A marginal element correlation denoising preprocessing method for coherent signal DOA estimation

Abstract

The application discloses a marginal array element correlation denoising preprocessing method for coherent signal DOA estimation and belongs to the field of radio direction finding. Based on the spatial independence of noise, the application proposes a preprocessing method for cross-correlation between a single marginal array element signal and a remaining continuous subarray signal constructing a Toeplitz matrix, filters out noise components generated by self-array element correlation and enlarged to square power in subsequent covariance matrix operation. Simulation results show that the estimation accuracy of the subsequent DOA algorithm is improved after the coherent array element signal is preprocessed by the method. The signal-to-noise ratio required by the method for the same RMSE is 3 dB lower than that of the prior art. In the case that the signal phase difference is close to 180 degrees, the RMSE divergence is slow and the highest is only 3 degrees, which is lower than that of the prior art.

Description

Technical Field

[0001] This invention belongs to the field of radio direction finding, specifically relating to a marginal element correlation denoising preprocessing method for coherent signal DOA estimation. Background Technology

[0002] Direction of Arrival (DOA) estimation is an important research direction in array signal processing, widely used in radar, sonar, wireless communication, and many other fields. With the deepening of theoretical research, DOA estimation methods have been continuously proposed and improved. Among them, subspace decomposition algorithms are the most typical super-resolution direction finding methods, such as the MUSIC method (multiple signal classification) and the ESPRIT method (rotation-invariant subspace). However, when coherent signals caused by multipath propagation exist, the covariance matrix rank deficit problem occurs, leading to reduced estimation performance or even failure. Based on this, corresponding decoherence algorithms have been proposed, mainly of two types: spatial smoothing and matrix reconstruction. Spatial smoothing methods (FBSS) divide a uniform linear array into several overlapping uniform continuous subarrays. The received covariance matrices of the subarrays are averaged, and the resulting equivalent covariance matrix can be proven to be full-rank. However, the subarrays have fewer elements than the original array, resulting in a loss of the effective aperture of the array, especially in low signal-to-noise ratio environments where the performance loss is more severe. Matrix reconstruction methods (TOEP) construct a Toeplitz matrix using the covariance matrix. The rank of this matrix is ​​unaffected by the correlation of the incident signal and depends only on the direction of arrival (DOA). Zhang proposed a multiple-toeplitz matrices reconstruction method (MTOEP) that directly constructs a Toeplitz matrix from the received signal and fully utilizes all covariance information to improve the algorithm's robustness (ZHANG W, HAN Y, JIN M, et al. Multiple-Toeplitz matrices reconstruction algorithm for DOA estimation of coherent signals[J].IEEE Access,2019,7:49504-49512.). However, in the transformed equivalent covariance matrix, the noise component is expanded to the square of the original noise power, leading to weakened noise immunity and degraded direction-finding performance. Summary of the Invention

[0003] To address the performance issues caused by noise component amplification in multiple data matrix reconstruction methods, this invention provides a marginal element correlation denoising preprocessing method for coherent signal DOA estimation.

[0004] The specific technical solution adopted in this invention is as follows:

[0005] This invention provides a marginal element correlation denoising preprocessing method for DOA estimation of coherent signals, comprising the following steps:

[0006] Step 1: Extract marginal array elements from the established uniform linear array receiving signal model, and use the remaining continuous array elements as subarrays. Reconstruct the received signals of the subarrays using the Toeplitz matrix.

[0007] Step 2: Perform cross-correlation operation on the reconstruction matrix of the subarray received signal and the received signal of the corresponding marginal array element of the subarray, filter out the noise related to the array element, and sum the squares of the two sets of results.

[0008] As a preferred embodiment, the method for establishing the uniform linear array receiving signal model in step one is as follows: Let the number of array elements be M = 2M. t The unit spacing between array elements is d = λ / 2, M t Let λ be the matrix dimension, λ be the carrier wavelength, and there be K distinct incident directions, θ1, ..., θ2. K The narrowband far-field signal s(t) is represented as s(t) = [s1(t), ..., s2(t)]. K (t)] T The model for the uniform linear array receiving the signal x(t) is then expressed as follows:

[0009]

[0010] Where x(t)=[x1(t),…,x m (t),…,x M (t)] T x m (t) is the received signal of the m-th array element; n(t) = [n1(t), ..., n m (t),…,n M (t)] T n m (t) represents the m-th array element with a mean of 0 and a power of... Gaussian white noise; A = [a(θ1), ..., a(θ)] k ),…,a(θ K [)] is an M*K dimensional direction matrix, and the direction vectors are...

[0011] Furthermore, the marginal array elements are extracted as follows: Based on the uniform linear array receiving signal model, marginal array elements with indices m=1 and m=M are extracted respectively, and the remaining continuous array elements are used as subarrays. That is, the array received signal x(t) is divided in the following two ways: the first group extracts the right marginal array element signal x. M (t), the remaining left continuous subarray signal x f (t), that is, x(t) = [x f(t); x M (t)]; The second group extracts the left inter-array element signal x1(t), leaving the right continuous sub-array signal x b (t), that is, x(t) = [x1(t); x b (t)].

[0012] Furthermore, the Toeplitz matrix reconstruction method is as follows: For the two subarray signals x... f (t) and x b (t) Reconstructs the Toeplitz matrix, represented as

[0013]

[0014]

[0015] Preferably, the cross-correlation operation in step two is as follows: The Toeplitz reconstruction matrix X... f (t) and X b (t) and the corresponding marginal array element signal x M Performing a conjugate cross-correlation operation on () and x1(t) yields

[0016]

[0017] Among them, X f (t) comes from the array element with indices m = 1, ..., M-1, x M () comes from the array element with index m = M. Due to the independence between the array elements of noise, R f There are no noise components generated by self-element correlation; X b (t) comes from the array element with index m = 2, ..., M, and x1(t) comes from the array element with index m = 1. Due to the independence of the array elements in the noise, R b There are no noise components generated by self-element correlation.

[0018] Furthermore, in step two, the cross-correlation result R of the received signals from the two sets of subarrays and the edge array elements is obtained. f and R b Then, perform conjugate squares and sum them, i.e.

[0019]

[0020] The self-element noise component, whose power is multiplied by a square after covariance matrix operations, is in R x The middle part is also filtered out; then R is processed. x Perform forward and backward spatial smoothing to improve decoherence capability.

[0021]

[0022] Where J is a set of M elements, with all positions except the second diagonal element being 1. t ×M t The dimensional exchange matrix is ​​given; R is the equivalent covariance matrix obtained after marginal element correlation denoising preprocessing; finally, the DOA is estimated by using the traditional DOA algorithm.

[0023] Compared with the prior art, the present invention has the following advantages:

[0024] This invention fully utilizes the independence of noise between array elements, eliminating noise components in the equivalent covariance matrix by avoiding autocorrelation calculations of array element signals, thereby better suppressing noise. Compared with existing matrix reconstruction techniques, the method of this invention has two significant advantages: First, when the signal incident angle interval is small, the root mean square error (RMSE) of the estimation result of the method of this invention is significantly lower than that of existing methods, and the signal-to-noise ratio required for the same RMSE is 3 dB lower than that of existing techniques. Second, as the signal phase difference approaches 180°, the time when the RMSE of the method of this invention begins to be affected is significantly delayed, and the divergence speed is significantly slower, reaching a maximum of only 3°, which is lower than that of existing techniques. These two points demonstrate that the method of this invention has higher estimation performance and stronger decoherence capability. Attached Figure Description

[0025] Figure 1 Here are flowchart (a) and schematic diagram (b) of the method of the present invention;

[0026] Figure 2 A graph showing the root mean square error of DOA estimation as a function of signal-to-noise ratio;

[0027] Figure 3 The graph shows the root mean square error of DOA estimation as a function of phase difference. Detailed Implementation

[0028] The present invention will be further described and illustrated below with reference to the accompanying drawings and specific embodiments. The technical features of each embodiment of the present invention can be combined accordingly, provided that there is no mutual conflict.

[0029] First, establish a uniform linear array signal receiving model. Assume the number of array elements is M = 2M. t The unit spacing between array elements is d = λ / 2, M t Let λ be the matrix dimension, λ be the carrier wavelength, and there be K distinct incident directions θ1, ..., K The narrowband far-field signal s() is represented as s()=[s1(),…,s K ()] T Then the model for the uniform linear array receiving the signal x(t) is expressed as:

[0030]

[0031] Where x()=[x1(),…,x m (t),…, M ()] T x m (t) is the received signal of the m-th array element. n()=[n1(),…,n m (t),…, M (t)] T n m (t) represents the m-th array element with a mean of 0 and a power of... Gaussian white noise. A=[a(θ1),…,a( k ),…,a( K ] is an M*K dimensional direction matrix and direction vector. Here, j is a complex number in mathematics. It can be seen that A is a Vandermonde matrix. When the K incident signals have different directions, A satisfies the condition of full column rank, and the column rank is equal to the number of signal sources K. However, when there are coherent signals in the received signal, A will have a rank deficit, which will affect the subsequent DOA estimation.

[0032] After establishing the uniform linear array signal receiving model, the marginal array elements are first defined as follows: Figure 1 During placement, array elements with indices m=1 and m=M are used. Next, the received signal of the array is divided. For example... Figure 1 As shown, array elements with index m = 1 are extracted from the left side of the array, and array elements with index m = M are extracted from the right side of the array. The remaining consecutive array elements are used as subarrays. That is, the array received signal x(t) is divided in the following two ways: the first group extracts the rightmost array element signal x. M (), the remaining left continuous subarray signal x f (), that is, c(t) = [ f (t); M (t)];The second group extracts the left inter-array element signal x1(), leaving the right continuous sub-array signal x b (), that is, x(t) = [x1(t); b (t)]. Next, for x respectively f (t), x b () performs Toeplitz matrix reconstruction, represented as

[0033]

[0034]

[0035] Here, Y f (t), N f (t), Yb (t), N b (t) is a Toeplitz data matrix constructed in the same way. It is M t *K-dimensional equivalent array direction matrix, and They are respectively m=M t m = M t When the +1 array element is the reference array element, it is the diagonal matrix formed by the complex envelopes of the K received signal sources. For the Toeplitz matrix X... f (t), X b (t) and the corresponding marginal element signal x M Performing a conjugate cross-correlation operation on x1(t) and x2(t) yields...

[0036]

[0037] (·) * Indicates conjugate. X b Performing conjugate correlation operations on x(t) and x1(t) yields...

[0038]

[0039]

[0040] X f (t) comes from the array element with indices m = 1, ..., M-1, x M (t) comes from the array element with index m = M. Due to the independence between the noise array elements, R f There are no noise components generated by self-element correlation, R b Similarly, for R... f and R b Perform conjugate summation, i.e.

[0041]

[0042] in,(·) H This represents the conjugate transpose. This yields the required equivalent covariance matrix, containing all information about the direction of the incident signal. The covariance matrix of the equivalent signal source is... It can be seen that, due to doing X f (t) and x M The correlation of (t) and X bWhen x(t) and x1(t) are correlated, both are correlation operations of the received signals of the cross-array elements. Therefore, the noise term in the formula is 0, thus avoiding the amplification of noise components caused by the subsequent square operation of the covariance matrix. Compared with existing technologies, this effectively improves the noise suppression capability. To further improve the decoherence capability, spatial smoothing technology is applied to R. x Perform a forward and backward spatial smoothing

[0043]

[0044] Where J is an M t ×M t The commutative matrix is ​​given, with all elements except the second diagonal elements being 1 and all others being 0. R is the equivalent covariance matrix obtained after the marginal element correlation denoising preprocessing method. Finally, the DOA estimation of the obtained R is performed using the traditional DOA algorithm.

[0045] To verify the correctness and advancement of the method of the present invention, simulation experiments were conducted, and the results are illustrated in the following examples.

[0046] The simulation environment was set as follows: number of array elements M = 10, two coherent signals with frequencies of 9MHz and incident angles of 6° and 8° respectively, number of snapshots of 100, and element spacing d = λ / 2. After obtaining the equivalent covariance matrix through a marginal element coherent denoising preprocessing method, the ESPRIT algorithm was selected for DOA estimation. The performance criterion was the root mean square error (RMSE), defined as:

[0047]

[0048] Where N is the number of Monte Carlo experiments, and each simulation uses N = 1000 experimental data points to obtain the results. K is the number of signal sources, here K = 2. and λ k These are the estimated angle value of the Kth signal source in the Nth experiment and the theoretical angle value of the Kth signal source, respectively. The simulation results are compared with the existing methods TOEP, MTOEP, and FBSS described in the background section.

[0049] Simulation 1:

[0050] This study analyzes the performance variation of DOA estimation RMSE with signal-to-noise ratio. The independent variable SNR increases from 0 to 40 dB in 5 dB increments. Figure 2It can be seen that among the three matrix reconstruction methods, the performance of the method described in this invention is consistently superior to the other two. For the same RMSE, the signal-to-noise ratio required by the method described in this invention differs from that of MTOEP by 3dB, and the difference is even more significant compared to TOEP. When SNR>35dB, the performance convergence trend of FBSS accelerates, exceeding that of the method described in this invention, meaning that FBSS is more suitable for high signal-to-noise ratio environments.

[0051] Simulation 2:

[0052] Analyze the performance variation of DOA estimation RMSE with phase difference. The signal-to-noise ratio is 20 dB, and a fixed phase difference exists between two coherent signals. From... Figure 3 As can be seen, the curves exhibit a roughly symmetrical distribution with a 0° phase difference, consistent with the theory. When the phase difference approaches 180°, the RMSE of all four methods increases to varying degrees, indicating that the signal phase difference also affects estimation performance. For TOEP and FBSS, performance is affected earlier and diverges faster as the phase difference approaches 180°. The divergence rate of MTOEP and the method of this invention slows down significantly, and the curve of the method of this invention remains below that of MTOEP. The RMSE of the method of this invention is only 3° at most, while that of MTOEP is 5°, meaning that the method of this invention maintains its performance advantage.

[0053] Therefore, this invention proposes a preprocessing method based on the spatial independence of noise. This method involves cross-correlation between the Toeplitz matrix constructed from single-element array signals and remaining continuous subarray signals, filtering out noise components generated by self-element correlation and amplified to square times their power in subsequent covariance matrix operations. Simulation results show that the preprocessing of coherent element signals improves the estimation accuracy of the subsequent DOA algorithm. The signal-to-noise ratio required by this method for the same RMSE differs by up to 3 dB from existing techniques. Even with a signal phase difference close to 180°, the RMSE divergence is slow and only reaches a maximum of 3°, lower than existing techniques.

[0054] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A marginal element correlation denoising preprocessing method for coherent signal DOA estimation, characterized in that, Includes the following steps: Step 1: Extract marginal array elements from the established uniform linear array receiving signal model, and use the remaining continuous array elements as subarrays. Reconstruct the received signals of the subarrays using the Toeplitz matrix. Step 2: Perform cross-correlation operation on the reconstruction matrix of the subarray received signal and the received signal of the corresponding marginal array element of the subarray, filter out the noise related to the array element, and sum the squares of the two sets of results; In step one, the method for establishing the uniform linear array signal receiving model is as follows: Let the number of array elements be... Array element unit spacing , For matrix dimensions, For the carrier wavelength, there is The incident directions are all different and are respectively Narrowband far-field signal , represented as Then the uniform linear array receives the signal. The model is represented as ； in, , It is the first Each array element receives the signal; , It is the first The average value of each element is 0, and the power is... Gaussian white noise; yes 3D direction matrix, direction vector ; The marginal array elements are extracted as follows: Based on the uniform linear array signal receiving model, the indices are extracted respectively. and The edge array elements, and the remaining continuous array elements are used as subarrays, that is, the array receives signals. They are divided into two groups according to the following two methods: the first group extracts the right edge array element signals. The remaining left continuous subarray signals ,Right now The second group extracts the signal from the left inter-element array. The remaining right continuous subarray signals ,Right now .

2. The marginal element correlation denoising preprocessing method for coherent signal DOA estimation according to claim 1, characterized in that, The Toeplitz matrix reconstruction method is as follows: For the signals of the two subarrays respectively... and Perform Toeplitz matrix reconstruction, denoted as ； 。 3. The marginal element correlation denoising preprocessing method for coherent signal DOA estimation according to claim 1, characterized in that, The cross-correlation operation in step two is as follows: Reconstructing the Toeplitz matrix... and and the corresponding edge array element signals and Perform conjugate cross-correlation operation to obtain ； ； in, From index ,…, The array element, From index The array elements, due to the independence of noise between the array elements, There are no noise components generated by self-element correlation; From index ,…, The array element, From index The array elements, due to the independence of noise between the array elements, There are no noise components generated by self-element correlation.

4. The marginal element correlation denoising preprocessing method for coherent signal DOA estimation according to claim 3, characterized in that, In step two, the cross-correlation results of the received signals from the two sets of subarrays and the edge array elements are obtained. and Then, perform conjugate squares and sum them, i.e. ； The self-element noise component, after covariance matrix operation, is expanded to a squared power. The middle part is also filtered out; then the middle part is... Perform forward and backward spatial smoothing to improve decoherence capability. ； in, It is a set of elements where all positions except the second diagonal element are 0. 3D commutative matrix; It is the equivalent covariance matrix obtained after marginal element correlation denoising preprocessing; finally, the traditional DOA algorithm is used to... Perform DOA estimation.

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