more, and include products of the second space and all integers from 1 to a second predetermined value.

In the radar device of the present disclosure, the plurality of transmission antennas are arranged such that Nt1×Nt2 takes the largest value, and the plurality of reception antennas are arranged such that Na1×Na2 takes the largest value.

In the radar device of the present disclosure, a set of the plurality of transmission antennas and a set of the plurality of reception antennas are each arranged in a L-shape, a T-shape, or a cross shape.

The present disclosure is suitable for a radar device which detects a wide range.