A passive sonar anti-jamming method under multipath coherent and incoherent mixed broadband signals

Abstract

The application provides a passive sonar anti-interference method under multipath coherent and incoherent mixed broadband signals. The method comprises the following steps: step 1, constructing the space-time covariance matrix of the entire hydrophone array by adopting a frequency domain construction method of the space-time covariance matrix; step 2, based on the constructed space-time covariance matrix, adopting a space-time minimum variance distortionless response (STMVDR) beamformer to obtain the angle-frequency two-dimensional power spectrum of all signals; step 3, calculating the similarity between the frequency spectrum sequences of the expected signal and the interference, judging whether the two are in a multipath coherent relationship according to the similarity value, and obtaining the angle of the expected signal and the angle of the multipath coherent interference; step 4, setting a zero point constraint in the direction of the angle of the multipath coherent interference and setting a unit gain constraint in the direction of the angle of the expected signal, and calculating the optimal weight vector by using an FCSTBB algorithm based on the optimal phase center reference point to realize the anti-interference reception of the signal.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic communication technology, and in particular to a passive sonar anti-interference method for multipath coherent and incoherent hybrid broadband signals. Background Technology

[0002] In the research of broadband signal anti-jamming technology for passive sonar, anti-jamming techniques based on adaptive beamforming have received increasing attention from scholars. Classical broadband adaptive beamforming mainly falls into two categories: space-frequency methods and space-time methods.

[0003] Spatial-frequency methods rely on narrowband filtering techniques such as the Discrete Fourier Transform (DFT) to decompose broadband signals into multiple narrowband signals before applying narrowband adaptive beamforming. Unlike spatial-frequency methods, spatial-temporal methods do not require narrowband decomposition and possess two-dimensional optimization capabilities in both space and frequency. When the direction and duration of interference sources remain stable for extended periods, spatial-frequency methods have sufficient signal samples to achieve adequate narrowband decomposition, achieving similar performance to spatial-temporal methods with significantly lower computational complexity. However, when facing moving interference sources or short-duration bursts, the useful signal sample length is short. In such cases, DFT-based narrowband filtering suffers from significant spectral energy leakage, leading to a decrease in the anti-interference capability of spatial-frequency methods. Spatial-temporal methods, with their two-dimensional optimization capabilities, effectively suppress spectral energy leakage, maintaining good anti-interference performance even with short signal sample lengths.

[0004] However, in real-world underwater acoustic interference environments, multipath propagation is prevalent due to the refraction effect of seawater and the reflection from the sea surface and seabed. The signal received by a passive sonar array may be a mixture of multipath coherent and incoherent signals. In this case, the coherence between the target signal and the multipath coherent interference causes a rank deficiency in the data covariance matrix, leading to the cancellation of the desired signal and the multipath coherent interference signal during broadband adaptive beamforming. To achieve anti-interference reception of broadband signals under multipath coherent interference conditions, decoherence methods for broadband signals have been extensively studied. Two classic decoherence methods are spatial smoothing methods and non-spatial smoothing methods.

[0005] Spatial smoothing methods first divide the array into several overlapping subarrays, and then obtain the full-rank data covariance matrix by averaging the data covariance matrices of the subarrays. The coherence interference suppression effect of this method depends on the number of subarrays, and the array aperture is lost while decohering.

[0006] Non-spatial smoothing methods do not lose array aperture. Existing non-spatial smoothing methods mainly include matrix reconstruction methods, low sidelobe beamforming methods, Duvall beamforming methods, and linear constraint methods. Matrix reconstruction methods reconstruct the decoherent data covariance matrix by Toeplitzing the data covariance matrix or signal eigenvectors. Matrix reconstruction methods can still achieve decoherence of the data covariance matrix under low signal-to-noise ratio and small snapshot number conditions, but Toeplitzing can only approximate the true signal subspace, resulting in a significant deviation from the true results.

[0007] The low-sidelobe broadband beamforming algorithm based on space-time structure proposed by Ren Chao et al. has a good suppression effect on coherent interference, but its ability to suppress high-power coherent interference signals is weak. Widrow et al. proposed a Duvall beamforming structure, which achieves decoherence by removing the desired signal component from the array received data, but this method requires accurate knowledge of the desired signal direction and a pre-steering delay structure to "align" the desired signal. Yeh et al. proposed a coherent interference suppression method based on zero-point constraints. This method first estimates the coherent interference direction based on signal subspace theory, and then places zero-point constraints on the coherent interference direction based on the LCMV criterion to achieve decoherence. At the same time, derivative constraints are added to improve the robustness of the algorithm to the estimation error of the coherent interference direction. However, this method is proposed in the context of narrowband signals, and the estimation method of the coherent interference direction is not applicable to broadband signals.

[0008] In mixed signal scenarios, the frequency spectrum distribution of the desired signal and its multipath coherent interference should be similar. Based on this, if the angle-frequency two-dimensional power spectrum of all signals can be obtained, the multipath relationship between signals can be determined using the frequency spectrum distribution information, thereby obtaining the angle of multipath coherent interference. The STMVDR algorithm can effectively suppress the "leakage" of spectral energy and output a relatively "refined" frequency spectrum under short signal sample lengths due to its frequency optimization capability. However, this algorithm cannot solve multipath coherent interference and its performance is poor at low signal-to-noise ratios. Summary of the Invention

[0009] In order to achieve anti-interference reception of signals under the condition of multipath coherent interference, the present invention provides a passive sonar anti-interference method under mixed multipath coherent and incoherent broadband signals.

[0010] This invention provides a passive sonar anti-interference method for multipath coherent and incoherent hybrid broadband signals, comprising:

[0011] Step 1: Construct the space-time covariance matrix of the entire hydrophone array using the frequency domain construction method of the space-time covariance matrix;

[0012] Step 2: Based on the constructed space-time covariance matrix, the angle-frequency two-dimensional power spectrum of all signals is obtained using a space-time minimum variance distortion-free response STMVDR beamformer.

[0013] Step 3: Calculate the similarity between the frequency spectrum sequences of the desired signal and the interference, determine whether the two are multipath coherent based on the similarity value, and obtain the angle of the desired signal and the angle of the multipath coherent interference;

[0014] Step 4: Set zero-point constraints in the angular direction of multipath coherent interference and unity-gain constraints in the angular direction of the desired signal. Calculate the optimal weight vector using the FCSTBB algorithm based on the optimal phase center reference point to achieve interference-resistant signal reception.

[0015] Furthermore, step 1 specifically includes:

[0016] Step 1.1: Use a conventional beamforming algorithm to initially estimate the angles of all signals to determine the focusing angle β;

[0017] Step 1.2: Divide the entire hydrophone array into K subarrays and estimate the frequency domain data covariance matrix of each subarray. f j This indicates a specific frequency point within the frequency band;

[0018] Step 1.3: Based on the frequency domain data covariance matrix of each subarray The frequency domain data covariance matrix of the entire hydrophone array was calculated using a spatial smoothing algorithm.

[0019] Step 1.4: Determine the number of time-domain taps L based on the signal bandwidth and sampling frequency, and construct the time-domain steering vector S of the entire hydrophone array. t (f j );

[0020] Step 1.5: Based on the frequency domain data covariance matrix of the entire hydrophone array Time-domain steering vector S t (f j The spatiotemporal covariance matrix of the entire hydrophone array is constructed by combining the focusing angle β with the rotating subspace algorithm.

[0021] Furthermore, step 1.2 specifically includes:

[0022] The data snapshot vector set of each subarray χ k (nT s ), n=1,2,…,N t k = 1, 2, ..., K, divided into N p There are N data blocks, with no overlap between them; where N is...t T represents the total number of data snapshots. s Indicates the sampling interval;

[0023] Perform a DFT transform on the time-domain data of each element in all data blocks to obtain the corresponding frequency-domain data χ. k (f j ,k1); where k1=1,2,…,N p ;

[0024] The frequency domain data covariance matrix of each subarray is estimated according to formula (3).

[0025]

[0026] Furthermore, step 1.3 specifically includes:

[0027]

[0028] Furthermore, step 1.4 specifically includes:

[0029]

[0030] Among them, T s =1 / f s f represents the sampling time interval. s Indicates the sampling frequency.

[0031] Furthermore, step 1.5 specifically includes:

[0032]

[0033] Where J1 and J2 are the boundaries of the signal frequency range, J represents the number of snapshot vectors contained in a data block, J = ΣL, Σ is a positive integer, and T RSS (f j ,β) represents a focusing matrix constructed using the Rotation Subspace RSS algorithm.

[0034] Furthermore, step 2 specifically includes:

[0035] The azimuth-frequency two-dimensional power spectrum of all signals is obtained according to formula (17).

[0036]

[0037] in, The desired direction θ p The estimation of the space-time two-dimensional steering vector corresponding to Q frequency points, q=1,2,…,Q; Represents the space-time covariance matrix;

[0038] Based on the azimuth-frequency two-dimensional power spectrum, the spatial spectrum of all signals is obtained:

[0039]

[0040] Where P represents the number of spatial spectrum scan points;

[0041] Based on the peak angle of the spatial spectrum, the angles of all signals are estimated. Where, N s Indicates the number of sound sources;

[0042] The corresponding frequency spectrum is obtained based on the angle of the signal:

[0043]

[0044] Where s = 1, 2, ..., N s .

[0045] Furthermore, step 3 specifically includes:

[0046] The Pearson correlation coefficient between the frequency spectrum sequences of the desired signal and the interference is calculated as their similarity. If the similarity value ρ is not less than a set threshold, the desired signal and the interference are considered to be multipath signals; otherwise, they are considered to be incoherent signals.

[0047] Furthermore, step 4 specifically includes:

[0048] Re-estimate the spatiotemporal covariance matrix of the array data according to equation (27).

[0049]

[0050] Where, x ST (nT s ) represents a spacetime ML-dimensional observation vector;

[0051] Based on the re-estimated spatiotemporal covariance matrix The beamforming weighting vector w′ is calculated according to equation (28). opt Calculate the output signal w′ opt x ST (nT d ):

[0052]

[0053] Where C′ and F′ represent the constraint matrix and gain response vector formed after setting zero-point constraints in the angular direction of multipath coherent interference and setting unity-gain constraints in the angular direction of the desired signal, respectively.

[0054] Furthermore, the hydrophone array is a uniform linear array.

[0055] The beneficial effects of this invention are:

[0056] (1) Spatial smoothing technology and coherent subspace method based on rotating subspace are used to preprocess the spatiotemporal covariance matrix to improve the decoherence capability and beamforming performance of STMVDR algorithm under low signal-to-noise ratio.

[0057] (2) Combining zero-point constraints and space-time broadband adaptive beamformer to achieve anti-interference reception of signals, while adding derivative constraints to improve the robustness of the algorithm to angle estimation errors, it can achieve accurate and robust anti-interference reception of the desired signal under the conditions of short signal samples and no loss of array aperture.

[0058] (3) Simulation results show that the method proposed in this invention can effectively suppress the multipath coherent signal cancellation problem under the condition of multipath coherent and incoherent mixed signals, while adaptively suppressing incoherent interference. Attached Figure Description

[0059] Figure 1 A flowchart illustrating a passive sonar anti-interference method for multipath coherent and incoherent hybrid broadband signals provided in an embodiment of the present invention;

[0060] Figure 2 A schematic diagram of the geometric structure of a uniform linear array provided in an embodiment of the present invention;

[0061] Figure 3 This invention provides a space-time broadband beamformer without pre-steering delay.

[0062] Figure 4 A schematic diagram illustrating the principle of spatial smoothing technology provided in an embodiment of the present invention;

[0063] Figure 5 This is a schematic diagram comparing the spatial spectra of different algorithms provided in embodiments of the present invention;

[0064] Figure 6 A schematic diagram comparing the root mean square error of angle estimation using different algorithms provided in embodiments of the present invention;

[0065] Figure 7 A beam pattern without zero-point constraints provided in an embodiment of the present invention;

[0066] Figure 8 A beam pattern with zero-point constraints is provided for an embodiment of the present invention. Detailed Implementation

[0067] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0068] like Figure 1 As shown, this embodiment of the invention provides a passive sonar anti-interference method for multipath coherent and incoherent hybrid broadband signals, comprising the following steps:

[0069] S101: The space-time covariance matrix of the entire hydrophone array is constructed using the frequency domain construction method of the space-time covariance matrix;

[0070] S1011: Assume there exists N in the far field. s A sound source, using a conventional beamforming algorithm to initially estimate the N... s The angle of each sound source is used to determine the focusing angle β;

[0071] S1012: To simplify the signal model, it is assumed that the hydrophone array used in this embodiment of the invention is a uniform linear array composed of M hydrophones (it should be noted that this invention is also applicable to other array types), serving as a multipath coherent and incoherent hybrid broadband signal array receiving model, with its geometric distribution as follows. Figure 2 As shown, the entire hydrophone array is divided into K interleaved subarrays, each subarray having m elements, as shown... Figure 4 As shown, the frequency domain data covariance matrix of each subarray is estimated. f j This indicates a specific frequency point within the frequency band;

[0072] Specifically, assuming s i (t) represents the i-th element (i = 1, 2, ..., N) in the sound field. s The emitted signal from the sound source, due to the multipath propagation of sound waves underwater, assumes that the i-th sound source receives a total of L signals at the array. i If the signal is of diameter, then the signal received by the m-th element of the uniform linear array is...

[0073]

[0074] In the formula, δ i,j θ represents the time required for the j-th path of the i-th sound source to reach the phase center reference point of the array; i,j τ represents the incident angle of the j-th path of the i-th sound source; m (θ i,j ) represents for θ i,jThe incident signal in the direction, and the time delay of the m-th array element relative to the phase center reference point of the array. Considering that, under far-field plane wave conditions, the time delay of the sound source reaching different array elements can be replaced by the time delay of the plane wave signal between different array elements, therefore τ m (θ i,j ) can be represented as

[0075]

[0076] Based on the signal receiving model described in formula (1), taking the k-th subarray as an example, firstly, the received signal of this subarray is sampled quickly at a sampling frequency of f. s Sampling time interval T s =1 / f s The data snapshot vector set χ of this subarray is obtained. k (nT s ), n=1,2,…,N t k = 1, 2, ..., K; where N t T represents the total number of data snapshots. s Indicate the sampling interval; then, divide the data snapshot vector set into N... p There are J = ΣL data blocks, each containing J = ΣL snapshot vectors, where Σ is a positive integer. There is no overlap between data blocks. The time-domain data of each element in all data blocks is then subjected to a DFT transform to obtain the corresponding frequency-domain data χ. k (f j ,k1); where k1=1,2,…,N p Finally, the frequency domain data covariance matrix of each subarray is estimated according to formula (3).

[0077]

[0078] Figure 3 The basic array structure of a space-time broadband adaptive beamformer without a pre-steering delay structure is shown. For example... Figure 3 As shown, the space-time broadband beamformer connects a tapped delay line (TDL) of length L after each hydrophone in the uniform linear array. s Indicates the sampling time interval; x m (nT s ) represents the sampled signal input at the m-th TDL; the input signal of each tap can be represented as

[0079]

[0080] The output of the space-time broadband beamformer can be expressed as

[0081]

[0082] Represented in vector form

[0083] y(t)=w H x ST (6)

[0084] In the formula,

[0085]

[0086] S1013: Based on the frequency domain data covariance matrix of each subarray The frequency domain data covariance matrix of the entire hydrophone array was calculated using a spatial smoothing algorithm.

[0087] Specifically, the frequency domain data covariance matrix based on forward spatial smoothing is shown in Equation (8):

[0088]

[0089] S1014: Determine the number of time-domain taps L based on the signal bandwidth and sampling frequency, and construct the time-domain steering vector S of the entire hydrophone array. t (f j );

[0090] Specifically, as shown in formula (9):

[0091]

[0092] S1015: Based on the frequency domain data covariance matrix of the entire hydrophone array Time-domain steering vector S t (f j The spatiotemporal covariance matrix of the entire hydrophone array is constructed by combining the focusing angle β with the rotating subspace algorithm.

[0093] Specifically, this invention primarily employs the coherent signal subspace method to estimate the spatiotemporal covariance matrix. The core idea of ​​the coherent signal subspace method is to focus the signal subspace at non-overlapping frequency points within a frequency band onto a reference frequency point using a focusing matrix T. A key issue in the coherent signal subspace method is constructing the focusing matrix. The Rotational Signal-Subspace (RSS) algorithm is a classic method for constructing the focusing matrix. The RSS algorithm constructs the focusing matrix T(f q The core idea of ​​(β) is to minimize the error between the focused array manifold and the reference frequency point array manifold, that is...

[0094]

[0095] In the formula, Indicates frequency subband f q The frequency domain array manifold. f0 is the reference frequency, and β is the preliminarily estimated focusing angle.

[0096] The constraint is: T(f) q ,β) is a unitary matrix, and

[0097] T H (f q ,β)T(f q ,β)=I (11)

[0098] In the formula, ||·|| F Let I be the Frobenius modulus, and I represent the identity matrix. The number of focus angles is set. The number of signal sources N should be as large as possible. s .

[0099] Equation (10), under constraint (11), yields a focusing matrix as follows:

[0100] T RSS (f q ,β)=V(f q ,β)U H (f q ,β) (12)

[0101] In the formula, U(f) q ,β) and V(f q ,β) are respectively A(f q ,β),A H The left and right singular vectors of (f0,β).

[0102] Finally, based on the RSS algorithm, the constructed spatiotemporal covariance matrix can be expressed as:

[0103]

[0104] Where J1 and J2 are the boundaries of the signal frequency range, J represents the number of snapshot vectors contained in a data block, and T RSS (f j ,β) represents a focusing matrix constructed using the Rotation Subspace RSS algorithm.

[0105] S102: Based on the constructed space-time covariance matrix, the angle-frequency two-dimensional power spectrum of all signals is obtained by using a space-time minimum variance distortion-free response STMVDR beamformer.

[0106] Specifically, while focusing on the frequency domain covariance matrix, the spatiotemporal covariance matrix also retains frequency information. Therefore, the angle-frequency two-dimensional power spectrum of the signal can be obtained by scanning the frequency and angle using an STMVDR beamformer.

[0107] based on Establish the following STMVDR problem

[0108]

[0109] In the formula,

[0110]

[0111] The optimal weight vector satisfying (11) can be obtained using the Lagrange multiplier method.

[0112]

[0113] Correspondingly, the output azimuth-frequency two-dimensional power spectrum is

[0114]

[0115] Based on the azimuth-frequency two-dimensional power spectrum, the spatial spectrum of the hybrid broadband signal can be obtained.

[0116]

[0117] Where P represents the number of spatial spectrum scan points;

[0118] Based on the peak angle of the spatial spectrum, the angles of all signals are estimated. Where, N s Indicates the number of sound sources;

[0119] The corresponding frequency spectrum is obtained based on the angle of the signal:

[0120]

[0121] Where s = 1, 2, ..., N s .

[0122] S103: Calculate the similarity between the frequency spectrum sequences of the desired signal and the interference, determine whether the two are multipath coherent based on the similarity value, and obtain the angle of the desired signal and the angle of the multipath coherent interference.

[0123] Specifically, assume the directions of the two signals are θ. s1 and θ s2 The frequency spectrum sequences output from step S102 are as follows: and q = 1, 2, ..., Q. When two signals have a multipath relationship, theoretically their frequency spectrum sequences have a high degree of similarity. Therefore, the degree of similarity between the frequency spectrum sequences of two signals can be used to determine whether they have a multipath relationship.

[0124] Preferably, in this embodiment, the Pearson correlation coefficient is considered to measure the similarity of the frequency spectrum sequences of the two signals.

[0125] The Pearson correlation coefficient between two sequences X(n) and Y(n) is defined as the quotient of the covariance and standard deviation of the two variables:

[0126]

[0127] In the formula, μ represents the sequence mean, and σ represents the standard deviation of the sequence. The method for determining the multipath relationship between two signals based on the Pearson correlation coefficient of their frequency spectrum sequences is as follows:

[0128]

[0129] In the formula, λ1 is the discrimination threshold.

[0130] By setting an appropriate threshold, the multipath relationship between the desired signal and the interference can be determined, and the angles of the desired signal and the multipath coherent interference can be obtained.

[0131] S104: Set zero-point constraints in the angular direction of multipath coherent interference, set unity gain constraints in the angular direction of the desired signal, and calculate the optimal weight vector using the FCSTBB algorithm based on the optimal phase center reference point.

[0132] Specifically, assume that the angle of the multipath coherent interference estimated in step S103 is ε=[ε1,ε2,…,ε I The expected source angle is θ. d After setting zero-point constraints in the angular direction of multipath coherent interference and unity-gain constraints in the angular direction of the desired signal, the resulting constraint matrix can be expressed as follows:

[0133] C′=[C′0,C′1,…,C′ I ] (twenty two)

[0134] in

[0135]

[0136] In the formula, i=1,2,…,I,Γ opt This is the reference point location for the array phase center of the beamformer.

[0137] The resulting gain response vector can be expressed as

[0138] F′=[F′0,F′1,…,F′ I ] T (twenty four)

[0139] in,

[0140]

[0141] In this embodiment of the invention, considering that multipath coherent interference is not strong interference, the gain at the zero point can be set to 0.01 to reduce the degree of freedom loss of the zero-point constraint, i.e., F i = [0.01, 0.01, ..., 0.01] 1×Q .

[0142] Next, given the M-dimensional independent snapshot vector set {χ(nT)} s ); n = 1, 2, ..., N t}, N t The total number of data snapshots represents the spatiotemporal ML-dimensional observation vector, which can be represented as:

[0143] x ST (nT s )=[χ T (nT s ),χ T ([n-1]T s ),…,χ T ([n-L+1]T s )] T (26)

[0144] Among them, T s =1 / f s f represents the sampling time interval. s Indicates the sampling frequency;

[0145] Based on the spatiotemporal ML-dimensional observation vector, the spatiotemporal covariance matrix is ​​re-estimated using formula (27).

[0146]

[0147] Based on the re-estimated spatiotemporal covariance matrix The optimal weight vector of the FCSTBB algorithm based on the optimal phase center reference point can be expressed as:

[0148]

[0149] Finally, the signal output by the receiving model is w o ′ pt x ST (nT s ).

[0150] Update the data snapshot vector set, and repeat steps S101 to S104 above to perform anti-interference processing on the next set of snapshot vector sets.

[0151] In this embodiment, FCSTBB stands for Frequency-Domain Constrained Space-Time Broadband Beamforming. The derivation of formula (28) is as follows:

[0152] The optimal weight vector of FCSTBB can be obtained by solving the linear constraint minimum variance problem (29) shown in formula (29).

[0153]

[0154] In the formula, Represents the spatial-temporal covariance matrix of the data. and Let a(θ) represent the constraint matrix and the gain response vector, respectively. p ,f q ) is the desired direction θ p The space-time two-dimensional steering vector corresponding to Q frequency points,

[0155]

[0156] In the formula, Represents the Kronecker product;

[0157]

[0158] Using the Lagrange multiplier method, the optimal weight vector satisfying equation (29) can be derived as follows:

[0159]

[0160] Formula (28) is an adaptive adjustment of formula (32).

[0161] When Q=1, this beamformer is also known as a space-time minimum variance distortion-free response (STMVDR) beamformer, and its optimal weight vector can be expressed as:

[0162]

[0163] Example 2

[0164] To verify the effectiveness of the passive sonar anti-interference method provided in the embodiments of the present invention, the present invention also conducted the following simulation.

[0165] The simulation considers a 16-element uniform linear array, with each element followed by 5 tapped delay lines. Assume the signal sampling rate is f. s The spacing between array elements is f s / 2 corresponds to half the wavelength. The frequency range of broadband signals is [0.25f]. s 0.45f s The broadband signal is a broadband signal with a flat spectrum superimposed with multiple single-frequency line spectrum signals, and the simulated noise is Gaussian white noise. This invention mainly focuses on the frequency domain construction method of the spatiotemporal covariance matrix. It employs SS and RSS techniques to preprocess the spatiotemporal covariance matrix, and then proposes a novel beamforming algorithm based on the STMVDR criterion. This beamforming algorithm is used to obtain the angle-frequency two-dimensional power spectrum of the signal. For ease of description, the beamforming algorithm used in this invention is referred to as the SS-RSS-STMVDR algorithm.

[0166] Simulation 1: Angular resolution capability of the SS-RSS-STMVDR algorithm

[0167] In the simulation, a broadband signal is expected to impact the array from 20° with a signal-to-noise ratio of 10dB. The mixed interference consists of a multipath coherent interference from 35° (multipath delay is 5 / f). s () and an incoherent interference from 10°, both with an interference-to-noise ratio of 0dB.

[0168] In the SS-RSS-STMVDR algorithm, when constructing the spatiotemporal covariance based on the frequency domain method, the number of independent snapshot vector sets used is 1280, which is equally divided into 5 data blocks, i.e., N. t =1280, N p =5.

[0169] The number of subarrays in the spatial smoothing is p = 3, and the focusing angle of the RSS algorithm is β = [8°:4°:40°]. Figure 5 Normalized spatial spectra of different algorithms are presented. The algorithms compared are the STMVDR algorithm based on STMVDR beamforming (STMVDR algorithm), the STMVDR algorithm based on RSS preprocessing (RSS-STMVDR algorithm), and the STMVDR algorithm based on spatial smoothing preprocessing (SS-STMVDR algorithm).

[0170] from Figure 5It can be seen that: in the STMVDR algorithm, the two multipath coherent signals cancel each other out severely, and the angle of multipath interference can no longer be distinguished; although the RSS-STMVDR algorithm can distinguish the two multipath coherent signals, the cancellation problem of the two multipath coherent signals is still serious; the SS-STMVDR algorithm achieves better decoherence effect, and the output power of the two multipath coherent signals is significantly improved; the angle resolution capability of the SS-RSS-STMVDR algorithm is improved compared with the SS-STMVDR algorithm and is significantly better than the STMVDR algorithm and the RSS-STMVDR algorithm.

[0171] Simulation 2: Root Mean Square Error of Angle Estimation Using the SS-RSS-STMVDR Algorithm

[0172] Figure 6 The root mean square error (RMSE) of the angle estimation using the SS-RSS-STMVDR algorithm is presented, with a signal direction of 30° and focusing angles of 27°, 31°, and 35°. It can be seen that the angle estimation accuracy of the SS-RSS-STMVDR algorithm is better than that of the STMVDR algorithm at low SNR, but slightly lower at high SNR.

[0173] Simulation 3: Determining Multipath Relationships Based on Signal Power Spectrum Similarity

[0174] Assume the desired signal originates from 20° with an input SNR of 10dB. A multipath coherent interference signal is incident from 35° with an input Interference-Signal Ratio (SIR) of 0dB; an incoherent interference signal is incident from 10° with an input ISR of 0dB. The SS-RSS-STMVDR algorithm can simultaneously obtain the frequency spectrum sequences of all signals at the three angles. Table 1 shows the Pearson correlation coefficients between the frequency spectrum sequences at the three angles. In Table 1, all four algorithms can obtain frequency spectrum sequences with high similarity at 20° and 35°, indicating that the signals at these two angles are multipath signals. However, the Pearson correlation coefficients of the STMVDR and SS-STMVDR algorithms for the two multipath coherent signals are lower than those of the RSS-STMVDR and SS-RSS-STMVDR algorithms, indicating that RSS preprocessing can enhance the similarity of the power spectrum sequences of the two multipath coherent signals output by the algorithm.

[0175] Table 1. Pearson correlation coefficients between mixed signal frequency spectrum sequences (multipath delay 5 / f)

[0176]

[0177] Simulation 4: Coherence Performance of Zero-Point Constraints

[0178] This section determines whether multipath coherent interference cancels out the desired signal by observing whether a null is formed in the desired direction. Assume the FCSTBB beam pointing at 0°, and other conditions are the same as in Simulation 4. Figure 7 and Figure 8 Beam response diagrams of the FCSTBB algorithm without zero-point constraints and with zero-point constraints placed in the multipath coherent interference direction are presented respectively. As shown in the diagrams, due to the mutual cancellation of the desired signal and multipath coherent interference, no effective nulls can be formed in the 20° and 35° directions. Therefore, the FCSTBB algorithm without zero-point constraints cannot effectively decohere the desired signal and multipath coherent interference in the 20° and 35° directions. However, the FCSTBB algorithm based on adaptive zero-point constraints uses zero-point constraints to suppress multipath coherent interference in the 35° direction, while the desired signal is not canceled in the 20° direction, thus forming a deep null in the 20° direction.

[0179] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A passive sonar anti-interference method for multipath coherent and incoherent hybrid broadband signals, characterized in that, include: Step 1: Construct the space-time covariance matrix of the entire hydrophone array using the frequency domain construction method of the space-time covariance matrix; Step 2: Based on the constructed space-time covariance matrix, the angle-frequency two-dimensional power spectrum of all signals is obtained using a space-time minimum variance distortion-free response STMVDR beamformer. Step 3: Calculate the similarity between the frequency spectrum sequences of the desired signal and the interference, determine whether the two are multipath coherent based on the similarity value, and obtain the angle of the desired signal and the angle of the multipath coherent interference; Step 4: Set zero-point constraints in the angular direction of multipath coherent interference and unity-gain constraints in the angular direction of the desired signal. Calculate the optimal weight vector using the FCSTBB algorithm based on the optimal phase center reference point to achieve interference-resistant signal reception.

2. The passive sonar anti-interference method for multipath coherent and incoherent hybrid broadband signals according to claim 1, characterized in that, Step 1 specifically includes: Step 1.1: Use a conventional beamforming algorithm to initially estimate the angles of all signals to determine the focusing angle. ; Step 1.2: Divide the entire hydrophone array into K subarrays and estimate the frequency domain data covariance matrix of each subarray. , ; This indicates a specific frequency point within the frequency band; Step 1.3: Based on the frequency domain data covariance matrix of each subarray The frequency domain data covariance matrix of the entire hydrophone array was calculated using a spatial smoothing algorithm. ; Step 1.4: Determine the number of time-domain taps L based on the signal bandwidth and sampling frequency, and construct the time-domain steering vector of the entire hydrophone array. ; Step 1.5: Based on the frequency domain data covariance matrix of the entire hydrophone array Time-domain steering vector and focusing angle The spatiotemporal covariance matrix of the entire hydrophone array is obtained by combining the rotation subspace algorithm.

3. The passive sonar anti-interference method under multipath coherent and incoherent hybrid broadband signals according to claim 2, characterized in that, Step 1.2 specifically includes: Data snapshot vector set for each subarray Divided into There are 10 data blocks, with no overlap between them; among them, This indicates the total number of data snapshots. Indicates the sampling interval; Perform a DFT transform on the time-domain data of each element in all data blocks to obtain the corresponding frequency-domain data. ;in, ; The frequency domain data covariance matrix of each subarray is estimated according to formula (3). ; （3）。 4. The passive sonar anti-interference method under multipath coherent and incoherent hybrid broadband signals according to claim 2, characterized in that, Step 1.3 specifically includes: （8）。 5. The passive sonar anti-interference method for multipath coherent and incoherent hybrid broadband signals according to claim 2, characterized in that, Step 1.4 specifically includes: （9） in, Indicates the sampling time interval. Indicates the sampling frequency.

6. The passive sonar anti-interference method for multipath coherent and incoherent hybrid broadband signals according to claim 2, characterized in that, Step 1.5 specifically includes: （13） in, Represents the space-time covariance matrix. and The boundary of the signal frequency range, This indicates the number of snapshot vectors contained in a data block. , It is a positive integer. This represents a focusing matrix constructed using the Rotation Subspace RSS algorithm.

7. The passive sonar anti-interference method for multipath coherent and incoherent hybrid broadband signals according to claim 1, characterized in that, Step 2 specifically includes: Obtain the angle-frequency two-dimensional power spectrum of all signals according to formula (17). （17） in, It is the expected direction The above corresponds Estimation of the space-time two-dimensional steering vector at each frequency point Indicates the first One frequency point, ; Represents the space-time covariance matrix. express The inverse matrix; Based on the angle-frequency two-dimensional power spectrum, the spatial spectrum of all signals is obtained: （18） in, Indicates the number of spatial spectrum scan points; Based on the peak angle of the spatial spectrum, the angles of all signals are estimated. ;in, Indicates the number of sound sources; The corresponding frequency spectrum is obtained based on the angle of the signal: （19） in, .

8. The passive sonar anti-interference method under multipath coherent and incoherent hybrid broadband signals according to claim 7, characterized in that, Step 3 specifically includes: Calculate the Pearson correlation coefficient between the frequency spectrum sequences of the desired signal and the interference as their similarity; if the similarity value is... If the signal is not less than the set threshold, the signal and the interference are considered to be multipath signals; otherwise, they are considered to be incoherent signals.

9. A passive sonar anti-interference method for multipath coherent and incoherent hybrid broadband signals according to claim 3, characterized in that, Step 4 specifically includes: Re-estimate the spatiotemporal covariance matrix of the array data according to equation (27). : （27） in, Represents a spacetime ML-dimensional observation vector; Based on the re-estimated spatiotemporal covariance matrix The beamforming weighting vector is calculated according to equation (28). Calculate the output signal : （28） in, and These represent the constraint matrix and gain response vector formed after setting zero-point constraints in the angular direction of multipath coherent interference and setting unity-gain constraints in the angular direction of the desired signal, respectively.

10. A passive sonar anti-interference method for multipath coherent and incoherent hybrid broadband signals according to claim 1, characterized in that, The hydrophone array is a uniform linear array.

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