A DOA estimation method based on the anti-diagonal of the second-order statistics matrix of a non-circular near-field quasi-stationary signal

Abstract

This invention discloses a DOA estimation method based on the anti-diagonal line of the second-order statistical matrix of a non-circular near-field quasi-stationary signal, belonging to the field of array signal processing. Addressing the difficulty in discerning DOA estimation for non-circular near-field quasi-stationary signals when the source angle difference is small, this invention reconstructs a virtual equivalent signal by using the anti-diagonal line of the pseudo-covariance matrix and the parallel lines of the anti-diagonal line of the covariance matrix, thus achieving DOA estimation for non-circular near-field signals. The method implementation steps include: calculating the covariance matrix and pseudo-covariance matrix of the signal at each time frame of the quasi-stationary signal; extracting the parallel lines of the anti-diagonal line of the covariance matrix and the elements of the anti-diagonal line of the pseudo-covariance matrix, reconstructing them into an equivalent signal; and using the classical MUSIC algorithm to estimate the parameters of the equivalent signal. This scheme avoids the spectral peak overlap problem that occurs when the source angle difference is small, improving the accuracy of DOA estimation.

Description

Technical Field

[0001] This invention relates to a DOA estimation method based on the antidiagonal of the second-order statistics matrix of a non-circular near-field quasi-stationary signal, belonging to the field of wireless communication system technology. Background Technology

[0002] Direction-of-arrival (DOA) estimation is an important area in array signal processing. By extracting information from the statistics of the received signal from the antenna and performing mathematical processing, the azimuth angle of the signal source relative to the array reference point can be obtained. It has wide applications in sonar, radar, and wireless communication. Quasi-stationary signals represent a class of non-stationary signals whose second-order statistics remain unchanged over short periods but change over long periods, exhibiting different characteristics. In practical applications, speech and audio signals are often considered quasi-stationary signals, leading to the important application of DOA estimation for audio signals in environments such as microphone array processing of speech signals.

[0003] In current DOA estimation research, most incident signals are modeled as circular signals, with the in-phase (real) and quadrature (imaginary) components of the corresponding transmitted signal being uncorrelated real-valued Gaussian random variables with the same variance. This approach primarily utilizes information from the signal covariance matrix to achieve DOA estimation. However, non-circular signals are very common in modern mobile communications and other fields. Some common digital modulation signals, such as binary phase-shift keying, minimum phase-shift keying, amplitude shift keying, and pulse amplitude modulation, all exhibit non-circularity. Intersecting with circular signals, non-circular signals utilize in-phase and quadrature components that are correlated or have different variances, leading to IQ imbalance. Appropriately applying the additional information introduced by IQ imbalance can improve DOA estimation performance.

[0004] In DOA estimation, spatial sources can be categorized into far-field and near-field signals based on their distance from the receiving array. Far-field sources are located in the Fraunhofer region of the array, and their propagation in space can be considered as parallel waves. Near-field sources are located in the Fresnel region of the array aperture; these sources cannot be considered as parallel waves, and DOA estimation in this case depends not only on the angle but also on the distance. In recent years, DOA estimation for near-field signals has received increasing attention. Since it involves multi-parameter joint estimation, reducing the estimation dimensionality has become an important metric for evaluating near-field signal algorithms.

[0005] DOA estimation for non-circular near-field quasi-stationary signals is still in its early stages but has broad development prospects. Most DOA estimation algorithms for non-circular near-field signals first estimate the angle parameter θ, and then... The distance parameter r is estimated. However, when the angular distance is relatively small, the estimation of the angle may result in spectral peak overlap or even peak mixing, leading to errors in the estimated angle or the inability to properly identify the number of spectral peaks, thus affecting the estimation of the distance r. Summary of the Invention

[0006] Purpose of the invention: In order to overcome the shortcomings of the existing technology, this invention proposes a DOA estimation method based on the anti-diagonal of the second-order statistics matrix of non-circular near-field quasi-stationary signals. When the source angles are close together, it can avoid the problem of overlapping spectral peaks in the estimated spectrum and improve the estimation accuracy of non-circular near-field signals. In terms of algorithm complexity, it is also much less than the traditional two-dimensional MUSIC algorithm.

[0007] Technical solution: To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for estimating DOA based on the anti-diagonal of the second-order statistics matrix of a non-circular near-field quasi-stationary signal includes the following steps:

[0009] Step 1: Model the quasi-stationary signal under near-field conditions. The near-field quasi-stationary incident signal vector is s(t), consisting of K signals, each divided into F frames, with S snapshots per frame. It is assumed that the signals are uncorrelated. s(t) is received by a symmetrical uniform linear array, with array elements ranging from -L to L. Assuming the noise is additive white Gaussian noise, the received signal vector x(t) can be expressed as:

[0010] x(t) = A(ω, φ)s(t) + n(t)

[0011] Where n(t) is the Gaussian white noise vector, and s0(t) is the real signal vector. Let ψ be the non-circular phase matrix, and A(ω, φ) be the array manifold containing two parameters θ and r. For ease of engineering processing, these are replaced with electrical angles ω and φ, and their relationship is as follows:

[0012]

[0013]

[0014] Where λ is the signal wavelength and d is the element spacing.

[0015] Step 2: Calculate the estimated value of the signal covariance matrix within each time frame i. and pseudo-covariance matrix estimates

[0016]

[0017]

[0018] Where S is the number of snapshots in each time frame, F is the number of time frames, H is the conjugate transpose symbol, and T is the transpose symbol.

[0019] Step 3: Extract the estimated value of the covariance matrix Anti-diagonal vector parallel line and pseudo-covariance matrix estimates anti-diagonal As an equivalent received signal, Perform a mean-reduction operation to obtain an equivalent received signal with zero mean. Each signal has an F-frame snapshot:

[0020]

[0021]

[0022] Extracting covariance matrix estimates Anti-diagonal vector parallel line and pseudo-covariance matrix estimates anti-diagonal and Its position in the matrix is:

[0023]

[0024]

[0025]

[0026]

[0027] Where r i，j and c i，j They are and The element in the i-th row and j-th column, represent The l-th parallel line of the anti-diagonal (l is an integer, ranging from {-2L…2L}, positive numbers represent...) The parallel line to the lower right of the anti-diagonal line, represented by a plural. (The parallel line to the upper left of the anti-diagonal line) represent The opposite diagonal; This can be considered as an equivalent received signal, with each signal having an F-frame snapshot. Perform a mean-reduction operation to obtain an equivalent received signal with zero mean.

[0028]

[0029]

[0030] This section explains the equivalent signal through theoretical derivation. The construction principle ignores the influence of noise. and Theoretical value u l [i] and v0[i] are respectively:

[0031]

[0032]

[0033] Where ψ k For the non-circular phase of the k-th signal, u l [i] is converted to matrix form as follows

[0034]

[0035] This is a virtual direction vector. Let p[i] be a virtual array manifold, and p[i] be the equivalent incident signal, which can be specifically represented as:

[0036]

[0037]

[0038]

[0039] If we consider i as a snapshot, then u l [i] can be considered as an equivalent received signal, since u l The mean of [i] is not zero, so u needs to be adjusted. l [i] Mean reduction processing, the equivalent received signal after mean reduction is defined as... Then we have:

[0040]

[0041] Where E is the sign of the expected value, using the covariance matrix R x The equivalent received signal formed by the l-th anti-diagonal element of [i] The estimated parameter is actually ω+lφ;

[0042] Similarly, v0[i] can be converted into matrix form as follows:

[0043]

[0044] This is a virtual direction vector. Let p[i] be a virtual array manifold, and p[i] be the equivalent incident signal, which can be specifically represented as:

[0045]

[0046]

[0047]

[0048] If we consider i as a snapshot, then v0[i] is the equivalent received signal. Since the mean of v0[i] is not zero, we need to de-mean v0[i]. The equivalent received signal after de-meaning is defined as follows: Then there is

[0049]

[0050] Using the pseudo-covariance matrix C x The equivalent received signal formed by the anti-diagonal elements of [i] The estimated parameter is φ.

[0051] In summary use ω+lφ can be estimated using The parameter φ can be estimated. By combining the two, ω and φ can be estimated, and then θ and r can be estimated.

[0052] Step 4, Calculation covariance matrix estimate and covariance matrix estimate

[0053]

[0054]

[0055] Step 5, for and Perform eigenvalue decomposition:

[0056]

[0057]

[0058] in, and Represent and The signal subspace spanned by the eigenvectors corresponding to the K largest eigenvalues; and Represent and The remaining smaller eigenvalues ​​correspond to the noise subspace spanned by the eigenvectors; These represent diagonal matrices formed by the eigenvalues.

[0059] Step 6: Perform a spectral space search on φ; the K largest values ​​are the parameter values ​​to be estimated. The constructed spatial spectrum P(φ) is:

[0060]

[0061] It is important to note that The corresponding virtual array is not a continuous uniform linear array, but this does not affect the final parameter estimation because the array's direction vector is known:

[0062]

[0063] Step 7: Perform a spectral space search on ω+lφ, l∈{-2L, ..., 2L}. The K largest values ​​are the parameter values ​​to be estimated. The spatial spectrum P(ω+lφ) is:

[0064]

[0065] in

[0066]

[0067] Step 8: Obtain the result through parameter pairing. corresponding Through parameters and Solve and

[0068]

[0069]

[0070] Furthermore, in step 1, the array manifold A(ω, φ) is represented as

[0071] A(ω,φ)=[a(ω1,φ1),a(ω2,φ2),…,a(ω K , φ K )]

[0072] Since the array is a symmetrical array, the direction vector a(ω) k , φ k )for

[0073]

[0074]

[0075]

[0076] Since s(t) is a non-circular signal, for the sake of convenience, we assume it to be a completely non-circular signal, then we have:

[0077] s(t)=Ψ 1 / 2 s0(t)

[0078] Where s0(t) is a real signal vector, Given a non-circular phase matrix and parameter ψ representing the non-circular phase, the received vector x(t) can be rewritten as:

[0079] x(t)=A(ω,φ)Ψ 1 / 2 s0(t)+n(t)

[0080] Furthermore, in step 2 and The corresponding theoretical values ​​are respectively

[0081]

[0082]

[0083] in, Let sk(t) be the power of the i-th frame of the signal. This represents the white noise power. Note that since s(t) is a non-circular signal, the pseudo-covariance matrix is ​​not zero. The additional information introduced by the pseudo-covariance matrix can be used to improve the estimation accuracy. For ordinary circular signals, the pseudo-covariance matrix is ​​zero due to rotation invariance.

[0084] Furthermore, in step 4 and The corresponding theoretical value is:

[0085]

[0086]

[0087] Furthermore, the estimated value of the spatial spectrum function P(ω+lφ) obtained in step 7 is ω+lφ. When the incident signal angles are close, a suitable value is selected. That is, selecting the covariance matrix Appropriate diagonal parallel lines can widen the difference between estimated values ​​and avoid spectral peak overlap.

[0088] Furthermore, after performing parameter estimation using the spatial spectra P(ω) and P(ω+lφ) in step 8, parameter pairing is also required: for any Search all Obtain m that is paired with k:

[0089]

[0090] After parameter pairing is completed, the paired parameters can be obtained. and

[0091]

[0092]

[0093] Through parameters and It can be solved and

[0094]

[0095]

[0096] Beneficial effects:

[0097] This invention provides a DOA estimation method based on the anti-diagonal of the second-order statistical matrix of a non-circular near-field quasi-stationary signal, which can effectively improve the accuracy of DOA estimation. Utilizing the information carried by the anti-diagonal of the pseudo-covariance matrix of the non-circular signal, it reconstructs the signal into an equivalent signal, achieving separate estimation of electrical angle parameters under near-field conditions. Simultaneously, by utilizing the information carried in the parallel lines of the anti-diagonal of the covariance matrix, it solves the problem of spectral peak overlap that occurs when the angle difference is small. Its advantages are:

[0098] 1. Based on the equivalent signal, the estimation of parameters ω and φ is decoupled, and the high-complexity two-dimensional joint parameter spectrum search is transformed into two separate one-dimensional parameter spectrum searches, which effectively reduces the complexity of the near-field DOA estimation algorithm.

[0099] 2. By fully utilizing the characteristic that the pseudo-covariance matrix of non-circular signals is not zero, an equivalent incident signal based on the anti-diagonal of the pseudo-covariance matrix of non-circular signals is constructed, thereby realizing the independent estimation of the electrical angle φ.

[0100] 3. By constructing an equivalent incident signal with anti-diagonal parallel lines of the covariance matrix, the parameter to be estimated is changed from ω to ω+lφ, which expands the spacing between spectral peaks and avoids peak overlap. Even when the angle difference of the incident signals is small, it can still achieve good DOA estimation results. Attached Figure Description

[0101] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following description is provided with accompanying drawings of the relevant technical solutions in the embodiments of the present invention or the prior art. It should be understood that the accompanying drawings described below are only for the purpose of clearly illustrating some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0102] Figure 1 This is a schematic diagram of the array structure of the present invention;

[0103] Figure 2 This is a simulation result diagram of the present invention, which estimates the ω spectrum of the incident signal using only the antidiagonal elements of the covariance matrix.

[0104] Figure 3 This is a simulation result diagram of the present invention, which uses the anti-diagonal parallel line elements of the covariance matrix to estimate the ω+3φ spectrum of the incident signal.

[0105] Figure 4 This is a simulation result diagram of the estimation of the φ spectrum of the incident signal using the antidiagonal elements of the pseudo-covariance matrix according to the present invention.

[0106] Figure 5 This is a comparison chart of the root mean square error of the algorithm in angle estimation under different signal-to-noise ratios.

[0107] Figure 6 This is a comparison chart of the root mean square error of the algorithm in distance estimation under different signal-to-noise ratios. Detailed Implementation

[0108] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to specific embodiments.

[0109] This invention provides a DOA estimation method based on the anti-diagonal of the second-order statistical matrix of a non-circular near-field quasi-stationary signal. The antenna structure used in this embodiment is a symmetrical uniform linear array with M = 2L + 1 array elements, the element values ​​range from [-L, L], and the reference point is zero. The incident signal used is a quasi-stationary BPSK signal with F frames, each frame having S snapshots, and the signal is distributed in the near-field region of the array antenna.

[0110] The implementation steps are as follows:

[0111] 1. Building a data model

[0112] Suppose K data come from (θ) k r k Narrowband quasi-stationary non-circular near-field signal s k(t) The signal is incident on a symmetrical uniform linear array with elements ranging from [-L, L]. The signals are uncorrelated with each other. The array structure is as follows: Figure 1 As shown. If additive white Gaussian noise is considered, the array-received signal can be expressed in vector form as:

[0113] x(t) = A(θ, r)s(t) + n(t)

[0114] Where s(t) is the incident signal vector, x(t) is the received signal vector, A(θ, r) is the array manifold, and n(t) is the Gaussian white noise vector. Since the incident signal is a near-field signal, for ease of expression, θ and r can be replaced by electrical angles ω and φ:

[0115]

[0116]

[0117] The array manifold can be re-represented as:

[0118] A(θ,r)=A(ω,φ)=[a(ω1,φ1),a(ω2,φ2),…,a(ω K , φ K )]

[0119] Because a symmetrical uniform linear array is used, the direction vector a(ω) k , φ k )for:

[0120]

[0121] Since the incident signal is non-circular, assuming it is a completely non-circular signal, the received signal model can be further characterized as:

[0122] x(t)=A(ω,φ)Ψ 1 / 2 s0(t)+n(t)

[0123] in, This is a non-circular phase matrix, where parameter ψ represents the non-circular phase. Since the incident signal is a quasi-stationary signal, the power at each time frame i... The sequence formed It exhibits a wide stability property.

[0124] 2. Calculate the second-order statistics matrix.

[0125] Calculate the estimated value of the signal covariance matrix for each time frame i. and pseudo-covariance matrix estimates

[0126]

[0127]

[0128] and The corresponding theoretical values ​​are respectively

[0129]

[0130]

[0131] in, For s k The power of the i-th frame signal in (t), This represents the white noise power. Note that since s(t) is a non-circular signal, the pseudo-covariance matrix is ​​not zero. The additional information introduced by the pseudo-covariance matrix can be used to improve the estimation accuracy. For ordinary circular signals, the pseudo-covariance matrix is ​​zero due to rotation invariance.

[0132] 3. Constructing an equivalent signal

[0133] 3.1 Constructing the equivalent signal

[0134] Extracting covariance matrix estimates Anti-diagonal vector parallel line As an equivalent signal, its position in the matrix can be represented as

[0135]

[0136]

[0137] Where r i，j yes The element in the i-th row and j-th column, represent The l-th parallel line of the anti-diagonal (l is an integer, ranging from {-2L…2L}, positive numbers represent...) The parallel line to the lower right of the anti-diagonal line, represented by a plural. (The parallel line to the upper left of the anti-diagonal line) Perform a mean-reduction operation to obtain an equivalent received signal with zero mean.

[0138]

[0139] The following analysis uses theoretical values ​​to determine the zero-mean equivalent signal. The construction principle. Ignoring the influence of noise, Theoretical value u l [i] can be represented as

[0140]

[0141] will u l [i] is converted to matrix form as follows

[0142]

[0143] in

[0144]

[0145]

[0146]

[0147] If we consider i as a snapshot, then p[i] can be considered as the equivalent incident signal. Considered as an equivalent virtual array manifold, u l [i] is the equivalent received signal, since u l The mean of [i] is not zero, for u l [i] Mean reduction processing, defined use The estimated parameter is ω+lφ;

[0148] 3.2 Constructing the equivalent signal

[0149] Extracting the pseudo-covariance matrix estimate anti-diagonal Its position in the matrix is:

[0150]

[0151]

[0152] Where c i，j yes The element in the i-th row and j-th column, represent The opposite diagonal, for Perform a mean-reduction operation to obtain an equivalent received signal with zero mean.

[0153]

[0154] The following analysis uses theoretical values ​​to examine the zero-mean equivalent signal. The construction principle. Expand v0[i] as

[0155]

[0156] Converted to matrix form as

[0157]

[0158] in

[0159]

[0160]

[0161]

[0162] If we consider i as a snapshot, then p[i] can be considered as the equivalent incident signal. Considering it as an equivalent virtual array manifold, v0[i] is the equivalent received signal. Since the mean of v0[i] is not zero, we perform de-meaning processing on v0[i] and define... use The estimated parameter is φ.

[0163] 4. Calculate the covariance matrix of the equivalent signal.

[0164] calculate covariance matrix estimate and covariance matrix estimate

[0165]

[0166]

[0167] The following theoretical analysis demonstrates why the DOA algorithm for subspaces based on the covariance matrix of equivalent signals is feasible. and The corresponding theoretical value is:

[0168]

[0169]

[0170] If you want to base and To perform eigenvalue decomposition and then use subspace-like algorithms for spatial spectrum search, one of the first conditions that needs to be met is... The rank should be K. If the rank is less than K, the eigenvectors of the signal will diverge into the noise subspace during the estimation process. A brief proof follows. The rank of is K.

[0171] Due to the incident signal s k (t) represents the power of a quasi-stationary signal at each time frame i. The sequence formed It exhibits wide stationarity and can be considered as a wide stationary signal with a non-zero mean. p[i] consists of K incident signals and can be considered as a set of wide stationary incident signals. After removing the mean, This can be viewed as a set of zero-mean, wide-stable signals. It is also important to note that the incident signal s... k (t) are unrelated to each other, therefore It can be viewed as a set of mutually uncorrelated, zero-mean, wide-range stationary signals, thus obtaining

[0172] 5. Eigenvalue decomposition

[0173] right and Perform eigenvalue decomposition:

[0174]

[0175]

[0176] in, and Represent and The signal subspace spanned by the eigenvectors corresponding to the K largest eigenvalues; and Represent and The remaining smaller eigenvalues ​​correspond to the noise subspace spanned by the eigenvectors; These represent diagonal matrices formed by the eigenvalues;

[0177] 6. Perform a spectral space search on φ.

[0178] Based on the principle of the MUSIC-class subspace algorithm, the spatial spectrum P(φ) is constructed as follows:

[0179]

[0180] The K largest values ​​in the search space spectrum are the parameter values ​​to be estimated. The following theoretical analysis explains how the parameter ψ is eliminated:

[0181] Based on the principle of the MUSIC class subspace algorithm, using and The orthogonality of the space spectrum yields the spatial spectrum estimation function as follows:

[0182]

[0183] because It can be represented as

[0184]

[0185] P(φ, ψ) can be re-expressed as a function that depends only on φ, i.e.

[0186]

[0187] That is, φ can be estimated independently using P(φ).

[0188] 7. Perform a spectral space search on ω+lφ

[0189] Based on the principle of the MUSIC-class subspace algorithm, the spatial spectrum P(ω+lφ) is constructed as follows:

[0190]

[0191] The following theoretical derivation explains why using the spatial spectrum P(ω+lφ) for DOA estimation can avoid peak overlap at small angles:

[0192] Using P(ω+lφ), ω+lφ can be estimated separately. Compared to estimating ω alone, estimating ω+lφ can better avoid spectral peak overlap when the angles are close together. For example, if signals 1 and 2 are close in angle, traditional methods typically estimate the angle variable (i.e., ω) separately, obtaining an estimate of... and When the angle difference is small, the estimated values ​​differ. Spectral peak overlap is prone to occur; while the estimated value obtained by using P(ω+lφ) is and Their difference is Compared to traditional algorithms, the difference is expanded. If a suitable value for l is selected, the distance between corresponding peaks in the signal spatial spectrum can be artificially increased, thereby reducing the probability of peak overlap.

[0193] 8. Parameter pairing and solution

[0194] After performing parameter estimation using the spatial spectra P(ω) and P(ω+lφ), parameter pairing is still required: for any Search all Obtain m that is paired with k:

[0195]

[0196] After parameter pairing is completed, the paired parameters can be obtained. and

[0197]

[0198]

[0199] Through parameters and It can be solved and

[0200]

[0201]

[0202] Next, we will conduct a performance analysis.

[0203] 1. Complexity Analysis

[0204] Assume each frame has S snapshots, a total of F frames, K signals, and M physical array elements. Let M be the degrees of freedom of the equivalent virtual signal after selecting l. l =M-|l|, the number of searches for P(φ) is n φ The number of searches for P(ω+lφ) is n. ω+lφ The algorithm complexity analysis is as follows:

[0205]

[0206] The total complexity of the algorithm is

[0207] 2. Simulation Experiment

[0208] For ease of explanation, the proposed algorithm is denoted as AD-NN-MUSIC (Anti-Diagonal Non-circular Near-field MUSIC), and the algorithm that estimates the ω spectrum of the incident signal using only the anti-diagonal elements of the covariance matrix is ​​denoted as NE-MUSIC (Near-field Efficient MUSIC).

[0209] Simulation 1:

[0210] Using a non-Gaussian BPSK signal, with K=2 signals, L=5 array element parameters, incident angles θ={-0.5°, 0.5°}, non-circular phase ψ={10°, 20°}, r={2λ, 4λ}, signal-to-noise ratio snr=20dB, frame length F=32, and snapshots=128 per frame, the simulation results of estimating the ω spectrum of the incident signal using only the anti-diagonal elements of the covariance matrix are as follows: Figure 2 As shown, when the angles to be estimated are very close, estimating only the angle will result in overlapping spectral peaks. The two original spectral peaks will overlap into a single peak, making normal angle estimation impossible and even affecting distance estimation.

[0211] Simulation 2:

[0212] The simulation conditions are the same as in Simulation 1, and the proposed algorithm (AD-NN-MUSIC) is used for DOA estimation of non-circular near-field signals. Generally, near-field signal estimation satisfies...

[0213]

[0214] r k =β k λβ k >1

[0215] At this point, the search range for ω and φ is

[0216]

[0217]

[0218] The search range for ω+lφ is ω+lφ∈[-1.6, 1.6+0.2l]. Taking l=3, then ω+3φ∈[-1.6, 2.2]. Based on the above constraints, the estimate of ω+lφ is as follows: Figure 3 As shown, the estimate of φ is as follows Figure 4 As shown, both estimations correctly estimate the parameters, and there is no spectral peak overlap even when the angles θ are very close, proving that the AD-NN-MUSIC algorithm performs better.

[0219] Simulation 3:

[0220] A non-Gaussian BPSK signal was used, with K=2 signals, M=11 array elements, an incident angle of θ={-2°, 2°}, a non-circular phase of ψ={10°, 20°}, a distance of r={1.5λ, 4λ}, a signal-to-noise ratio (SNR) snr ranging from 0dB to 28dB, a step size of 4dB, a frame length of F=32, 128 snapshots per frame, and 300 Monte Carlo experiments (MOT). The root mean square error (RMSE) of the angle was observed and compared under different SNRs. θ and the mean square error of distance RMSE r The definition is as follows:

[0221]

[0222]

[0223] Simulation results are as follows Figure 5 and Figure 6 As shown, the AD-NN-MUSIC algorithm outperforms the NE-MUSIC algorithm in both angle and distance estimation.

Claims

1. A method for estimating DOA based on the antidiagonal of the second-order statistical matrix of a non-circular near-field quasi-stationary signal, characterized in that, Includes the following steps: Step 1: Receive the non-circular near-field signal s(t) using a symmetrical uniform linear array. The array elements range from [-L, L]. Assuming the noise is additive white Gaussian noise, the received signal vector x(t) is expressed as: x(t)=A(θ,r)s(t)+n(t) =A(ω,φ)Ψ 1 / 2 s0(t)+n(t) Where n(t) is the Gaussian white noise vector, and s0(t) is the real signal vector. Let ψ be the non-circular phase matrix, and ψ be the non-circular phase parameter. A(ω,φ) is the array manifold, containing two parameters θ and r. For ease of engineering processing, these are replaced with electrical angles ω and φ, and their relationship is as follows: Where λ is the signal wavelength and d is the element spacing; Step 2: Calculate the estimated value of the signal covariance matrix for each time frame i. and pseudo-covariance matrix estimates Where S is the number of snapshots in each time frame, F is the number of time frames, H is the conjugate transpose sign, and T is the transpose sign; Step 3: Extract the estimated value of the covariance matrix Anti-diagonal vector parallel line and pseudo-covariance matrix estimates anti-diagonal As an equivalent received signal, Perform a mean-reduction operation to obtain an equivalent received signal with zero mean. Each signal has an F-frame snapshot: and Its position in the matrix is: Where r i,j yes The element in the i-th row and j-th column, c j,j yes The element in the i-th row and j-th column, represent The l-th parallel line to the anti-diagonal, where l is an integer ranging from {-2L...2L}, and a positive number represents... The parallel line to the lower right of the anti-diagonal line, represented by a plural. The parallel line to the upper left of the anti-diagonal line, represent The opposite diagonal; Considered as equivalent received signals, each signal has F-frame snapshots. Perform a mean-reduction operation to obtain an equivalent received signal with zero mean. use DOA estimation was performed, and the estimated parameter was ω+lφ; using DOA estimation is performed, and the estimated parameter is φ; Step 4, Calculation covariance matrix estimate and covariance matrix estimate Step 5, for and Perform eigenvalue decomposition: in, represent The signal subspace spanned by the eigenvectors corresponding to the K largest eigenvalues; represent The signal subspace spanned by the eigenvectors corresponding to the K largest eigenvalues; represent The remaining smaller eigenvalues ​​correspond to the noise subspace spanned by the eigenvectors; represent The remaining smaller eigenvalues ​​correspond to the noise subspace spanned by the eigenvectors; These represent diagonal matrices formed by the eigenvalues; Step 6: Perform a spectral space search on φ; the K largest values ​​are the parameter values ​​to be estimated. The constructed spatial spectrum P(φ) is: in, Step 7: Perform a spectral space search on ω+lφ, l∈{-2L,...,2L}. The K largest values ​​are the parameter values ​​to be estimated. The spatial spectrum P(ω+lφ) is: in Step 8: Obtain the result through parameter pairing. corresponding Through parameters and Solve and 2. The DOA estimation method based on the antidiagonal of the second-order statistical matrix of a non-circular near-field quasi-stationary signal according to claim 1, characterized in that, In step 1, the array manifold A(ω,φ) is represented as: A(ω,φ)=[a(ω1,φ1),a(ω2,φ2),…,a(ω K ,f K )] Since the array is a symmetrical array, the direction vector a(ω,φ) k )for ω k and φ k Let be the electrical angle parameter of the k-th incident signal.

3. The DOA estimation method based on the antidiagonal of the second-order statistical matrix of a non-circular near-field quasi-stationary signal according to claim 1, characterized in that, In step 2, the theoretical values ​​of the covariance matrix and the pseudo-covariance matrix are R0 and R1, respectively. x [i] and C x [i] is specifically represented as: in, For the k-th incident signal s k The power of the i-th frame signal in (t), where I is the identity matrix.

4. The DOA estimation method based on the antidiagonal of the second-order statistical matrix of a non-circular near-field quasi-stationary signal according to claim 1, characterized in that, In step 4 and Theoretical value and They are respectively 。 5. The DOA estimation method based on the antidiagonal of the second-order statistical matrix of a non-circular near-field quasi-stationary signal according to claim 1, characterized in that, In step 7, the estimated value obtained by searching the spatial spectrum function P(ω+lφ) is ω+lφ. When the incident signal angles are close, a suitable value is selected. That is, selecting the covariance matrix Appropriate diagonal parallel lines can widen the difference between estimated values ​​and avoid spectral peak overlap.

6. The DOA estimation method based on the antidiagonal of the second-order statistical matrix of a non-circular near-field quasi-stationary signal according to claim 1, characterized in that, The parameter pairing process in step 8 is specifically as follows: For any Where k∈{1,…,K}), search all Where m∈{1,…,K}, we obtain m paired with k: After parameter pairing, the paired parameters are obtained:

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