KR product expansion radar signal processing device and KR product expansion radar signal processing program

Abstract

To provide a KR (Khatri-Rao) product extension radar signal processing device and a program for reducing the number of times of multiplication of a reception signal and a complex conjugate of the reception signal, reducing a memory amount of a matrix element of a covariance matrix, and facilitating mounting on built-in equipment.SOLUTION: The signal processing device calculates one of an upper triangular component and a lower triangular component including a diagonal component in the covariance matrix, performs Fourier transform on the reception signal of the first antenna arrangement to calculate a first target angular spectrum of every other sample, performs Fourier transform on the reception signal of the first antenna arrangement multiplied by a predetermined twiddle factor to calculate a second target angular spectrum of every other sample, and integrates the first target angular spectrum and the second target angular spectrum of every other sample to calculate a target angular spectrum in all samples.SELECTED DRAWING: Figure 6

Description

[Technical Field]

[0001] The present disclosure relates to radar signal processing using Khatri-Rao (KR) product extension. [Background technology]

[0002] Radar signal processing using KR product expansion is disclosed in Patent Document 1 and the like, which effectively expands the aperture length of an array antenna by approximately two times and effectively interpolates missing antenna elements. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 2019-070558 Summary of the Invention [Problem to be solved by the invention]

[0004] The procedure for the conventional KR product expansion radar signal processing is shown in Figure 1. First, the received signal Ae from the receiving antenna elements R0, R1, and R3 (the receiving antenna element R2 is missing) is i0 , Ae iθ , Ae i3θ Calculate the covariance matrix of the KR product expansion for the row vector (Ae i0 , Ae iθ , Ae i3θ ) is a column vector of the complex conjugate of the received signal (Ae -i0 , Ae -iθ , Ae -i3θ ) T is multiplied from the left.

[0005] Next, the received signals of the virtual array antenna of the KR product expansion are calculated based on the independent components (components that do not overlap with each other) of the covariance matrix. Here, the virtual array antenna of the KR product expansion includes virtual antenna elements V1, V2, V3, V4, V5, V6, and V7. The received signals of the virtual antenna elements V1, V2, V3, V4, V5, V6, and V7 are calculated as follows: 2 e -i3θ , A 2 e -i2θ , A 2 e -iθ , A 2 e i0 , A 2 e iθ , A 2 e i2θ , A 2 e i3θ is.

[0006] Next, DBF (Digital Beam Forming) processing is performed, and the received signal of the virtual array antenna is Fourier transformed to calculate the target angle spectrum. Here, the Fourier transform of the received signal of the virtual array antenna can be performed using a fast Fourier transform (FFT) or the like.

[0007] However, when calculating the covariance matrix of KR product expansion, it is not possible to reduce the number of multiplications of the received signal and its complex conjugate, and it is not possible to reduce the memory required for the matrix elements of the covariance matrix. Furthermore, when calculating the target angle spectrum, it is not possible to reduce the amount of calculations, such as FFT, on the order of 2N log 2N, when the number of virtual antenna elements is 2N-1. Therefore, it is difficult to implement radar signal processing using KR product expansion in embedded devices.

[0008] Therefore, in order to solve the above-mentioned problems, firstly, an object of the present disclosure is to reduce the number of multiplications of a received signal and its complex conjugate when calculating the covariance matrix of KR product expansion, thereby reducing the memory amount required for the matrix elements of the covariance matrix and facilitating implementation in an embedded device.

[0009] In order to solve the above-mentioned problems, a second object of the present disclosure is to further reduce the amount of calculations such as FFT on the order of 2N log 2N by setting the number of virtual antenna elements to 2N-1 when calculating the target angle spectrum, thereby facilitating implementation in embedded devices. [Means for solving the problem]

[0010] To solve the above problem, we focused on the fact that the covariance matrix of the KR product expansion has Hermitianity. Therefore, we calculate either the upper triangular component or the lower triangular component of the covariance matrix, including the diagonal components. Then, we calculate the other of the upper triangular component or the lower triangular component of the covariance matrix as the complex conjugate of either the upper triangular component or the lower triangular component of the covariance matrix.

[0011] Specifically, the present disclosure provides a KR product expansion radar signal processing device comprising: a covariance matrix calculation unit that calculates either an upper triangular component or a lower triangular component including a diagonal component of a KR product expansion covariance matrix for received signals of a plurality of antenna elements; and a received signal calculation unit that calculates, based on either the upper triangular component or the lower triangular component of the covariance matrix, received signals of a first antenna array having a central antenna element at one end and either one of the end antenna elements at the other end of a KR product expansion virtual array antenna.

[0012] According to this configuration, when calculating the covariance matrix of the KR product expansion, the number of multiplications of the received signal and the complex conjugate of that received signal is reduced to about half of that of the conventional technology, and the memory size for the matrix elements of the covariance matrix is ​​reduced to about half of that of the conventional technology, making it easier to implement in embedded devices.

[0013] The present disclosure also provides a KR product expansion radar signal processing device, characterized in that the received signal calculation unit calculates the received signal of a second antenna array having the central antenna element at one end and either the other of the end antenna elements at the other end as a complex conjugate of either the upper triangular component or the lower triangular component of the covariance matrix, or calculates the received signal of the second antenna array as a complex conjugate of the received signal of the first antenna array.

[0014] According to this configuration, when calculating the covariance matrix of the KR product expansion, the number of multiplications of the received signal and its complex conjugate is reduced to about half that of the conventional technology, and the remaining matrix elements of the covariance matrix are calculated using complex conjugates rather than multiplication processes, making it easier to implement in embedded devices.

[0015] The present disclosure also provides a KR product expansion radar signal processing device, further comprising a Fourier transform unit that performs a Fourier transform on the received signals of the first antenna array and the second antenna array and calculates a target angle spectrum for all samples.

[0016] According to this configuration, the amount of calculations such as FFT cannot be reduced when calculating the target angle spectrum, but the number of multiplications of the received signal and its complex conjugate when calculating the covariance matrix of the KR product expansion can be reduced to about half that of the conventional technology, making it easier to implement in embedded devices.

[0017] To solve the above problem, we focused on the fact that the elements of the virtual array antenna are arranged symmetrically with respect to the central antenna element, and that the received signals of the virtual array antenna are complex conjugates with respect to the symmetric antenna elements. Therefore, the received signals of the first antenna array are Fourier transformed to calculate a first target angle spectrum for every other sample. Then, the received signals of the first antenna array are multiplied by a predetermined twiddle factor and then Fourier transformed to calculate a second target angle spectrum for every other sample. Furthermore, the first target angle spectrum and the second target angle spectrum for every other sample are integrated to calculate the target angle spectrum for all samples.

[0018] Specifically, the present disclosure provides a KR product expansion radar signal processing device further comprising: a first Fourier transform unit that performs a Fourier transform on the received signals of the first antenna array excluding the central antenna element to calculate a first target angle spectrum for every other sample; a second Fourier transform unit that performs a Fourier transform on the received signals of the first antenna array excluding the central antenna element multiplied by the nth power of the complex 2Nth root of 1 (the number of antenna elements in the virtual array antenna is 2N-1, and each antenna number in the virtual array antenna is n) to calculate a second target angle spectrum for every other sample other than the first target angle spectrum; and a spectrum integration unit that integrates the first target angle spectrum and the second target angle spectrum for every other sample to calculate the target angle spectrum for all samples.

[0019] According to this configuration, when calculating the target angle spectrum, the number of virtual antenna elements is set to 2N-1, and the amount of calculations such as FFT is reduced from the order of 2N log 2N to the order of 2 × N log N, making it easier to implement in embedded devices.

[0020] The present disclosure also provides a KR product expansion radar signal processing device, wherein the first Fourier transform unit calculates the first target angle spectrum by extracting only the real part from the Fourier transform result of every other sample and doubling the result, and the second Fourier transform unit calculates the second target angle spectrum by extracting only the real part from the Fourier transform result of every other sample and doubling the result.

[0021] According to this configuration, the received signals of the virtual array antenna are complex conjugates for symmetric antenna elements, so that only the real part can be extracted and doubled.

[0022] The present disclosure also provides a KR product expansion radar signal processing device, wherein the first Fourier transform unit adds the received signal of the central antenna element to the Fourier transform result of every other sample to calculate the first target angle spectrum, and the second Fourier transform unit subtracts the received signal of the central antenna element from the Fourier transform result of every other sample to calculate the second target angle spectrum.

[0023] According to this configuration, the received signal of the central antenna element that is not input to the first and second Fourier transform processes can be reflected in the first and second target angle spectra.

[0024] The present disclosure also provides a KR product expansion radar signal processing device, wherein the first Fourier transform unit calculates the first target angle spectrum after performing zero padding on the received signals of the first antenna array excluding the central antenna element, and the second Fourier transform unit calculates the second target angle spectrum after performing zero padding on the received signals of the first antenna array excluding the central antenna element.

[0025] According to this configuration, even when the number N-1 of received signals input to the first and second Fourier transform processes is not equal to a power of two, Fourier transform processes such as FFT can be performed.

[0026] The present disclosure also provides a KR product expansion radar signal processing device, wherein the first Fourier transform unit multiplies the received signal of the first antenna array including the central antenna element by a window function and then calculates the first target angle spectrum, and the second Fourier transform unit multiplies the received signal of the first antenna array including the central antenna element by the window function and then calculates the second target angle spectrum.

[0027] According to this configuration, the received signals input to the first and second Fourier transform processes are multiplied by a window function, and the side lobe level and angular resolution of the target angle spectrum can be adjusted.

[0028] The present disclosure also provides a KR expansion radar signal processing program to be installed on a computer to cause the computer to sequentially execute the processing steps executed by each processing unit provided in the KR expansion radar signal processing device described above.

[0029] According to this configuration, it is possible to provide a program having the above-described effects.

[0030] The above-disclosed inventions can be combined as much as possible. [Effects of the Invention]

[0031] In this way, the present disclosure firstly reduces the number of multiplications of a received signal and its complex conjugate when calculating the covariance matrix of a KR product expansion, reduces the amount of memory required for the matrix elements of the covariance matrix, and facilitates implementation in an embedded device.

[0032] Secondly, the present disclosure can further reduce the amount of calculations such as FFT on the order of 2N log 2N when calculating the target angle spectrum by setting the number of virtual antenna elements to 2N-1, thereby facilitating implementation in embedded devices. [Brief explanation of the drawings]

[0033] [Figure 1] FIG. 1 is a diagram showing the procedure of KR product expansion radar signal processing in the prior art. [Figure 2] FIG. 1 is a diagram illustrating a configuration of a KR product expansion radar system according to a first embodiment. [Figure 3] FIG. 4 is a diagram showing a procedure of KR product expansion radar signal processing in the first embodiment. [Figure 4] FIG. 3 is a diagram illustrating a procedure of Fourier transform processing according to the first embodiment. [Figure 5] FIG. 1 is a diagram showing the configuration of a KR product expansion radar system according to second to sixth embodiments. [Figure 6] FIG. 10 is a diagram showing a procedure of KR product expansion radar signal processing according to the second embodiment. [Figure 7]FIG. 10 is a diagram illustrating a procedure of a Fourier transform process according to the second embodiment. [Figure 8] FIG. 11 is a diagram showing a procedure of KR product expansion radar signal processing according to the third embodiment. [Figure 9] FIG. 10 is a diagram illustrating a procedure of Fourier transform processing according to the third embodiment. [Figure 10] FIG. 10 is a diagram illustrating a procedure of a Fourier transform process according to the fourth embodiment. [Figure 11] FIG. 13 is a diagram illustrating a procedure of a Fourier transform process according to the fifth embodiment. [Figure 12] FIG. 13 is a diagram showing a procedure of KR product expansion radar signal processing according to the sixth embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0034]

[0023] The following embodiments of the present disclosure will be described with reference to the accompanying drawings. The embodiments described below are examples of implementation of the present disclosure, and the present disclosure is not limited to the following embodiments.

[0035] (KR product expansion radar signal processing of the first embodiment) The configuration of the KR product expansion radar system of the first embodiment is shown in Figure 2. The KR product expansion radar system S includes a radar transceiver A, a KR product expansion radar signal processing device K, and a radar display device D. The radar transceiver A emits a radar transmission signal and receives a radar reflection signal. The KR product expansion radar signal processing device K performs KR product expansion radar signal processing. The radar display device D displays the angle of the target based on the target angle spectrum.

[0036] The KR product expansion radar signal processing device K includes a covariance matrix calculation unit 1, a received signal calculation unit 2, and a Fourier transform unit 3, and can be realized by installing the KR product expansion radar signal processing program shown in Figures 3 and 4 on a computer.

[0037] The procedure for KR product expansion radar signal processing in the first embodiment is shown in Fig. 3. The covariance matrix calculation unit 1 calculates the received signal Ae from the receiving antenna elements R0, R1, and R3 (the receiving antenna element R2 is missing). i0, Ae iθ , Ae i3θ For the covariance matrix of the KR product extension, either the upper triangular element (upper right column in FIG. 3) including the diagonal element or the lower triangular element (upper left column in FIG. 3) is calculated.

[0038] Here, the covariance matrix of the KR product expansion is the row vector of the received signal (Ae i0 , Ae iθ , Ae i3θ ) is a column vector of the complex conjugate of the received signal (Ae -i0 , Ae -iθ , Ae -i3θ ) T When there are multiple targets, the received signals of the receiving antenna elements R0, R1, and R3 are multiplied by Ce from the left side, just like when there is a single target. i0 (=Ae i0 +Be i0 ), Ce iΦ (=Ae iθ +Be iφ ), Ce i3Φ (=Ae i3θ +Be i3φ ) Furthermore, the diagonal components of the covariance matrix A 2 e i0 It is not necessary to calculate it multiple times, but it is sufficient to calculate it only once.

[0039] The received signal calculation unit 2 calculates the received signal of the first antenna array, which has the central antenna element at one end and either one of the end antenna elements at the other end, of the KR product expanded virtual array antenna, based on the independent components (components that do not overlap with each other) of either the upper triangular components (top right column in Figure 3) or the lower triangular components (top left column in Figure 3) of the covariance matrix.

[0040] Here, the first antenna array based on the lower triangular component (top left column of FIG. 3) includes virtual antenna elements V1 (edge), V2, V3, and V4 (center). The received signals of the virtual antenna elements V1, V2, V3, and V4 are expressed as A 2 e -i3θ , A 2 e -i2θ , A 2 e -iθ , A2 e i0 On the other hand, the first antenna arrangement based on the upper triangle component (top right column of FIG. 3) includes virtual antenna elements V4 (center), V5, V6, and V7 (edges). The received signals of the virtual antenna elements V4, V5, V6, and V7 are expressed as follows: 2 e i0 , A 2 e iθ , A 2 e i2θ , A 2 e i3θ is.

[0041] The received signal calculation unit 2 calculates either the upper triangular component (lower left column of FIG. 3 ) or the lower triangular component (lower right column of FIG. 3 ) of the covariance matrix as the complex conjugate of either the upper triangular component (upper right column of FIG. 3 ) or the lower triangular component (upper left column of FIG. 3 ). Then, the received signal of a second antenna array, which is a virtual array antenna of the KR product expansion, with the central antenna element at one end and either of the two end antenna elements at the other end, is calculated. Here, the second antenna array based on the upper triangular component (lower left column of FIG. 3 ) includes virtual antenna elements V4 (center), V5, V6, and V7 (ends). Meanwhile, the second antenna array based on the lower triangular component (lower right column of FIG. 3 ) includes virtual antenna elements V1 (end), V2, V3, and V4 (center).

[0042] In a separate embodiment, the received signal calculation unit 2 may calculate the received signal of the second antenna array as the complex conjugate of the received signal of the first antenna array. Here, if the first antenna array based on the lower triangle component (top left column of FIG. 3) includes virtual antenna elements V1 (end), V2, V3, and V4 (center), the second antenna array based on the complex conjugate of the received signal includes virtual antenna elements V4 (center), V5, V6, and V7 (end). On the other hand, if the first antenna array based on the upper triangle component (top right column of FIG. 3) includes virtual antenna elements V4 (center), V5, V6, and V7 (end), the second antenna array based on the complex conjugate of the received signal includes virtual antenna elements V1 (end), V2, V3, and V4 (center).

[0043] The received signal calculation unit 2 integrates the first antenna array based on the lower triangular component (upper left column in FIG. 3) etc. and the second antenna array based on the complex conjugate of the received signal etc. to calculate the received signal of the KR product expanded virtual array antenna. Here, the KR product expanded virtual array antenna includes virtual antenna elements V1, V2, V3, V4, V5, V6, and V7.

[0044] Therefore, when calculating the covariance matrix of the KR product expansion, the number of multiplications of the received signal and the complex conjugate of that received signal can be reduced to approximately half of that of the conventional technology, and the memory amount for the matrix elements of the covariance matrix can be reduced to approximately half of that of the conventional technology, making it easier to implement in the KR product expansion radar system S.

[0045] Alternatively, when calculating the covariance matrix of the KR product expansion, the number of multiplications of the received signal and the complex conjugate of the received signal can be reduced to approximately half of that of the prior art, and the remaining matrix elements of the covariance matrix can be calculated by complex conjugation rather than by multiplication processing, making it easier to implement in the KR product expansion radar system S.

[0046] The Fourier transform unit 3 executes DBF processing, performs Fourier transform on the received signals of the virtual (first and second) antenna array, and calculates the target angle spectrum for all samples. Here, FFT or the like can be applied as the Fourier transform of the received signals of the virtual (first and second) antenna array. However, as will be explained below, this does not further reduce the amount of calculations such as FFT.

[0047] The procedure of the Fourier transform processing in the first embodiment is shown in Fig. 4. The Fourier transform unit 3 includes an FFT unit 31. The target angle spectrum A at the k-th sample is k is expressed by the following equation.

number

[0048] The covariance matrix calculation unit 1 calculates the received signals Ae from the receiving antenna elements R0, R1, and R3 at the input terminals 0, 1, and 3. i0 , Ae iθ , Ae i3θ The received signal calculation unit 2 outputs received signals a1, a2, a3, a4, a5, a6, and a7 of the virtual antenna elements V1, V2, V3, V4, V5, V6, and V7 from output terminals -3, -2, -1, 0, 1, 2, and 3.

[0049] The FFT unit 31 receives received signals a1, a2, a3, a4, a5, a6, and a7 of virtual antenna elements V1, V2, V3, V4, V5, V6, and V7 at input terminals 0, 1, 2, 3, 4, 5, 6, and 7. The FFT unit 31 outputs target angle spectra A0, A1, A2, A3, A4, A5, A6, and A7 at output terminals 0, 1, 2, 3, 4, 5, 6, and 7.

[0050] Therefore, when calculating the target angle spectrum, the amount of calculations such as FFT (on the order of 2N log 2N, assuming that the number of virtual antenna elements is 2N-1) cannot be reduced. However, when calculating the covariance matrix of the KR product expansion, the number of multiplications of the received signal and the complex conjugate of that received signal can be reduced to about half that of the conventional technology, making it easier to implement in the KR product expansion radar system S.

[0051] (KR product expansion radar signal processing of the second embodiment) The configuration of a KR product expanded radar system of the second embodiment is shown in Fig. 5. The KR product expanded radar system S includes a radar transceiver A (similar to the first embodiment), a KR product expanded radar signal processing device K, and a radar display device D (similar to the first embodiment). The KR product expanded radar signal processing device K includes a covariance matrix calculation unit 1, a received signal calculation unit 2, a first Fourier transform unit 4, a second Fourier transform unit 5, and a spectrum integration unit 6, and can be realized by installing the KR product expanded radar signal processing program shown in Figs. 6 and 7 on a computer.

[0052] The procedure for KR product expansion radar signal processing in the second embodiment is shown in Fig. 6. The covariance matrix calculation unit 1 calculates the received signal Ae from the receiving antenna elements R0, R1, and R3 (the receiving antenna element R2 is missing). i0 , Ae iθ , Ae i3θ The lower triangular elements including the diagonal elements of the covariance matrix of the KR product extension are calculated for: Here, the covariance matrix of the KR product extension is almost the same as that in the first embodiment.

[0053] The received signal calculation unit 2 calculates the received signals of a first antenna array, which has a central antenna element at one end and either of the end antenna elements (corresponding to the lower triangular element) at the other end, of a virtual array antenna of KR product expansion, based on the independent elements (components that do not overlap with each other) of the lower triangular element of the covariance matrix. Here, the first antenna array based on the lower triangular element includes virtual antenna elements V1 (end), V2, V3, and V4 (center). The received signals of the virtual antenna elements V1, V2, V3, and V4 are calculated as follows: 2 e -i3θ , A 2 e -i2θ , A 2 e -iθ , A 2 e i0 is.

[0054] Therefore, when calculating the covariance matrix of the KR product expansion, the number of multiplications of the received signal and the complex conjugate of that received signal can be reduced to approximately half of that of the conventional technology, and the memory amount for the matrix elements of the covariance matrix can be reduced to approximately half of that of the conventional technology, making it easier to implement in the KR product expansion radar system S.

[0055] In the first embodiment, the Fourier transform unit 3 can apply FFT or the like when performing DBF processing, and receives all received signals from the virtual (first and second) antenna arrays. In the second embodiment, the first Fourier transform unit 4 and the second Fourier transform unit 5 can apply FFT or the like when performing DBF processing, and receive only received signals from the first antenna array based on the lower triangular component. In the second embodiment, the amount of calculations such as FFT can be further reduced compared to the first embodiment, and the target angle spectrum can be calculated for all samples.

[0056] The procedure of the Fourier transform processing of the second embodiment is shown in Fig. 7. The first Fourier transform unit 4 includes a first FFT unit 41, a real part doubling calculation unit 42, and a center signal addition unit 43. The second Fourier transform unit 5 includes a twiddle factor multiplication unit 51, a second FFT unit 52, a real part doubling calculation unit 53, and a center signal subtraction unit 54. The target angle spectrum A at the k-th sample is k is expressed by the following equation 2.

number

[0057] where a n is the received signal of the nth (n=1 to 2N-1) virtual antenna element, a0 is 0 for zero padding such as FFT, and W 2N is the complex 2Nth root of 1. And the received signal of the virtual (1st + 2nd) antenna array is complex conjugate with respect to the symmetric antenna elements, so a 2N-n =a n * The fact that holds is used in the third and fourth lines of Mathematical Formula 2.

[0058] Target angle spectrum A at even-numbered samples 2k is expressed by the following equation 3.

number

[0059] Target angle spectrum A at odd-numbered samples 2k+1 is expressed by the following equation 4.

number

[0060] The covariance matrix calculation unit 1 calculates the received signals Ae from the receiving antenna elements R0, R1, and R3 at the input terminals 0, 1, and 3. i0 , Ae iθ , Ae i3θ The received signal calculation unit 2 outputs received signals a1, a2, a3, a4 (a1 to a4 are lower triangular components, a4 is the center component) of virtual antenna elements V1, V2, V3, V4 from output terminals -3, -2, -1, 0.

[0061] The first FFT unit 41 receives the received signals a1, a2, and a3 of the virtual antenna elements V1, V2, and V3 at input terminals 0, 1, 2, and 3, and outputs the Fourier transform results (Σa n W4 0 , Σa n W4 n , Σa n W4 2n , Σa n W4 3n The real part doubling calculation unit 42 outputs the real part extraction and doubling result (2ReΣa n W4 0 , 2ReΣa n W4 n , 2ReΣa n W4 2n , 2ReΣa n W4 3n ) is output from the central signal adder 43. The central signal adder 43 outputs the target angle spectrum (A0=2ReΣa n W4 0 +a4, A2=2ReΣa n W4 n +a4, A4=2ReΣa n W4 2n +a4, A6=2ReΣa n W4 3n +a4).

[0062] The twiddle factor multiplication unit 51 receives the received signals a1, a2, and a3 of the virtual antenna elements V1, V2, and V3 in the multipliers 1, 2, and 3, and calculates the twiddle factor multiplication results (a1W8 1 , a2W8 2 , a3W8 3 The second FFT unit 52 receives 0 and the twiddle factor multiplication result (a1W8 1 , a2W8 2 , a3W8 3 ) is input, and the Fourier transform results (Σa n W8 n W4 0 , Σa n W8 n W4 n , Σa n W8 n W4 2n , Σa n W8 n W4 3n The real part doubling calculation unit 53 outputs the real part extraction and doubling result (2ReΣa n W8 n W4 0 , 2ReΣa n W8 n W4 n , 2ReΣa n W8 n W4 2n , 2ReΣa n W8 n W4 3n ) is output from the center signal subtractor 54. The center signal subtractor 54 subtracts the target angle spectrum (A1=2ReΣa n W8 n W4 0 -a4, A3=2ReΣa n W8 n W4 n -a4, A5=2ReΣa n W8 n W4 2n -a4, A7=2ReΣa n W8 n W4 3n -a4).

[0063] Spectrum integrating unit 6 integrates target angle spectra A0, A2, A4, A6 of even-numbered samples and target angle spectra A1, A3, A5, A7 of odd-numbered samples to calculate target angle spectra A0 to A7 for all samples.

[0064] Therefore, when calculating the target angle spectrum, the number of virtual antenna elements is set to 2N-1, and the amount of calculations such as FFT can be reduced from the order of 2N log 2N to the order of 2 × N log N, making it easier to implement in the KR product expansion radar system S.

[0065] Then, by utilizing the fact that the received signals of the virtual array antenna are complex conjugates for the symmetric antenna elements, it is possible to extract only the real part and perform processing to double it. Furthermore, the received signals of the central antenna element that are not input to the first and second Fourier transform processing can be reflected in the target angle spectrum of the even-numbered and odd-numbered samples.

[0066] (KR product expansion radar signal processing of the third embodiment) The configuration of a KR product expanded radar system of the third embodiment is shown in Fig. 5. The KR product expanded radar system S includes a radar transceiver A (similar to the first embodiment), a KR product expanded radar signal processing device K, and a radar display device D (similar to the first embodiment). The KR product expanded radar signal processing device K includes a covariance matrix calculation unit 1, a received signal calculation unit 2, a first Fourier transform unit 4, a second Fourier transform unit 5, and a spectrum integration unit 6, and can be realized by installing the KR product expanded radar signal processing program shown in Figs. 8 and 9 on a computer.

[0067] The procedure for KR product expansion radar signal processing in the third embodiment is shown in Fig. 8. The covariance matrix calculation unit 1 calculates the received signal Ae i0 , Ae iθ , Ae i3θ The upper triangular elements including the diagonal elements of the covariance matrix of the KR product extension are calculated for: Here, the covariance matrix of the KR product extension is almost the same as that in the first embodiment.

[0068] The received signal calculation unit 2 calculates the received signals of a first antenna array, which has a central antenna element at one end and either of the end antenna elements (corresponding to the upper triangular element) at the other end, of a virtual array antenna of KR product expansion, based on the independent elements (components that do not overlap with each other) of the upper triangular element of the covariance matrix. Here, the first antenna array based on the upper triangular element includes virtual antenna elements V4 (center), V5, V6, and V7 (ends). The received signals of the virtual antenna elements V4, V5, V6, and V7 are calculated as follows: 2 e i0 , A 2 e iθ , A 2 e i2θ , A 2 e i3θ is.

[0069] Therefore, when calculating the covariance matrix of the KR product expansion, the number of multiplications of the received signal and the complex conjugate of that received signal can be reduced to approximately half of that of the conventional technology, and the memory amount for the matrix elements of the covariance matrix can be reduced to approximately half of that of the conventional technology, making it easier to implement in the KR product expansion radar system S.

[0070] In the first embodiment, the Fourier transform unit 3 can apply FFT or the like when performing DBF processing, and receives all received signals from the virtual (first and second) antenna arrays. In the third embodiment, the first Fourier transform unit 4 and the second Fourier transform unit 5 can apply FFT or the like when performing DBF processing, and receive only received signals from the first antenna array based on the upper triangular component. In the third embodiment, the amount of calculation for FFT or the like is further reduced compared to the first embodiment, and the target angle spectrum for all samples can be calculated.

[0071] The procedure of the Fourier transform processing of the third embodiment is shown in Fig. 9. The first Fourier transform unit 4 includes a first FFT unit 41, a real part doubling calculation unit 42, and a center signal addition unit 43. The second Fourier transform unit 5 includes a twiddle factor multiplication unit 51, a second FFT unit 52, a real part doubling calculation unit 53, and a center signal subtraction unit 54. The target angle spectrum A at the k-th sample is kis expressed by the number 5.

number

[0072] where a n is the received signal of the nth (n=1 to 2N-1) virtual antenna element, a0 is 0 for zero padding such as FFT, and W 2N is the complex 2Nth root of 1. And the received signal of the virtual (1st + 2nd) antenna array is complex conjugate with respect to the symmetric antenna elements, so a 2N-n =a n * The fact that holds is used in the third and fourth lines of Mathematical Formula 5.

[0073] Target angle spectrum A at even-numbered samples 2k is expressed by the following equation (6).

number

[0074] Target angle spectrum A at odd-numbered samples 2k+1 is expressed by the following equation:

number

[0075] The covariance matrix calculation unit 1 calculates the received signals Ae from the receiving antenna elements R0, R1, and R3 at the input terminals 0, 1, and 3. i0 , Ae iθ , Ae i3θ The received signal calculation unit 2 outputs from output terminals 0, 1, 2, 3 received signals a4, a5, a6, a7 (a4 to a7 are upper triangular components, a4 is the center component) of virtual antenna elements V4, V5, V6, V7.

[0076] The first FFT unit 41 receives the received signals a5, a6, and a7 of the virtual antenna elements V5, V6, and V7 at input terminals 0, 1, 2, and 3, and outputs the Fourier transform results (Σa n W4 0 , Σa n W4n , Σa n W4 2n , Σa n W4 3n The real part doubling calculation unit 42 outputs the real part extraction and doubling result (2ReΣa n W4 0 , 2ReΣa n W4 n , 2ReΣa n W4 2n , 2ReΣa n W4 3n ) is output from the central signal adder 43. The central signal adder 43 outputs the target angle spectrum (A0=2ReΣa n W4 0 +a4, A2=2ReΣa n W4 n +a4, A4=2ReΣa n W4 2n +a4, A6=2ReΣa n W4 3n +a4).

[0077] The twiddle factor multiplication unit 51 receives the received signals a5, a6, and a7 of the virtual antenna elements V5, V6, and V7 in the multipliers 1, 2, and 3, and calculates the twiddle factor multiplication results (a5W8 5 , a6W8 6 , a7W8 7 The second FFT unit 52 outputs 0 and the twiddle factor multiplication result (a5W8 5 , a6W8 6 , a7W8 7 ) is input, and the Fourier transform results (Σa n W8 n W4 0 , Σa n W8 n W4 n , Σa n W8 n W4 2n , Σa n W8 n W4 3n The real part doubling calculation unit 53 outputs the real part extraction and doubling result (2ReΣa n W8 n W4 0 , 2ReΣan W8 n W4 n , 2ReΣa n W8 n W4 2n , 2ReΣa n W8 n W4 3n ) is output from the center signal subtractor 54. The center signal subtractor 54 subtracts the target angle spectrum (A1=2ReΣa n W8 n W4 0 -a4, A3=2ReΣa n W8 n W4 n -a4, A5=2ReΣa n W8 n W4 2n -a4, A7=2ReΣa n W8 n W4 3n -a4).

[0078] Spectrum integrating unit 6 integrates target angle spectra A0, A2, A4, A6 of even-numbered samples and target angle spectra A1, A3, A5, A7 of odd-numbered samples to calculate target angle spectra A0 to A7 for all samples.

[0079] Therefore, when calculating the target angle spectrum, the number of virtual antenna elements is set to 2N-1, and the amount of calculations such as FFT can be reduced from the order of 2N log 2N to the order of 2 × N log N, making it easier to implement in the KR product expansion radar system S.

[0080] Then, by utilizing the fact that the received signals of the virtual array antenna are complex conjugates for the symmetric antenna elements, it is possible to extract only the real part and perform processing to double it. Furthermore, the received signals of the central antenna element that are not input to the first and second Fourier transform processing can be reflected in the target angle spectrum of the even-numbered and odd-numbered samples.

[0081] (KR product expansion radar signal processing of the fourth embodiment) The Fourier transform processing of the fourth embodiment is shown in FIG. 10. In the fourth embodiment, compared with the second and third embodiments, the KR product extended radar system S has a similar configuration, but the first Fourier transform unit 4 further includes a window function multiplication unit 44, and the second Fourier transform unit 5 further includes a window function multiplication unit 55. Hereinafter, the differences between the fourth embodiment and the second embodiment will be described.

[0082] The first Fourier transform unit 4 multiplies the received signal of the first antenna array including the central antenna element by a window function, and then calculates the target angle spectrum at the even-numbered samples. The second Fourier transform unit 5 multiplies the received signal of the first antenna array including the central antenna element by a window function, and then calculates the target angle spectrum at the odd-numbered samples.

[0083] The window function multiplication unit 44 inputs the received signals a1, a2, a3, a4 of the virtual antenna elements V1 (end), V2, V3, V4 (center) to the multipliers 1, 2, 3, 4, and outputs the window function w multiplication results (a1w1, a2w2, a3w3, a4w4). Although the input signals to the first FFT unit 41, the real part doubling calculation unit 42, and the central signal addition unit 43 are changed, the output processing is the same. Note that the window function w is set such that w1 (minimum) < w2 < w3 < w4 (maximum).

[0084] The window function multiplication unit 55 inputs the received signals a5, a6, a7 of the virtual antenna elements V5, V6, V7 (end) to the multipliers 1, 2, 3, and outputs the window function w multiplication results (a5w5, a6w6, a7w7). Although the input signals to the rotation factor multiplication unit 51, the second FFT unit 52, the real part doubling calculation unit 53, and the central signal subtraction unit 54 are changed, the output processing is the same. Note that the window function w is set such that w7 (= w1, minimum) < w6 (= w2) < w5 (= w3).

[0085] Therefore, by multiplying the received signal input to the first and second Fourier transform processes by a window function, the side lobe level and angle resolution of the target angle spectrum can be adjusted. Note that the fourth embodiment is applicable not only to the second embodiment but also to the first and third embodiments.

[0086] (KR product expansion radar signal processing of the fifth embodiment) The Fourier transform processing of the fifth embodiment is shown in Figure 11. In the fifth embodiment, compared to the second and third embodiments, the KR product expansion radar system S has a similar configuration, and the first Fourier transform unit 4 and the second Fourier transform unit 5 also have similar configurations, but the number of input / output terminals is changed. Below, we will explain the differences between the fifth embodiment and the second embodiment.

[0087] The first Fourier transform unit 4 performs zero padding (inputting 0 to terminal 1 in the second embodiment as well) on the received signals of the first antenna array excluding the central antenna element, and then calculates the target angle spectrum for even-numbered samples. The second Fourier transform unit 5 performs zero padding (inputting 0 to terminal 1 in the second embodiment as well) on the received signals of the first antenna array excluding the central antenna element, and then calculates the target angle spectrum for odd-numbered samples.

[0088] The first FFT unit 41 receives 0 at input terminals 0, . . . , x-1, x, receives received signals a1, a2, a3 of virtual antenna elements V1, V2, V3 at input terminals x+1, x+2, x+3, and outputs Fourier transform results at output terminals 0, . . . , x-1, x, x+1, x+2, x+3. Accordingly, the number of units in the real part doubling calculation unit 42 and the central signal addition unit 43 becomes x+4, and the number of even-numbered samples also becomes x+4.

[0089] The second FFT unit 52 receives 0 at input terminals 0, . . . , x-1, x, and receives the twiddle factor multiplication result (a1W8 1 , a2W8 2 , a3W8 3 ) and outputs the Fourier transform results at output terminals 0, , x-1, x, x+1, x+2, and x+3. Accordingly, the number of units in the real part doubling calculation unit 53 and the center signal subtraction unit 54 becomes x+4, and the number of odd-numbered samples also becomes x+4.

[0090] Therefore, it is possible to perform Fourier transform processing such as FFT even when the number N-1 of received signals input to the first and second Fourier transform processing is not equal to a power of 2. The fifth embodiment is applicable not only to the second embodiment but also to the first, third, and fourth embodiments.

[0091] (KR product expansion radar signal processing of the sixth embodiment) The KR product expansion radar signal processing of the sixth embodiment is shown in Fig. 12. In the sixth embodiment, unlike the second and third embodiments, the radar transceiver A of the KR product expansion radar system S uses a MIMO (Multiple-Input Multiple Output) radar. The following describes the differences between the sixth embodiment and the second embodiment.

[0092] The transmission signals of the transmitting antenna elements T0, T1, and T3 (the transmitting antenna element T2 is missing) are Ae i0 , Ae iθ , Ae i3θ The received signals of receiving antenna elements R0, R1, and R3 (receiving antenna element R2 is missing) are superimposed with the reflected signals of the transmitted signals of transmitting antenna elements T0, T1, and T3, and therefore need to be orthogonally separated. The received signals of virtual antenna elements V1, V2, V4, V5, V6, V8, V13, V14, and V16 (virtual antenna elements V3, V7, V9 to V12, and V15 are missing) are i0 , Be iφ , Be i3φ , Be iθ , Be i(θ+φ) , Be i(θ+3φ) , Be i3θ , Be i(3θ+φ) , Be i(3θ+3φ) Let's say.

[0093] As in the second embodiment, the covariance matrix calculation unit 1 calculates the received signals Be i0 , Be iφ , Be i3φ , Be iθ , Be i(θ+φ) , Be i(θ+3φ) , Be i3θ, Be i(3θ+φ) , Be i(3θ+3φ) For the covariance matrix of the KR product extension, the lower triangular elements including the diagonal elements (the matrix in FIG. 12) are calculated.

[0094] As in the second embodiment, the received signal calculation unit 2 calculates the received signal of the first antenna array (first array in Figure 12) of the KR product expanded virtual array antenna, which has the central antenna element at one end and either one of the antenna elements at both ends (corresponding to the lower triangular component) at the other end, based on the independent components (components that do not overlap with each other) of the lower triangular component of the covariance matrix (matrix in Figure 12).

[0095] Here, the first antenna array (first array in FIG. 12) based on the lower triangular component includes virtual antenna elements K1 (ends), K2, K3, K4, K5, K6, K7, K8, K9, K10, K11, K12, K13, K14, K15, and K16 (center). The received signals of the virtual antenna elements K1, K2, K3, K4, K5, K6, K7, K8, K9, K10, K11, K12, K13, K14, K15, and K16 (B in FIG. 12) are 2 e -i* ) are respectively B 2 e -i(3θ+3φ) , B 2 e -i(3θ+2φ) , B 2 e -i(3θ+φ) , B 2 e -i3θ , B 2 e -i(2θ+3φ) , B 2 e -i(2θ+2φ) , B 2 e -i(2θ+φ) , B 2 e -i2θ , B 2 e -i(θ+3φ) , B 2 e -i(θ+2φ) , B 2 e -i(θ+φ) , B 2 e -iθ , B 2 e -i3φ , B 2 e -i2φ , B 2 e -iφ , B 2 e -i0 is.

[0096] The input signals of the first FFT unit 41, the real part doubling unit 42, and the center signal adder 43 are changed, but the output processing is the same. The input signals of the twiddle factor multiplier 51, the second FFT unit 52, the real part doubling unit 53, and the center signal subtracter 54 are changed, but the output processing is the same.

[0097] Therefore, when applying MIMO radar and calculating the covariance matrix of KR product expansion, the number of multiplications of a received signal and its complex conjugate can be reduced to approximately half of that of the conventional technology, and the memory amount for the matrix elements of the covariance matrix can be reduced to approximately half of that of the conventional technology, making it possible to easily implement the sixth embodiment in the KR product expansion radar system S. When applying MIMO radar and calculating the target angle spectrum of KR product expansion, the number of virtual antenna elements is set to 2N-1, and the amount of calculations such as FFT can be reduced from the order of 2N log 2N to the order of 2×N log N, making it possible to easily implement the sixth embodiment in the KR product expansion radar system S. Note that the sixth embodiment can be applied not only to the second embodiment but also to the first, third, fourth, and fifth embodiments.

[0098] In the present disclosure, signal processing using KR product expansion and calculation of target angle spectrum are performed for a one-dimensional "horizontal" array. As a variant, signal processing using KR product expansion and calculation of target angle spectrum may be performed for a one-dimensional "vertical" array. [Industrial Applicability]

[0099] The KR product expanded radar signal processing device and KR product expanded radar signal processing program disclosed herein (1) reduce the number of multiplications of a received signal and its complex conjugate when calculating a covariance matrix of KR product expansion, thereby reducing the memory requirements for the matrix elements of the covariance matrix; (2) when calculating a target angle spectrum, the number of virtual antenna elements is set to 2N-1, thereby further reducing the amount of calculations such as FFT on the order of 2N log 2N; and (3) facilitate implementation in embedded devices. [Explanation of symbols]

[0100] S:KR product expansion radar system A: Radar transmitter and receiver K:KR product expansion radar signal processing device D: Radar display device 1: Covariance matrix calculation part 2: Received signal calculation section 3: Fourier transform section 4: First Fourier transform section 5: Second Fourier transform section 6: Spectral integration section 31:FFT section 41: 1st FFT part 42: Real part double calculation part 43: Central signal addition section 44: Window function multiplication unit 51: Twiddle factor multiplication unit 52: 2nd FFT section 53: Real part double calculation part 54: Center signal subtraction section 55: Window function multiplication unit T0, T1, T3: Transmitting antenna elements R0, R1, R3: receiving antenna elements V1, V2, V3, V4, V5, V6, V7: Virtual antenna elements V8, V13, V14, V16: Virtual antenna elements K1, K2, K3, K4, K5, K6, K7, K8, K9, K10, K11, K12, K13, K14, K15, K16: Virtual antenna elements

Claims

1. a covariance matrix calculation unit that calculates either an upper triangular component including a diagonal component or a lower triangular component of a covariance matrix of a KR product expansion for received signals of a plurality of antenna elements; a received signal calculation unit that calculates received signals of a first antenna array having a central antenna element at one end and either one of the end antenna elements at the other end of a virtual array antenna of a KR product expansion based on either one of the upper triangular component and the lower triangular component of the covariance matrix; A KR product expansion radar signal processing device comprising:

2. The received signal calculation unit calculates a received signal of a second antenna array having the central antenna element at one end and either one of the end antenna elements at the other end as a complex conjugate of either the upper triangular component or the lower triangular component of the covariance matrix, or calculates the received signal of the second antenna array as a complex conjugate of a received signal of the first antenna array.

2. The KR product expansion radar signal processing device according to claim 1.

3. a Fourier transform unit that performs a Fourier transform on the received signals of the first antenna array and the second antenna array to calculate a target angle spectrum for all samples; The KR product expansion radar signal processing device according to claim 2, further comprising:

4. a first Fourier transform unit that performs a Fourier transform on the received signals of the first antenna array excluding the central antenna element and calculates a first target angular spectrum for every other sample; a second Fourier transform unit that performs a Fourier transform on a signal received from the first antenna array excluding the central antenna element by the complex 2Nth root of 1 to the nth power (the number of antenna elements in the virtual array antenna is 2N-1, and each antenna number in the virtual array antenna is n) to calculate a second target angle spectrum for every other sample other than the first target angle spectrum; a spectrum integration unit that integrates the first target angle spectrum and the second target angle spectrum for every other sample to calculate a target angle spectrum for all samples; The KR product expansion radar signal processing device according to claim 1 , further comprising:

5. the first Fourier transform unit calculates the first target angle spectrum by extracting only a real part from the Fourier transform result of every other sample and multiplying it by two; The second Fourier transform unit extracts only the real part from the Fourier transform result of every other sample and doubles it to calculate the second target angle spectrum.

5. The KR product expansion radar signal processing device according to claim 4.

6. the first Fourier transform unit adds the received signal of the central antenna element to the Fourier transform result of every other sample to calculate the first target angle spectrum; The second Fourier transform unit subtracts the received signal of the central antenna element from the Fourier transform result of every other sample to calculate the second target angle spectrum.

5. The KR product expansion radar signal processing device according to claim 4.

7. the first Fourier transform unit performs zero padding on the received signals of the first antenna array excluding the central antenna element, and then calculates the first target angle spectrum; The second Fourier transform unit performs zero padding on the received signals of the first antenna array excluding the central antenna element, and then calculates the second target angle spectrum.

5. The KR product expansion radar signal processing device according to claim 4.

8. the first Fourier transform unit multiplies the received signal of the first antenna array including the central antenna element by a window function, and then calculates the first target angle spectrum; The second Fourier transform unit multiplies the received signal of the first antenna array including the central antenna element by the window function and then calculates the second target angle spectrum.

5. The KR product expansion radar signal processing device according to claim 4.

9. 9. A KR area expansion radar signal processing program to be installed in a computer to cause the computer to sequentially execute each processing step executed by each processing unit provided in the KR area expansion radar signal processing device according to claim 1.

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