A Multiple Signal Separation Method Based on Coupled Trilinear Decomposition

Abstract

The present invention discloses a multi-signal separation method based on coupled trilinear decomposition, comprising the following steps: using a coprime array to collect a mixed electromagnetic signal containing multiple signals, and using the mixed electromagnetic signal as a received sampling signal; defining a received signal model, and constructing the received sampling signal into a coupled trilinear model according to the received signal model; decomposing the constructed coupled trilinear model until the convergence condition is met to obtain an estimated source matrix; and extracting a separated signal from the source matrix. The present invention can solve the problem of signal separation of different incoming wave directions in a coprime array, has good signal separation performance, and has low computational complexity.

Description

Technical Field

[0001] The invention belongs to the technical field of array signal processing, and in particular relates to a multi-signal separation method based on coupled trilinear decomposition. Background Art

[0002] Signal separation is a key issue in radio spectrum monitoring, electronic reconnaissance and wireless communications. Its main implementation method is to use an array composed of multiple sensors to receive electromagnetic signals propagating in space, and to estimate the source signal from the mixed signal contaminated by noise through modern digital signal processing methods.

[0003] At present, the main technologies used for multi-signal separation are independent component analysis, beamforming, and subspace estimation, which have been widely used in traditional non-sparse uniform arrays. For planar array scenarios, subspace rotation methods such as 2D ESPRIT and 2D PM are widely used. They use the signal subspace rotation invariance of the signal vector to estimate parameters and reconstruct signals, and can achieve good results in uniform planar arrays. However, uniform planar arrays are limited by antenna size and the mutual coupling effect between array elements, making it difficult to further improve the performance of signal separation. In recent years, coprime planar arrays have attracted much attention because they have larger array apertures than traditional uniform planar arrays. The invention patent with application date of 20170109 and patent number CN106785486B discloses a generalized mutually prime array antenna structure, which consists of two rectangular uniform arrays, with the number of antennas N1×M1 and N2×M2 respectively, where N1 and N2 are the number of antennas in the x-axis direction, M1 and M2 are the number of antennas in the y-axis direction, and N1, N2 and M1, M2 are two sets of mutually prime numbers; the two subarrays have only one array element overlapped at the origin. The method for angle estimation of the antenna structure of the present invention is: first, according to the MUSIC or ESPRIT algorithm, an angle estimation value with ambiguity is obtained; then, the mutually prime characteristic is used to find the angle estimation value with the coincidence of the ambiguity value, which is the true value of the corresponding theoretical value. The advantages and merits of the antenna structure of the present invention are that the antenna aperture is expanded, the antenna array layout is more flexible, and a relatively high degree of freedom can be obtained. The two subarrays maintain uniform characteristics, and the classic signal arrival angle estimation algorithm can be directly applied. By using the mutually prime characteristics, the angle ambiguity problem can be eliminated. However, the multi-signal separation algorithm for coprime arrays has just started, and there are still obvious deficiencies in related research. Summary of the invention

[0004] Purpose of the invention: In view of the above-mentioned prior art, a multi-signal separation method based on coupled trilinear decomposition is proposed;

[0005] Technical solution: The present invention provides a multi-signal separation method based on coupled trilinear decomposition, comprising the following steps:

[0006] (1) Using a mutually prime array to collect mixed electromagnetic signals containing multiple signals and use them as received sampling signals;

[0007] (2) defining a received signal model, and constructing the received sampled signal into a coupled trilinear model according to the received signal model;

[0008] (3) Decomposing the constructed coupled trilinear model until the convergence condition is met to obtain the estimated source matrix;

[0009] (4) Extract the separation signal from the source matrix.

[0010] Furthermore, the mutually prime arrays described in step (1) satisfy the following characteristics:

[0011] The total number of elements in the mutually prime array is N 1 M 1 +N 2 M 2 -1, the array elements are arranged according to the structure of generalized coprime array; the entire array can be decomposed into two scales of N 1 ×M 1 and N 2 ×M 2 uniform rectangular subarray; where N i 、M i are the number of array elements of sub-array i (i∈{1,2}) along the x-axis and y-axis respectively, N 1 、N 2 and M 1 、M 2 are two pairs of mutually prime numbers.

[0012] Furthermore, the implementation process of step (2) is as follows:

[0013] Decompose the coprime array into two uniform rectangular sub-arrays, then the received signal model of sub-array i (i∈{1,2}) is:

[0014]

[0015] in, represents the array manifold matrix of the entire subarray i, represents the direction matrix of sub-matrix i in the y-axis direction, represents the direction matrix of sub-matrix i in the x-axis direction, represents the source matrix, represents the noise matrix of subarray i, ⊙ represents the Kronecker product of the matrix, R represents the number of incident signals, and L represents the number of time domain sampling points.

[0016] The received signal model The coupled trilinear model in tensor form under mutually prime arrays is expressed as:

[0017] for The tensor form of ;

[0018] in, and They are and The rth column vector of , which represents the steering vector of sub-matrix i on the x-axis and y-axis, s r is the rth column vector of the source matrix, which represents the rth source signal vector, 1≤r≤R, and the operator represents the outer product of tensors;

[0019] Coupled trilinear model Three data matrices are obtained by splitting and concatenating along three different dimensions: and The data matrix and Merge to get the overall data matrix of the combined multi-subarray

[0020] Furthermore, the step (3) comprises the following steps:

[0021] (31) Initialize the matrix Where ∧ represents the least squares estimate;

[0022] (32) Calculate the least squares estimate of S, Among them, the superscript represents pseudo-inverse;

[0023] (33) For each sub-matrix i, calculate the matrix The least squares estimate of T represents the transpose of the matrix;

[0024] (34) For each sub-matrix i, use The Vandermonde matrix structure characteristics reconstruct the least squares estimate

[0025] (35) For each submatrix i, calculate the matrix The least squares estimate of

[0026] (36) For each sub-matrix i, use The Vandermonde matrix structure characteristics reconstruct the least squares estimate

[0027] (37) Determine whether the set convergence condition is met. If it is met, the algorithm stops; otherwise, return to step (32) to continue calculating the new estimated value. The residual sum of squares is defined as Where k represents the kth iteration. When |ψ(k+1)-ψ(k)| / ψ(k)<ε, it is determined that the algorithm has reached a convergence state, and ε is a set threshold.

[0028] Furthermore, the specific process of step (34) is as follows:

[0029] For each subarray-source combination (i,r), i∈{1,2},r∈{1,...,R}, calculate its rotation factor Among them, the vector For vector The remaining part after deleting the last row of elements, vector For vector Delete the remaining part after deleting the first row of elements; according to the calculated rotation factor Reconstruction The new Replace the original The corresponding column vector in completes the least squares estimate Reconstruction of

[0030] Furthermore, the specific process of step (36) is as follows:

[0031] For each subarray-source combination (i,r), i∈{1,2},r∈{1,...,R}, calculate the rotation factor in, for Delete the remaining part after the last row of elements. for Delete the remaining part after deleting the first row of elements; according to the calculated rotation factor Reconstruction The new Replace the original The corresponding column vector in completes the least squares estimate reconstruction.

[0032] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1. The multi-signal separation method provided by the present invention applies the coupled tensor decomposition theory to the field of array signal processing, constructs the coprime array signal model into a coupled trilinear model, solves the problem of signal separation with different incoming wave directions in the coprime array, and has high separation accuracy;

[0034] 2. The method of the present invention makes full use of the Vandermonde structure of the factor matrix of the coupled trilinear model in the coprime array scenario, improves the coupled trilinear alternating least squares algorithm, enables the algorithm to reach the convergence stationary point faster, and reduces the computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a flow chart of the present invention;

[0036] Figure 2 It is a schematic diagram of the coprime array structure involved in the method of the present invention;

[0037] Figure 3 is a time domain waveform diagram of the source signal in this embodiment;

[0038] Figure 4 The time domain waveform diagram of the separated signal corresponding to the source signal obtained by the processing method of the present invention when the signal-to-noise ratio is 5dB;

[0039] Figure 5 A comparison chart of the calculation time of the method of the present invention, the standard coupled trilinear decomposition method and the subarray independent trilinear decomposition method under the conditions of the same array structure and the same number of sampling points;

[0040] Figure 6 It is a comparison chart of the signal separation performance of the method of the present invention, the standard coupled trilinear decomposition method and the subarray independent trilinear decomposition method under the conditions of the same array structure and the same number of sampling points. DETAILED DESCRIPTION

[0041] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0042] The present invention provides a multi-signal separation method based on coupled trilinear decomposition, such as Figure 1 As shown, the specific steps include:

[0043] Step 1: Use a mutually prime array to collect a mixed electromagnetic signal containing multiple signals and use it as a received sampling signal.

[0044] Figure 2 The schematic diagram of the coprime array structure involved in the method of the present invention is shown in FIG. The total number of array elements of the coprime array is N 1 M 1 +N 2 M 2 -1, the array elements are arranged according to the structure of generalized coprime array; the entire array can be decomposed into two scales of N 1 ×M 1 and N 2 ×M 2uniform rectangular subarrays, denoted as subarray 1 and subarray 2; where the spacings between adjacent array elements in subarray 1 along the x-axis and y-axis are and The spacings between adjacent array elements in subarray 2 along the x-axis and y-axis are and N 1 、N 1 and M 1 、M 2 are two pairs of mutually prime numbers, and λ is the signal wavelength.

[0045] Step 2: Define the received signal model and reconstruct the received sampled signal into a coupled trilinear model.

[0046] Assume that there are R far-field narrowband incoherent signals incident on this coprime array, and each signal has a different incident angle (θ r ,φ r ), r = 1, 2, ..., R, where θ r and φ r Represent the elevation angle and azimuth angle of the rth signal respectively. Decompose the coprime array into two uniform rectangular sub-arrays, then the received signal model of sub-array i (i∈{1,2}) is:

[0047]

[0048] in, represents the array manifold matrix of the entire subarray i, represents the direction matrix of sub-matrix i in the y-axis direction, represents the direction matrix of sub-matrix i in the x-axis direction, represents the source matrix, N (i) represents the noise matrix of sub-array i, ⊙ represents the Kronecker product of the matrix, and L represents the number of sampling points in the time domain.

[0049] According to the basic theory of array signals, the direction matrix and By the steering vector and It is related to the array structure and the signal incident direction. Under the ideal array model and free space propagation assumption, the direction matrix and With Vandermonde structure, the guiding vector and It can be written as:

[0050]

[0051]

[0052] Among them, u r = sinθ r cosφ r , r = sinθ r sinφ r .

[0053] According to the coupled tensor decomposition model, the coupled trilinear model in tensor form under coprime arrays is expressed as:

[0054]

[0055] Among them, s r is the r-th column vector of the source matrix, which represents the r-th source signal vector, 1≤r≤R, Represents a tensor outer product.

[0056] The received sampling signal of the subarray is re-used as a third-order tensor according to the coupled trilinear model Indicates that three data matrices are obtained by cutting and splicing along three different dimensions: and

[0057] The data matrix and Merge to get the overall data matrix of the joint multi-subarray, which is expressed as:

[0058]

[0059] Step 3: Decompose the coupled trilinear model using the improved coupled trilinear alternating least squares algorithm until the convergence condition is met to obtain the estimated source matrix.

[0060] (1) Initialize the matrix

[0061] (2) Calculate the least squares estimate of S, Among them, the superscript represents pseudo-inverse;

[0062] (3) For each sub-matrix i, calculate the matrix The least squares estimate of

[0063] (4) For each sub-array i, use The Vandermonde matrix structure features the reconstruction factor matrix The specific process is:

[0064] For each subarray-source combination (i,r), i∈{1,2},r∈{1,...,R}, calculate its rotation factor Among them, the vector For vector The remaining part after deleting the last row of elements, vector For vector Delete the remaining part after deleting the first row of elements; according to the calculated rotation factor Reconstruction The new Replace the original The corresponding column vector in completes the least squares estimate Reconstruction of

[0065] (5) For each sub-matrix i, calculate the matrix The least squares estimate of

[0066] (6) For each sub-array i, use The Vandermonde matrix structure features the reconstruction factor matrix The specific process is:

[0067] For each subarray-source combination (i,r), i∈{1,2},r∈{1,...,R}, calculate the rotation factor in, for Delete the remaining part after the last row of elements. for Delete the remaining part after deleting the first row of elements; according to the calculated rotation factor Reconstruction The new Replace the original The corresponding column vector in completes the least squares estimate reconstruction.

[0068] (7) Calculate the convergence rate of the residual sum of squares. When it is less than a certain smaller value, the algorithm stops; otherwise, return to step (32) to continue calculating the new estimated value.

[0069] Define the residual sum of squares as Where k represents the kth iteration. When |ψ(k+1)-ψ(k)| / ψ(k)<ε, it is determined that the algorithm has reached a convergence state, and ε is a set threshold.

[0070] Step 4: Extract the separation signal from the decomposed source matrix.

[0071] After the coupled trilinear decomposition algorithm in step 3 is completed, the final source matrix Extract by row and get R separated signal vectors {s r |1≤r≤R}.

[0072] Take a coprime array with 38 elements as an example, the size of subarray 1 is N 1 ×M 1 =5×3, the size of subarray 2 is N 2 ×M 2 =6×4, assuming that there are four modulation signals with different waveforms in the space, their mathematical expressions are s 1 (t) = cos(2π×6×10 6 t),s 2 t=π×8×10 11 t 2 +2π×2×10 6 t),s 3 (t) = cos(2π×4×10 5 t)cos(2π×5×10 6 t),s 4 (t) = cos(2π×(4×10 6 +8×10 4 cos(π×3×10 5 t))t), the arrival angles are (θ 1 ,φ 1 )=(10°,15°),(θ 2 ,φ 2 )=(20°,25°) and (θ 3 ,φ 3 )=(30°,35°),(θ 3 ,φ 3 )=(40°,45°), the sampling frequency is 100MHz.

[0073] In order to measure the signal separation performance of the algorithm, the definition of the relative error between the separated signal and the source signal is given:

[0074]

[0075] Among them, Λ and Π represent the optimal diagonal matrix and permutation matrix, respectively, which are used to solve the scale and permutation ambiguity effects in the signal separation algorithm. In addition, in order to compare the computational complexity of the algorithm, the running time of different algorithms is recorded during the simulation process.

[0076] Figure 3 is the time domain waveform diagram of the source signal in this embodiment, Figure 4The time domain waveform of the separated signal obtained by the processing method of the present invention when the signal-to-noise ratio is 5dB, the number of time domain sampling points L = 600. Figure 3 and Figure 4 It can be seen that the method of the present invention can effectively separate the source signals under the coprime array, and the separated signals have no obvious distortion.

[0077] Figure 5 This is a comparison chart of the computation time of the method of the present invention, the standard coupled trilinear decomposition method, and the subarray independent trilinear decomposition method under the same array structure and the same number of sampling points. The number of time domain sampling points L = 1000, and the number of simulation statistics is 400. The computation time of the subarray independent trilinear decomposition method is equal to the sum of the time consumed by the two subarray independent decompositions. Figure 5 It can be seen that the computational complexity of the method of the present invention is lower than that of the other two compared methods.

[0078] Figure 6 This is a comparison chart of the signal separation performance of the method of the present invention, the standard coupled trilinear decomposition method and the subarray independent trilinear decomposition method under the same array structure and the same number of sampling points. The number of time domain sampling points L = 1000, the number of simulation statistics is 400. Figure 6 It can be concluded that the signal separation performance of the method of the present invention is better than that of the subarray independent trilinear decomposition method, and is close to that of the standard coupled trilinear decomposition method. As the signal-to-noise ratio increases, the separation performance is also improved.

[0079] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. 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; and these modifications or replacements, without departing from the principles of the present invention, should be regarded as within the scope of protection of the present invention.

Claims

1. A multi-signal separation method based on coupled trilinear decomposition, characterized in that: The method comprises the following steps: 1) Using a mutually prime array to collect a mixed electromagnetic signal containing multiple signals, and using the mixed electromagnetic signal as a received sampling signal; 2) Define a received signal model, and construct the received sampled signal into a coupled trilinear model according to the received signal model; 3) Decompose the constructed coupled trilinear model until the convergence condition is met to obtain the estimated source matrix; 4) Extract the separation signal from the source matrix; The total number of elements of the coprime array in step 1) is The array elements are arranged according to the generalized mutually prime array antenna structure, and the mutually prime array is decomposed into two scales of and A uniform rectangular subarray of , Sub-array i， The number of array elements along the x-axis and the y-axis, , and , are two pairs of coprime numbers, through the submatrix i， receiving the mixed electromagnetic signal; The subarray described in step 2) i , The received signal model for: ； in, Represents a subarray i The array manifold matrix, Represents a subarray i The direction matrix in the y-axis direction, Represents a subarray i The direction matrix in the x-axis direction, represents the source matrix, Represents a subarray i The noise matrix, Represents the matrix Kronecker product, R represents the number of incident signals, L represents the number of sampling points in the time domain; the received signal model The coupled trilinear model in tensor form under mutually prime arrays is expressed as: , for The tensor form of ; in, and They are direction matrices and No. r column vectors, representing sub-matrices i Steering vectors on the x-axis and y-axis; is the source matrix r A column vector, representing the r source signal vector, , operator Represents the outer product of tensors; couples the trilinear model Three data matrices are obtained by splitting and concatenating along three different dimensions: , and ; The data matrix and Merge to get the overall data matrix of the combined multi-subarray , which is expressed as: ； Step 3) specifically includes the following steps: 31) Initialize the matrix , , , ; where ⋀ represents the least squares estimate; 32) Calculation The least squares estimate of , ;in, The superscript indicates pseudoinverse; 33) For each subarray i , calculate the matrix The least squares estimate of , ; T represents the transpose of the matrix; 34) For each subarray i ,use of Vandermonde Reconstructing the least squares estimate using matrix structural characteristics ; 35) For each subarray i , update the matrix The least squares estimate of , ; 36) For each subarray i ,use of Vandermonde Reconstructing the least squares estimate using matrix structural characteristics ; 37) Determine whether the set convergence condition is met. If so, the algorithm stops and outputs the source matrix; otherwise, return to step 32) to continue calculating the new estimate.

2. A multi-signal separation method based on coupled trilinear decomposition as claimed in claim 1, characterized in that: The specific steps of step 34 are as follows: for each subarray-source combination ( i , r ), , , calculate its rotation factor , where the vector For vector The remaining part after deleting the last row of elements, vector For vector Delete the remaining part after deleting the first row of elements; according to the calculated rotation factor , reconstruct ; The new Replace the original The corresponding column vector in completes the least squares estimate The specific steps of step 36 are as follows: for each sub-array-source combination ( i , r ), , , calculate the rotation factor ,in, for Delete the remaining part after the last row of elements. for Delete the remaining part after deleting the first row of elements; according to the calculated rotation factor , reconstruct ; The new Replace the original The corresponding column vector in completes the least squares estimate reconstruction.

Images