A multi-channel coherent integration method for FDA-MIMO radar based on range-frequency offset compensation

Abstract

The present invention discloses a multi-channel coherent accumulation method of an FDA-MIMO radar based on range-frequency offset compensation, which belongs to the technical field of radar moving target detection. The present invention comprises: obtaining the echo signal of the target by using a two-dimensional planar array FDA-MIMO radar; performing multi-channel matched filtering on the echo signal, and performing FFT transformation in slow time to realize pulse accumulation; then performing covariance matrix calculation to obtain the noise subspace and signal subspace; then performing azimuth and elevation angle search of the target, and obtaining the range-frequency offset coupling compensation vector based on eigendecomposition; multi-channel beamforming, coherently synthesizing the multi-channel signal energy and using a constant false alarm rate to detect the target. The present invention can significantly improve the output signal-to-noise ratio and reduce the computational complexity of coherent accumulation. Moreover, when there is an error in the target distance estimation or the Doppler effect is generated by the frequency offset, the present invention can obtain a higher coherent accumulation gain than the MUSIC algorithm.

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 integration method based on range-frequency offset compensation. Background Art

[0002] As a new radar system, the Frequency Diverse Array (FDA) radar has frequency offsets between array elements. Combining the Multiple Input Multiple Output (MIMO) system with FDA creates a Frequency Diverse Array Multiple-Input-Multiple-Output (FDA-MIMO) radar.

[0003] FDA-MIMO radar has unique advantages in detecting moving targets by using frequency offset. The paper "Zhang Shunsheng, Liu Meihui, Wang Wenqin. FDA-MIMO radar moving target detection based on Doppler spread compensation. Journal of Radar, 2022, 11(4): 666-675" proposes a FDA-MIMO radar moving target detection method based on Doppler spread compensation. However, in this scheme, the modulus of the signal amplitude of each channel is accumulated 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 high. 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 the 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, existing FDA-MIMO radar multi-channel coherent integration algorithms require a three-dimensional search, which increases computational complexity when the azimuth, elevation, and range search ranges are large. Furthermore, the algorithm is less robust in the presence of range errors and the Doppler effect. Summary of the Invention

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

[0006] The technical solution adopted in 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: Search for the angle of arrival based on the noise subspace, and then perform eigendecomposition based on the angle of arrival estimate and the range-frequency offset coupling correlation vector to obtain the 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 to detect targets.

[0013] Furthermore, step 1 specifically includes:

[0014] Step 11: Based on the array element frequency deviation Δf m,n Calculate the carrier frequency f of each transmitting element of the transmitting array and the reference carrier frequency f0 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 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 element (m, n) and received by the receiving 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 echo signal symbol 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, i.e. 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: Receive the single channel signal y at slow time b×d,m×n (ι,t k ) to perform FFT transformation and obtain the FFT transformed X b×d,m×n Indicates 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 noise Get the echo signal containing noise after pulse accumulation Where W represents the number of distance units, Represents a complex field.

[0026] Furthermore, step 3 specifically includes:

[0027] Step 31: echo signal Z of each channel of echo data Zi Each pulse takes the maximum value to obtain the 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 For the front (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 expressions 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 assistance 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 angles Perform arrival angle estimation, where det{·} represents the determinant of the matrix;

[0038] Step 42: Obtain 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 Single channel signal after beamforming, θ real 、 Represent the true 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, rather than the target range, thereby reducing the computational complexity of the coherent integration. In particular, when the azimuth, elevation, and range 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 range estimation or the Doppler effect is generated by frequency offset, the method of the present invention can obtain a higher coherent integration 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 following briefly introduces the drawings required for use in the description of the embodiments. 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 any creative work.

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

[0050] Figure 2 4 is a structural diagram of a planar array FDA-MIMO radar provided by an embodiment of the present invention.

[0051] Figure 3 This 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 4 is a computational complexity diagram of the algorithm of the present invention, direct search, and MUSIC algorithm provided in an embodiment of the present invention.

[0053] Figure 5 This 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 This is a comparison diagram of coherent accumulation results between 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] In order 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 part of the embodiments of the present application, not 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 embodiment of the present invention provides an FDA-MIMO radar multi-channel coherent integration method based on range-frequency offset compensation, comprising the following steps:

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

[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 signal subspace;

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

[0061] Step S5: Multi-channel beamforming, coherently combining the multi-channel signal energies and using a constant false alarm rate (CFAR) to perform 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 transmitting 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 represents 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 receiving 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: echo signal y(i,t 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, which is expressed as:

[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 r / c) term, 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. E 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 arrival 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 i-th 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 multi-channel coherently accumulated signal using a constant false alarm rate, which is expressed as:

[0126]

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

[0128] The present invention also further verifies the target detection performance of the method proposed in 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 cumulative 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 moving 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 the computational complexity diagram of the method proposed in the embodiment of the present invention, the direct search, and the MUSIC algorithm. Assume 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 As can be seen from the figure, when the search range of pitch angle, azimuth angle and distance is large, the method proposed in the embodiment of the present invention has obvious advantages over 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 Figures (6a) and (6b) are the coherent integration results of the method proposed in the embodiment of the present invention and the MUSIC algorithm, respectively, when the frequency offset causes the Doppler effect. As can be seen from the figure, the peak amplitude of the multi-channel coherent integration of the method proposed in the embodiment of the present invention is very large, while the MUSIC algorithm has mainlobe broadening and the peak amplitude of the coherent integration is significantly reduced. This shows that the method proposed in the embodiment of the present invention can achieve a higher coherent integration 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 various 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 inventive concept of the present invention, which all fall within the scope of protection 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: Search for the angle of arrival based on the noise subspace, and then perform eigendecomposition based on the angle of arrival estimate and the range-frequency offset coupling correlation vector to obtain the range-frequency offset coupling compensation vector; Step 5: Multi-channel beamforming, coherently synthesize the multi-channel signal energy and use constant false alarm rate to detect targets.

2. The method according to claim 1, wherein Step 1 specifically includes: Step 11: Based on the array element frequency deviation Δf m,n Calculate the carrier frequency f of each transmitting element of the transmitting array and the reference carrier frequency f0 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 element is expressed as: Where t is time, T s is the waveform duration; Step 13: The echo signal transmitted by the transmitting element (m, n) and received by the receiving 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 echo signal symbol 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, wherein 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: Receive signal y on single channel at slow time b×d,m×n (ι,t k ) to perform FFT transformation to obtain the pulse accumulation data of the single channel after FFT transformation X based on all channels b×d,m×n Obtain the 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 field.

4. The method according to claim 3, wherein Step 3 specifically includes: Step 31: echo signal Z of each channel of echo data Z i Each pulse takes the maximum value to obtain the 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 For the front (MN) 2 The eigenvector corresponding to the -1 minimum eigenvalue is called the noise subspace.

5. The method according to claim 4, wherein Step 4 specifically includes: Step 41: Based on the noise subspace E n Construct the expressions for arrival angle estimation and range-frequency offset coupling vector acquisition: in, For the angle of arrival The auxiliary quantity is expressed as: Delay assistance is the new transmit-receive joint steering vector The i-th element of Peak search expression based on elevation and azimuth angles Perform arrival angle estimation, where det{·} represents the determinant of the matrix; Step 42: Obtain 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, wherein 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 Single channel signal after beamforming, θ real 、 Represent the true pitch angle and azimuth angle respectively. The peak search result of 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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