FDA-MIMO radar multichannel coherent accumulation method based on distance-frequency offset compensation

Abstract

The invention discloses an FDA-MIMO radar multichannel coherent accumulation method based on distance-frequency offset compensation, and belongs to the technical field of radar moving target detection. The method comprises the following steps: obtaining an echo signal of a target by using a two-dimensional planar array FDA-MIMO radar; performing multi-channel matched filtering on the echo signal, and performing FFT (Fast Fourier Transform) at slow time to realize pulse accumulation; performing covariance matrix calculation to obtain a noise subspace and a signal subspace; searching an azimuth angle and a pitch angle of the target, and obtaining a distance-frequency offset coupling compensation vector based on characteristic decomposition; and performing multi-channel beam forming, performing coherent synthesis on multi-channel signal energy, and performing target detection by using a constant false alarm rate. According to the method, the output signal-to-noise ratio can be remarkably improved, the calculation complexity of coherent accumulation is reduced, and when an error exists in target distance estimation or a Doppler effect is generated by frequency offset, compared with a MUSIC algorithm, the method can obtain higher coherent accumulation gain.

Description

Technical Field

[0001] The present invention relates to the technical field of radar moving target detection, and in particular to a FDA-MIMO radar multi-channel coherent accumulation method based on range-frequency offset compensation. Background Art

[0002] As a new radar system, there is frequency offset between the array elements of Frequency Diverse Array (FDA) radar. Combining the Multiple Input Multiple Output (MIMO) system with FDA can form a Frequency Diverse Array Multiple-Input-Multiple-Output (FDA-MIMO) radar.

[0003] FDA-MIMO radar has unique advantages in moving target detection by using frequency offset. The paper "Zhang Shunsheng, Liu Meihui, Wang Wenqin. Moving target detection by FDA-MIMO radar based on Doppler spread compensation. Journal of Radar, 2022, 11(4): 666-675" proposed a moving target detection method for FDA-MIMO radar based on Doppler spread compensation. However, the scheme accumulates the modulus of the signal amplitude of each channel without considering the influence of the steering vector on the coherent accumulation. This method is considered to be non-coherent and will affect the output signal-to-noise ratio of the signal. To achieve multi-channel coherent accumulation, a simple method is to directly search the azimuth, pitch angle and distance of the target, but this method requires a three-dimensional joint search and the algorithm complexity is very large. In addition, the Multiple Signal Classification (MUSIC) algorithm is often used for Direction Of Arrival (DOA) estimation. However, when there is a target distance estimation error or a Doppler effect caused by frequency offset, using the MUSIC algorithm for multi-channel coherent accumulation will cause the accumulation gain to deteriorate sharply.

[0004] In summary, the existing FDA-MIMO radar multi-channel coherent integration algorithm requires three-dimensional search. When the azimuth angle, elevation angle and distance search range are large, the computational complexity is very large. Moreover, when there is distance error and Doppler effect, the algorithm robustness is poor. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a FDA-MIMO radar multi-channel coherent integration method based on range-frequency offset compensation to obtain higher coherent integration gain and reduce calculation complexity.

[0006] The technical solution adopted by the present invention is:

[0007] A multi-channel coherent integration method for FDA-MIMO radar based on range-frequency offset compensation, the method comprising the following steps:

[0008] Step 1: Use a two-dimensional planar array FDA-MIMO radar to obtain the target's echo signal;

[0009] Step 2: Perform multi-channel matched filtering on the target echo signal and perform FFT transformation in slow time to obtain the echo data after pulse accumulation;

[0010] Step 3: Calculate the covariance matrix of the echo data after pulse accumulation to obtain the noise subspace and signal subspace;

[0011] Step 4: perform an arrival angle search based on the noise subspace, and then perform feature decomposition based on the arrival angle estimation and the range-frequency offset coupling correlation vector to obtain a range-frequency offset coupling compensation vector;

[0012] Step 5: Multi-channel beamforming, coherently synthesize the multi-channel signal energy and use constant false alarm rate for target detection.

[0013] Furthermore, step 1 specifically includes:

[0014] Step 11: According to the array element frequency deviation Δf m,n And the reference carrier frequency f0 calculates the carrier frequency f of each transmitting array element m,n , where subscripts m and n are the row and column indices of the transmit array, 0≤m<M, 0≤n<N, MN is the number of elements in the transmit array; and the row and column spacing of the transmit array elements are d x and d y ;

[0015] Step 12, the transmit signal of the transmit array element is expressed as: 0<t≤T s , where t is time, T s is the waveform duration;

[0016] Step 13, the echo signal transmitted by the transmitting array element (m, n) and received by the receiving array element (b, d) is expressed as:

[0017]

[0018] Among them, t k =kT pr is the slow time, ι=tt k For fast time, T pr is the pulse duration, K is the number of pulses, ξ b×d,m×n is the complex amplitude of the signal, τ b×d,m×n (k) is the propagation delay, e is the natural base, and j is the imaginary unit;

[0019] Step 14, the echo signals received by the multi-channels are mixed to obtain the following echo signals:

[0020]

[0021] Among them, y b,d (ι,t k ) represents the symbol of the echo signal corresponding to the receiving array element (b, d), 0≤b<M, 0≤d<N, is the Kronecker product, ξ is the complex amplitude matrix, is the transmit-receive joint steering vector, To receive the steering vector, is the launch steering vector, θ and denote the elevation angle and azimuth angle respectively, that is, is the arrival angle of the target, Ω(r,v) is the coupling matrix of target velocity and distance, and γ(ι) is the echo signal envelope.

[0022] Furthermore, step 2 specifically includes:

[0023] Step 21, the echo signal y(ι,t k ) is down-converted and multi-channel matched filtering is performed to obtain a single-channel received signal y b×d,m×n (ι,t k );

[0024] Step 22, receiving the single channel signal y at a slow time b×d,m×n (ι,t k ) to perform FFT transformation and obtain the FFT transformed X b×d,m×n Represents the received signal y b×d,m×n Data after pulse accumulation, that is, data after pulse accumulation of a single channel;

[0025] X based on all channels b×d,m×n Get the signal data after pulse accumulation X = [X 0×0,0×0 …X 0×0,(M-1)×(N-1) …X (M-1)×(N-1),(M-1)×(N-1) ] T , that is, X represents the data after multi-channel pulse accumulation; based on X and Gaussian distribution of noise Get the echo signal containing noise after pulse accumulation Where W represents the number of distance units, Represents a complex number domain.

[0026] Furthermore, step 3 specifically includes:

[0027] Step 31: for each channel of the echo data Z, the echo signal Zi Each pulse takes the maximum value to obtain a two-dimensional matrix Z max ; and calculate the covariance matrix

[0028] The covariance matrix R can be expressed as: R = ΓR s Γ H +σ 2 I, where R s is the covariance matrix of the echo signal without noise, σ 2 represents the noise variance, I represents the identity matrix; the diagonal matrix Delay τ i ,i=0,1...,MN-1 is expressed as:

[0029]

[0030] Step 32, decompose the covariance matrix R into Among them, the diagonal matrix Λ s Composed of the largest eigenvalues, the diagonal matrix Λ n From the front (MN) 2 -1 minimum eigenvalue, E s The eigenvector corresponding to the largest eigenvalue is called the signal subspace, E n Forward (MN) 2 The eigenvector corresponding to the -1 minimum eigenvalue is called the noise subspace.

[0031] Furthermore, step 4 specifically includes:

[0032] Step 41: Based on the noise subspace E n Construct the expression for arrival angle estimation and range-frequency offset coupling vector acquisition:

[0033]

[0034] in, For the angle of arrival The auxiliary quantity is expressed as:

[0035]

[0036] Delay Auxiliary Amount Does not include τ i (i=kMN+1,k=0,1,2...MN-1), is the new transmit-receive joint steering vector The i-th element of

[0037] Peak search expression based on elevation and azimuth Perform arrival angle estimation, where det{·} represents the determinant of the matrix;

[0038] Step 42, obtaining the distance-frequency offset coupling compensation vector:

[0039]

[0040] Among them, u min {·} represents the eigenvector corresponding to the minimum eigenvalue after eigendecomposition, and [ξ]1 is the first element of ξ.

[0041] Furthermore, step 5 specifically includes:

[0042] Step 51, beamforming is performed on the pulse compressed signal, and the expression is:

[0043]

[0044] Among them, Y b×d,m×n Indicates X b×d,m×n The single channel signal after beamforming, θ real , Represent the actual pitch angle and azimuth angle respectively. The arrival angle estimated in step 4 is used as the calculation The value of Indicates the delay caused by the distance between transmitting array elements, represents the delay caused by the receiving array element spacing, {·} * represents the conjugation of {·}; that is

[0045] Step 52: Perform target detection on the multi-channel coherently accumulated signals based on a constant false alarm rate.

[0046] The technical solution provided by the present invention brings at least the following beneficial effects:

[0047] Compared with non-coherent integration, the coherent integration of the method of the present invention can greatly improve the output signal-to-noise ratio. In a two-dimensional planar array, only the azimuth and elevation angles of the target need to be searched without searching the target distance, thereby reducing the computational complexity of the coherent integration. In particular, when the azimuth, elevation and distance search ranges are large, the method of the present invention has obvious advantages over direct search and MUSIC. Moreover, when there are errors in the target distance estimation or the Doppler effect is generated by frequency deviation, the method of the present invention can obtain a higher coherent accumulation gain than the MUSIC algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0049] Figure 1 It is a flow chart of a multi-channel coherent integration method of FDA-MIMO radar based on range-frequency offset compensation provided by an embodiment of the present invention.

[0050] Figure 2 It is a structural diagram of a planar array FDA-MIMO radar provided by an embodiment of the present invention.

[0051] Figure 3 1 is a comparison chart of the results of the algorithm provided by the embodiment of the present invention and the non-coherent accumulation algorithm proposed in the document [1].

[0052] Figure 4 It is a computational complexity diagram of the algorithm of the present invention, direct search, and MUSIC algorithm provided by the embodiment of the present invention.

[0053] Figure 5 It is a comparison diagram of the coherent accumulation results of the algorithm of the present invention and the MUSIC algorithm provided in an embodiment of the present invention when the distance error occurs.

[0054] Figure 6 It is a comparison diagram of the coherent accumulation results of the algorithm of the present invention and the MUSIC algorithm provided in an embodiment of the present invention when the frequency offset causes the Doppler effect. DETAILED DESCRIPTION

[0055] To make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in detail and completely in conjunction with the drawings in the implementation of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings can be arranged and designed using different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the present application for protection, but merely represents selected embodiments of the present invention.

[0056] like Figure 1 As shown, an FDA-MIMO radar multi-channel coherent integration method based on range-frequency offset compensation provided by an embodiment of the present invention includes the following steps:

[0057] Step S1, using a two-dimensional planar array FDA-MIMO radar to obtain an echo signal of a target;

[0058] Step S2, performing multi-channel matched filtering on the echo signal and performing Fast Fourier Transform (FFT) transformation in slow time to achieve pulse accumulation;

[0059] Step S3, calculating the covariance matrix of the echo data after pulse accumulation to obtain the noise subspace and the signal subspace;

[0060] Step S4, searching for azimuth and elevation angles based on the noise subspace, and performing feature decomposition based on arrival angle estimation and range-frequency offset coupling correlation vector to obtain a range-frequency offset coupling compensation vector;

[0061] Step S5: multi-channel beamforming, coherently synthesizing the energy of multi-channel signals and using constant false alarm rate (CFAR) for target detection.

[0062] In one embodiment, step S1 of the embodiment of the present invention includes the following sub-steps:

[0063] Step S11: according to the array element frequency deviation Δf m,n And the reference carrier frequency f0 is used to calculate the carrier frequency of each transmitting array element, which can be expressed as f m,n =f0+Δf m,n , where Δf m,n represents the carrier frequency of the array element at coordinate (m,n), represents a natural number, M×N is the number of transmitting array elements, M and N represent the number of rows and columns of the transmitting array respectively, and the row and column spacing of the transmitting array elements are d x and d y ;

[0064] Step S12: The transmission waveform at the array element (m, n) is γ m,n (t) = ω m,n γ(t), where γ(t) and ω m,n represents the baseband waveform and transmission weight. The transmitted signal at the array element (m,n) can be written as 0<t≤T s , T s is the waveform duration;

[0065] Step S13: The target approaches the radar from the far field at a uniform speed. The echo signal emitted by the array element (m, n) and received by the array element (b, d) can be expressed as:

[0066]

[0067] Among them, t k =kT pr , Indicates slow time, ι=tt k Indicates fast time, T pr is the pulse duration, K represents the number of pulses, ξ b×d,m×n represents the complex amplitude of the corresponding signal, τ b×d,m×n (k) represents the propagation delay. (b, d) represents the element position of the receiving array, that is, b and d are the rows and columns of the receiving array respectively.

[0068] Under the far-field assumption, the time delay τ b×d,m×n (k) can be approximated as:

[0069]

[0070]

[0071] Where c is the speed of light, θ and The subscripts T and R are used to identify the transmitting antenna and the receiving antenna, respectively.

[0072] Step S14: Due to Δf m,n <<f0, there is an approximate relationship:

[0073]

[0074] The launch steering vector considering the distance and the launch steering vector not considering the distance are:

[0075]

[0076] The receive steering vector is:

[0077]

[0078] Step S15: The multi-channel received signals are mixed and written into the following matrix form:

[0079]

[0080] in, is the Kronecker product, and ξ is the complex amplitude matrix. is the transmit-receive joint steering vector, which is expressed as:

[0081]

[0082] Ω(r,v) is the coupling matrix of target speed and distance, which is expressed as:

[0083]

[0084] γ(ι) represents the echo signal envelope, and its expression is:

[0085] γ(ι)=[γ(ι-τ r -τ v (0))γ(ι-τ r -τ v (1))…γ(ι-τ r -τ v (K-1))] T

[0086] In practice, the structure of a two-dimensional transmit-receive FDA-MIMO radar is as follows: Figure 2 shown.

[0087] In one embodiment, step S2 of the embodiment of the present invention includes the following steps:

[0088] Step S21: k ) for down-conversion and multi-channel matched filtering, the expression can be obtained as follows:

[0089]

[0090] in,

[0091]

[0092] The received single-channel received signal after matched filtering can be expressed as:

[0093]

[0094] Step S22, perform FFT at slow time to achieve pulse accumulation, the expression is:

[0095]

[0096] X=[X 0×0,0×0 … X 0×0,(M-1)×(N-1) … X (M-1)×(N-1),(M-1)×(N-1) ] T

[0097] The echo data model after pulse accumulation can be expressed as:

[0098] Z=X+N

[0099] in, represents the echo signal matrix containing noise, represents the noise matrix of Gaussian distribution, W represents the number of distance units;

[0100] In one embodiment, step S3 of the embodiment of the present invention further includes the following sub-steps:

[0101] Step S31: At Zi (i=1,2…(MN) 2 ) takes the maximum value of each pulse to obtain a two-dimensional matrix Z max , where Z i represents the echo signal of the i-th channel of Z, and the covariance matrix can be expressed as:

[0102]

[0103] in, is from exp(-j4πΔf m,n The diagonal matrix obtained in the term r / c), R s represents the covariance matrix of the echo signal without noise, σ 2 represents the noise variance, I represents the identity matrix, represents the covariance matrix of the signal, E{·} represents the statistical expectation, where X max It is composed of the maximum value of each pulse of each channel of signal X;

[0104] Step S32: By eigenvalue decomposition, we can obtain:

[0105]

[0106] For a single target, the diagonal matrix Λ s Composed of the first largest eigenvalue, the diagonal matrix Λ n By the last (MN) 2 -1 small eigenvalue. s The eigenvector corresponding to the first large eigenvalue is called the signal subspace. n Representative (MN) 2 -1 The eigenvector corresponding to a small eigenvalue is called the noise subspace;

[0107] Through subspace theory, the true direction of the target can be expressed as:

[0108]

[0109] in, represents the new transmit-receive joint steering vector, In order to separate the coupling vector of the range-frequency offset term from the diagonal matrix Γ, the above equation can be written as:

[0110]

[0111] in, Does not include τ i (i=kMN+1,k=0,1,2...MN-1), is the arrival angle assistance, is a MN×(MN(MN-1)+1)-dimensional matrix, yes The ith element of .

[0112] In one embodiment, step S4 of the embodiment of the present invention further includes the following sub-steps:

[0113] Step S41, obviously (MN) 2 -1>MN(MN-1)+1 satisfies the rank loss condition. Therefore, the expression for arrival angle estimation and range-frequency offset coupling vector acquisition is:

[0114]

[0115] When the searched elevation and azimuth angles are different from the real angles Match, The determinant of has a minimum value. Therefore, the peak search expressions for the elevation angle and azimuth angle are:

[0116]

[0117] Where det{·} represents the determinant of the matrix;

[0118] Step S42: The coupling vector caused by distance and frequency offset coupling can be estimated, and its expression is:

[0119]

[0120] Among them, u min {·} represents the eigenvector corresponding to the minimum eigenvalue after eigendecomposition. [ξ]1 is the first element of ξ.

[0121] In one embodiment, step S5 of the embodiment of the present invention further includes the following steps:

[0122] Step S51: beamforming is performed on the pulse compressed signal, and the expression is:

[0123]

[0124] in,{·} * represents the conjugation of {·};

[0125] Step S52: Target detection is performed on the signal after multi-channel coherent accumulation using a constant false alarm rate, and the expression is:

[0126]

[0127] Among them, η is the detection threshold. When the multi-channel coherent accumulation result is greater than the threshold, the target is detected.

[0128] The embodiment of the present invention further verifies the target detection performance of the method proposed in the embodiment of the present invention through simulation experiments. The simulation parameters involved are shown in Table 1:

[0129] Table 1 Simulation parameters

[0130]

[0131] The target's moving speed is 150m / s and the radial distance is 10km. Figure 3 (3a) and (3b) are the accumulated results of the method proposed in the embodiment of the present invention and the comparative scheme (Zhang Shunsheng, Liu Meihui, Wang Wenqin. FDA-MIMO radar motion target detection based on Doppler spread compensation. Journal of Radar, 2022, 11(4): 666-675). It can be seen from the figure that the output signal-to-noise ratio of the method proposed in the embodiment of the present invention is higher than that of the comparative scheme. Figure 4 is a computational complexity diagram of the method proposed in the embodiment of the present invention, the direct search, and the MUSIC algorithm, assuming that the number of pitch angle searches, the number of azimuth angle searches, the number of distance searches, the number of slow times, and the number of fast times are all M c It can be seen from the figure that when the pitch angle, azimuth angle and distance search range are large, the method proposed in the embodiment of the present invention has obvious advantages over the direct search and MUSIC algorithm. Figure 5 (5a) and (5b) are the coherent accumulation results of the method proposed in the embodiment of the present invention and the MUSIC algorithm when distance error occurs. It can be seen from the figure that the method proposed in the embodiment of the present invention is almost unaffected because it does not need to estimate the target distance, while the signal amplitude of the multi-channel accumulation based on the MUSIC algorithm deteriorates sharply. Changing the target speed to 900m / s, Figure 6 (6a) and (6b) in the figure are the coherent accumulation results of the method proposed in the embodiment of the present invention and the MUSIC algorithm when the frequency offset causes the Doppler effect. It can be seen from the figure that the peak amplitude of the multi-channel coherent accumulation of the method proposed in the embodiment of the present invention is very large, while the MUSIC algorithm has a main lobe broadening, and the peak amplitude of the coherent accumulation is significantly reduced. This shows that the method proposed in the embodiment of the present invention can obtain a higher coherent accumulation gain than the MUSIC algorithm.

[0132] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0133] The above are only some embodiments of the present invention. For those skilled in the art, several modifications and improvements can be made without departing from the creative concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A multi-channel coherent integration method for FDA-MIMO radar based on range-frequency offset compensation, characterized in that: The following steps are involved: Step 1: Use a two-dimensional planar array FDA-MIMO radar to obtain the target's echo signal; Step 2: Perform multi-channel matched filtering on the target echo signal and perform FFT transformation in slow time to obtain the echo data after pulse accumulation; Step 3: Calculate the covariance matrix of the echo data after pulse accumulation to obtain the noise subspace and signal subspace; Step 4: perform an arrival angle search based on the noise subspace, and then perform feature decomposition based on the arrival angle estimation and the range-frequency offset coupling correlation vector to obtain a range-frequency offset coupling compensation vector; Step 5: Multi-channel beamforming, coherently synthesize the multi-channel signal energy and use constant false alarm rate for target detection.

2. The method according to claim 1, characterized in that Step 1 specifically includes: Step 11: According to the array element frequency deviation Δf m,n And the reference carrier frequency f0 calculates the carrier frequency f of each transmitting array element m,n , where subscripts m and n are the row and column indices of the transmit array, 0≤m<M, 0≤n<N, MN is the number of elements in the transmit array; and the row and column spacing of the transmit array elements are d x and d y ; Step 12, the transmit signal of the transmit array element is expressed as: Where t is time, T s is the waveform duration; Step 13, the echo signal transmitted by the transmitting array element (m, n) and received by the receiving array element (b, d) is expressed as: Among them, t k =kT pr is the slow time, ι=tt k For fast time, T pr is the pulse duration, K is the number of pulses, ξ b×d,m×n is the complex amplitude of the signal, τ b×d,m×n (k) is the propagation delay, e is the natural base, and j is the imaginary unit; Step 14, the echo signals received by the multi-channels are mixed to obtain the following echo signals: Among them, y b,d (ι,t k ) represents the symbol of the echo signal corresponding to the receiving array element (b, d), 0≤b<M, 0≤d<N, is the Kronecker product, ξ is the complex amplitude matrix, is the transmit-receive joint steering vector, To receive the steering vector, is the launch steering vector, θ and denote the pitch angle and azimuth angle respectively, Ω(r,v) is the coupling matrix of target velocity and distance, and γ(ι) is the echo signal envelope.

3. The method according to claim 2, characterized in that Step 2 specifically includes: Step 21, the echo signal y(ι,t k ) is down-converted and multi-channel matched filtering is performed to obtain a single-channel received signal y b×d,m×n (ι,t k ); Step 22, receiving the single channel signal y at a slow time b×d,m×n (ι,t k ) to perform FFT transformation to obtain the pulse accumulation data of a single channel after FFT transformation X based on all channels b×d,m×n Obtain data X after multi-channel pulse accumulation; Noise based on X and Gaussian distribution Get the echo signal containing noise after pulse accumulation Where W represents the number of distance units, Represents a complex number domain.

4. The method according to claim 3, characterized in that Step 3 specifically includes: Step 31: for each channel of the echo data Z, the echo signal Z i Each pulse takes the maximum value to obtain a two-dimensional matrix Z max ; and calculate the covariance matrix Step 32, decompose the covariance matrix R into Among them, the diagonal matrix Λ s Composed of the largest eigenvalues, the diagonal matrix Λ n From the front (MN) 2 -1 minimum eigenvalue, E s The eigenvector corresponding to the largest eigenvalue is called the signal subspace, E n Forward (MN) 2 The eigenvector corresponding to the -1 minimum eigenvalue is called the noise subspace.

5. The method according to claim 4, characterized in that Step 4 specifically includes: Step 41: Based on the noise subspace E n Construct the expression for arrival angle estimation and range-frequency offset coupling vector acquisition: in, For the angle of arrival The auxiliary quantity is expressed as: Delay Auxiliary Amount is the new transmit-receive joint steering vector The i-th element of Peak search expression based on elevation and azimuth Perform arrival angle estimation, where det{·} represents the determinant of the matrix; Step 42, obtaining the distance-frequency offset coupling compensation vector: Among them, u min {·} represents the eigenvector corresponding to the minimum eigenvalue after eigendecomposition, and [ξ]1 is the first element of ξ.

6. The method according to claim 5, characterized in that Step 5 specifically includes: Step 51, beamforming is performed on the pulse compressed signal, and the expression is: Among them, Y b×d,m×n Indicates X b×d,m×n The single channel signal after beamforming, θ real , They represent the true elevation angle and azimuth angle respectively. The peak search result in step 4 is used as the corresponding value during calculation. Indicates the delay caused by the distance between transmitting array elements, represents the delay caused by the receiving array element spacing, {·} * represents the conjugation of {·}; Step 52: Perform target detection on the multi-channel coherently accumulated signals based on a constant false alarm rate.

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