Robust Adaptive Beamforming Method for Coherent Signals Based on Virtual Antenna Array

Abstract

This invention proposes a robust adaptive beamforming method for coherent signals based on a virtual antenna array. The method includes: constructing a virtual antenna array symmetrical to the physical antenna array, and combining the physical and virtual antenna arrays to construct a virtual antenna array model; constructing observation vectors using the virtual antenna array and intermediate array elements, and then reconstructing a new covariance matrix using Toplitz; and using the ESPRIT-like algorithm to estimate the DOA of the signal using the newly reconstructed covariance matrix. This method not only maintains strong coherent signal processing capabilities without reducing the degrees of freedom, but also exhibits excellent output performance.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and particularly relates to a robust adaptive beamforming method for coherent signals based on a virtual antenna array. Background Technology

[0002] Adaptive beamforming is a major branch of array signal processing. It outputs useful information at the sensor output by enhancing the desired signal and suppressing interference signals. It is widely used in communications, radar, radio astronomy, medical imaging, and biomedical engineering. In communication systems, due to the complexity of the propagation environment, many uncontrollable factors can affect system performance. For example, when a signal originates from a distant location, the signal-to-noise ratio (SNR) will be very low due to the complexity of the channel environment, and coherent signals may appear, affecting both downlink and uplink channels since they share the same frequency band. By adjusting the weight vector, adaptive beamforming algorithms can not only form the main lobe in the direction of the desired signal but also create nulls in the direction of arrival (DOA) of the interference signal. Adaptive beamforming can suppress interference signals and enhance the desired signal, thus enabling reliable communication.

[0003] The Capon algorithm is one of the early, classic adaptive beamforming algorithms. Since obtaining the interference-plus-noise covariance matrix (INCM) is difficult in practical signal processing, the sampled covariance matrix (SCM) is usually used instead in subsequent processing. However, because the SCM contains the desired signal component, the performance of the Capon algorithm degrades significantly at high input signal-to-noise ratios. Furthermore, Capon's performance still degrades with limited sample data.

[0004] To eliminate the influence of desired signal components on output performance, many algorithms have been proposed. For example, beamformer performance can be improved by adding or subtracting the identity matrix before inverting the sampling covariance matrix, thus eliminating the influence of small eigenvalues ​​on output performance. However, in practical applications, the optimal value of the diagonal loading factor coefficients is difficult to determine.

[0005] Some algorithms use the uncertainty set of the desired signal direction vector as a constraint to maximize the output power, constructing an optimization problem to estimate the desired signal direction vector (DSDV). However, the worst case does not always occur in practical applications, and the upper bound of the norm of the mismatch vector is usually unknown.

[0006] In 2012, an algorithm was first proposed to reconstruct the INCM (Inductively Coupled Model) to replace the sample covariance matrix for subsequent signal processing. This not only almost completely eliminates the desired signal component but also reduces covariance matrix mismatch caused by the snapshot effect, thus significantly improving the robustness of the adaptive beamformer. However, its computational complexity is very high. Furthermore, the performance of this algorithm degrades sharply when coherent signals are present.

[0007] Furthermore, in practical applications, an unavoidable problem is coherent signal sources. Complex propagation environments lead to the presence of coherent signal sources, including co-channel interference and multipath propagation caused by reflections from background objects. In radar signal processing, interference from coherent signal sources can cause false alarms or target location errors. In mobile environments, coherent paths can enhance the received signal, but at the same time, the received signal may be attenuated due to changes in the reflection environment.

[0008] Current research on coherent signals mainly focuses on direction-of-arrival estimation, resulting in a series of decoherence algorithms, such as spatial smoothing, propagation, and ESPRIT-like algorithms. However, research on adaptive beamforming is relatively limited. Therefore, most existing coherent signal beamforming processing methods rely on these algorithms for decoherence. Summary of the Invention

[0009] To address the aforementioned issues, it is necessary to provide a robust adaptive beamforming method for coherent signals based on a virtual antenna array.

[0010] The first aspect of this invention provides a robust adaptive beamforming method for coherent signals based on a virtual antenna array, comprising:

[0011] Construct a virtual antenna array that is symmetrical to the physical antenna array, and combine the physical antenna array and the virtual antenna array to construct a virtual antenna array model;

[0012] An observation vector is constructed by using a virtual antenna array and intermediate array elements, and then a new covariance matrix is ​​obtained by Toplitz reconstruction.

[0013] The DOA of the signal is estimated using the new covariance matrix obtained from the reconstruction using the ESPRIT-like algorithm.

[0014] A second aspect of the present invention provides a robust adaptive beamforming apparatus for coherent signals based on a virtual antenna array, comprising a physical array and further comprising:

[0015] Memory; and

[0016] A processor coupled to the memory is configured to execute the coherent signal robust adaptive beamforming method based on virtual antenna arrays, based on instructions stored in the memory.

[0017] This invention has outstanding substantive features and significant progress compared to the prior art, specifically:

[0018] This invention proposes a robust adaptive beamforming method for coherent signals based on a virtual antenna array. This method not only maintains the processing capability of strong coherent signals without reducing the degrees of freedom, but also exhibits good output performance. The method first constructs a virtual array symmetrical to the physical array, and then combines the physical and virtual arrays to construct a virtual antenna array model. Observation vectors are constructed using the virtual antenna array and intermediate array elements, and then a new covariance matrix is ​​obtained through Toplitz reconstruction. Next, the DOA of the signal is estimated using the ESPRIT-like algorithm, and the direction vector is corrected using eigenvectors. Then, the correspondence between eigenvalues ​​and power is derived, and a correlation coefficient is defined to obtain a one-to-one correspondence between power and direction vectors. Finally, the INCM is reconstructed using the estimated power and direction vectors, and the weight vector is calculated. Compared with other algorithms, this method simplifies the processing of coherent signals, reduces complexity, and exhibits better robustness to coherent signals, demonstrating superior performance. Simulation results demonstrate the effectiveness and robustness of the proposed method.

[0019] Additional aspects and advantages of the invention will become apparent in the following description or may be learned by practice of the invention. Attached Figure Description

[0020] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0021] Figure 1 This is a diagram of a physical antenna array model.

[0022] Figure 2 This is a diagram of a virtual antenna array model.

[0023] Figure 3 It is a graph of two coherent signals: output SINR versus input signal-to-noise ratio.

[0024] Figure 4 It consists of three coherent signals: the output SINR versus the input signal-to-noise ratio.

[0025] Figure 5 This is a graph comparing the output value SINR with the number of snapshots.

[0026] Figure 6 It is a fixed direction error: Output SINR vs. DOA angle estimation error graph

[0027] Figure 7It is a fixed directional error: the output SINR versus the input signal-to-noise ratio diagram.

[0028] Figure 8 This is a random DSDV mismatch: output SINR vs. input signal-to-noise ratio plot. Detailed Implementation

[0029] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0030] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0031] The present invention provides the signal model and minimum variance distortionless response (MVDR) beamformer required by the present invention.

[0032] The uniform linear array ULA of the present invention is composed of Figure 1 The diagram shows M+1 physical arrays and K far-field narrowband signals with wavelengths of λ1 and λ2, incident on the array (M≥K). The first P signals are coherent, while the other signals are uncorrelated and independent of the first P signals. The element spacing d is set to half a wavelength (λ1, λ2, λ3). d = λ / 2). Assume the elements in the ULA are isotropic, and there are no issues such as channel inconsistency or mutual coupling. If the first element is considered the reference element, the output of the ULA at time t can be written as...

[0033]

[0034] in, It is a vector composed of the desired signal and the interference signal; The mean is 0 and the variance is Gaussian white noise, and they are independent of each other; It is an array manifold matrix, and the direction vector of the i-th signal is... a ( θ i Given Z snapshots, the above vector can be rewritten as:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] Wherein, the azimuth angle of the i-th signal is θ i ( i =1,2,…, K );

[0041] Assume the relationship between the first P signals is , i =1,2,…, P and (Without loss of generality, assume) β 1=1, The received signal of the k-th array element can be expressed as:

[0042]

[0043] Will s 1(t) and the other K-1 signals are defined as the desired signal and the interference signal, respectively. Then, the array received signal can be rewritten as...

[0044]

[0045] Wherein, the desired signal vector is d (t)= a ( θ 1) s 1(t), the vector of the interference signal is ;

[0046] The output of the adaptive beamformer can be expressed as

[0047] y (t)= ω H x (t)

[0048] Wherein, the weight vector is The output SINR used to evaluate beamformer performance is defined as follows:

[0049]

[0050] in, σ 1 2 Indicates the power of the desired signal, INCM. R i+n Given by the following formula

[0051]

[0052] in, σi 2 This represents the power of the i-th signal. σ n 2 The power representing the noise. This represents the identity matrix with 1s on the main diagonal;

[0053] The weight vector is constructed using the MVDR criterion, which can be achieved by solving the following minimization problem.

[0054]

[0055] The solution is given by the following equation.

[0056]

[0057] ω opt Also known as MVDR beamformer, because it is difficult to directly obtain INCM in practical applications. R i+n Therefore, the sampling covariance matrix is ​​obtained using the following formula. R x to replace

[0058]

[0059] in, Z It's the number of snapshots;

[0060] when Z When it is very small, you need to pay attention to the following: R x and R i+n The large gap between the input signal-to-noise ratio (INCM) and the input signal-to-noise ratio (SNR) causes the desired signal to be suppressed by interference. As the input SNR increases, the proportion of the desired signal component increases significantly, leading to self-cancellation and a decrease in algorithm performance. Therefore, the desired signal component needs to be removed when estimating INCM.

[0061] Example 1

[0062] This embodiment provides a robust adaptive beamforming method for coherent signals based on a virtual antenna array, including:

[0063] Construct a virtual antenna array that is symmetrical to the physical antenna array, and combine the physical antenna array and the virtual antenna array to construct a virtual antenna array model;

[0064] An observation vector is constructed by using a virtual antenna array and intermediate array elements, and then a new covariance matrix is ​​obtained by Toplitz reconstruction.

[0065] The DOA of the signal is estimated using the new covariance matrix obtained from the reconstruction using the ESPRIT-like algorithm.

[0066] Specific algorithm steps:

[0067] A. Construction of Virtual Antenna Array

[0068] To enhance the algorithm's ability to process coherent signals, a virtual array needs to be constructed:

[0069] like Figure 2 As shown, a virtual antenna array b is constructed that is rotationally conjugate symmetric to the physical antenna array a. The virtual antenna array b consists of M+1 virtual antenna array elements. The leftmost array element of the physical antenna array a and the rightmost array element of the virtual antenna array b are combined as intersection points to form the virtual antenna array c. v ( t Let ) represent the received signal of the virtual antenna array in b. According to the rotational conjugate symmetry relationship between a and b, we have v ( t )= I v x * ( t ),in, I v It is an inverse identity matrix of dimension M+1;

[0070] The received signal of the constructed virtual antenna array c is represented as follows: x v ( t )= v ( t )∪ x ( t ).

[0071] Toplitz matrix reconstruction

[0072] The method for constructing observation vectors using a virtual antenna array and intermediate array elements, and then reconstructing them using Toplitz to obtain a new covariance matrix is ​​as follows:

[0073] Based on the constructed virtual antenna array and its most central element, we have

[0074] (1)

[0075] in, r v ( g )express r v The element located at position g is represented as:

[0076] (2)

[0077] Since the first P signals are coherent and independent of other signals, the noise is independent of each other. The received signal and noise are also independent of each other. Formula (2) can be rewritten as:

[0078] (3)

[0079] in, ,

[0080] (4)

[0081] Substituting formulas (3) and (4) into (1), we can... r v Represented as

[0082] (5)

[0083] in, ; n 0 consists of zeros, except that the element at position g=0 is 1;

[0084] Due to the covariance matrix R d = r v r v H Not yet full rank, passed r v The constructed Toplitz matrix yields the covariance matrix of the received signal, where the newly constructed covariance matrix is ​​expressed as:

[0085]

[0086] in

[0087]

[0088]

[0089]

[0090] .

[0091] Direction vector estimation

[0092] The method for estimating the DOA of a signal using the reconstructed covariance matrix via the ESPRIT-like algorithm is as follows:

[0093] New covariance matrix Rv Similar to the covariance matrix obtained by combining M+1 virtual antenna arrays and K signals, where the incident signals are independent and their powers are respectively... , R v The eigenvalue decomposition can be written as:

[0094]

[0095] in, λ i ( i =1,2,…,M+1) is R v The eigenvalues ​​are arranged in descending order. e i It is the eigenvector corresponding to the eigenvalue, the signal subspace. U s =[ e 1, e 2, e 3,…, e K ], U N For noise subspace;

[0096] DOA estimation of the signal is obtained using the ESPRIT-like algorithm. ;

[0097] Substitute the DOA estimation result into the direction vector of the i-th signal. a ( θ i The estimated direction vector of the signal is as follows:

[0098]

[0099] in, .

[0100] However, in reality, many factors can cause direction errors. Therefore, it is necessary to optimize the estimated direction vector. Optimization is then performed. Since the signal direction vector and the signal subspace are in the same space, eigenvectors can be used to correct the estimated direction vector. The maximum inner product of the eigenvectors and direction vectors represents the correspondence between them. Therefore, a correlation coefficient is defined to find the correlation between the eigenvectors and the direction vectors. The corresponding feature vector;

[0101] set up The corresponding feature vector is e sm , m =1,2,…, K ;

[0102] Then the eigenvector e sm and direction vector The correlation coefficient is expressed as:

[0103] (6)

[0104] The signal subspace Us and the direction vector Substitute the obtained K eigenvectors into (6);

[0105] The correlation coefficient reaches its maximum value when the direction vector corresponds to the eigenvector, from which we obtain... e sm and The corresponding relationship between them;

[0106] Since the direction vectors of different signals are orthogonal to each other, and considering the norm constraint, we have

[0107]

[0108] Let the corrected direction vector be e sm Therefore, it exists.

[0109]

[0110] Then the desired direction vector is obtained.

[0111] .

[0112] D. Signal power estimation

[0113] When performing DOA estimation of a signal, the following method is used to estimate the signal power. Make an estimate:

[0114] The constructed new covariance matrix R v Rewritten as

[0115]

[0116] After transformation, we get

[0117] (7)

[0118] Will Substituting into formula (7), we get

[0119] (8)

[0120] Signal power is represented by the first K eigenvalues, and noise power corresponds to the remaining M+1-K eigenvalues. The noise power is estimated using the average value, which is:

[0121] (9)

[0122] By substituting formula (9) into formula (8), and considering that the fading coefficient is a complex number, we can obtain it by taking its modulus.

[0123]

[0124] Subtract the smaller eigenvalue corresponding to the noise power from the larger eigenvalue, then divide by... To estimate the power of the interference signal

[0125]

[0126] Because we cannot know accurately β and β j * The value of , therefore for The processing procedure is as follows:

[0127] The range of signals received by a uniform linear array ULA is Therefore, there are cosplays. φ j ≥0, and α j >0, get

[0128] .

[0129] If we assume

[0130]

[0131] The power of the interference signal can be excessive. However, when the power of the interference signal is overestimated, the performance of the beamformer will not be significantly affected. Therefore, using... It is reasonable to estimate the signal power using this method. However, a problem remains: the one-to-one correspondence between the estimated direction of arrival and the power cannot be determined. This problem is addressed by defining the following correlation coefficient.

[0132]

[0133] Using eigenvectors e i replace U s When the direction vector a sm Corresponding to the eigenvector e iAt that time, the relationship between them is not orthogonal, therefore the coherence coefficient reaches its maximum value. From In this process, the correspondence between eigenvectors and eigenvalues ​​was obtained, thus yielding the relationship between eigenvalues ​​and eigenvalues. a sm The correspondence between them. Due to the estimated direction vector a m By rotating a sm Then, by taking the conjugate, the power is obtained from the eigenvalues ​​of the formula, and finally, the estimated direction vector is obtained. a sm With estimated power A one-to-one correspondence between them.

[0134] Weight vector calculation

[0135] The reconstructed interference plus noise covariance matrix (INCM) is used to replace the sample covariance matrix for subsequent signal processing.

[0136] Replace the estimated power and direction vector with the original interference plus noise covariance matrix INCM.

[0137]

[0138] in, σ i 2 This represents the power of the i-th signal. σ n 2 The power representing the noise. This represents the identity matrix with 1s on the main diagonal;

[0139] The reconstructed interference plus noise covariance matrix INCM is:

[0140]

[0141] Finally, the desired signal direction vector a sm and reconstructed Substitution ω opt The weight vector of the algorithm is obtained as follows

[0142] .

[0143] Experimental comparison

[0144] In the simulation experiment, a ULA with an M+1=13 omnidirectional sensor and a half-wavelength spacing is considered. It is assumed that there is a sensor from... θ The expected signal of 1=5° and from θ 2 = -10° θ3 = -30° θ 4 = 20° and θ Four interfering signals with a 5 = 40° angle. Additive noise is modeled as a complex Gaussian random process with a mean of 0. Unless otherwise specified, the interference-to-noise ratio (INR) for each sensor is 30 dB, and the number of snapshots is fixed. Z =50. For each scenario, 1000 Monte Carlo experiments were conducted.

[0145] In the following simulation experiments, the algorithm of this embodiment was compared with traditional sampling covariance matrix inversion algorithms, diagonal loading algorithms, worst-case performance optimization algorithms based on beamforming, and covariance matrix reconstruction algorithms. In the figures, these algorithms are described using "PROPOSED", "SMI", "DLSMI", "WORST-CASE", and "RECONSTRUCTION". In the simulation experiments, a loading factor of 10 was selected. σ n 2 A diagonal loading algorithm and a worst-case performance-optimized beamformer with a parameter of 0.3(M+1) are presented. In both the reconstruction-based beamformer and the proposed beamformer, the angular region of the desired signal is assumed to be... ,therefore, .

[0146] Simulation Experiment 1: Comparison of Different Numbers of Coherent Signals

[0147] In this set of simulations, we analyzed cases with two coherent signals and three coherent signals. We assumed no error in the DOA estimation of both the desired and interfering signals. Figure 3 This shows the expected signal θ 1 and from θ The relationship between output SINR and input SNR is shown when the interference signal at 2=-10° is coherent, and when other signals are independent. Clearly, the performance of the algorithm in this embodiment is slightly higher than the reconstruction algorithm and significantly higher than other algorithms. This is because the proposed beamformer accurately reconstructs the INCM and avoids signal self-cancellation. Figure 4 This shows the expected signal θ 1 and θ 2 = -10° and θ The interference signal is coherent at 3 = -30°, and θ 4 and θ The signals of 5 are independent of each other, independent of θ The relationship between output SINR and input signal-to-noise ratio is given by equation 1. In this case, the algorithm in this embodiment exhibits the best performance. Simulation experiments show that the algorithm in this embodiment has good robustness to coherent signals and its output performance is superior to other algorithms.

[0148] Simulation Experiment 2: Quick Shot Count Variation Curve

[0149] The effect of snapshot number on beam performance was investigated under error-free DSDV conditions. The signal-to-noise ratio of the desired signal was set to 10 dB. Other simulation conditions were the same as... Figure 4 Same as above. Figure 5 The relationship between the output SINR and the number of snapshots is described. It can be seen that as the number of snapshots increases, the output SINR of several algorithms is usually constant, but the algorithm in this embodiment has a faster convergence speed and a higher output SINR than other algorithms.

[0150] Simulation Experiment 3: Fixed Directional Error

[0151] The impact of DSDV mismatch on beamforming performance was simulated. The actual direction of the desired signal was chosen as... θ 1 = 5°. Assume there is an error between the DOA estimation and the actual direction of the desired signal. Taking the signal-to-noise ratio of the desired signal as 10dB, the DOA estimation error decreases from 0° to 3°, while other conditions remain unchanged. Figure 6 The relationship between the output SINR of the beamformer and the DOA estimation error is described. Results show that the algorithm in this embodiment has strong resistance to DSDV mismatch and good performance. The performance of the algorithm in this embodiment slightly decreases with increasing error. When assuming a desired arrival signal direction of 8° and an observation direction mismatch of 3°, the relationship between the algorithm's output SINR and input signal-to-noise ratio is as follows: Figure 7 As shown, increasing the input signal-to-noise ratio (SNR) leads to an increase in both the covariance matrix reconstruction and the beamformer output SNR, as these exclude the desired signal. At high SNRs, the performance of SMI, DLSM, and worst-case beamformers degrades due to DSDV mismatch caused by directional mismatch. Simulation results demonstrate that the algorithm in this embodiment achieves optimal performance even with desired signal errors.

[0152] Simulation Experiment 4: Random DSDV Mismatch

[0153] Considering the presence of random errors in DSDV, if DSSV has uncertain perturbations in practical applications, then the real DSDV can be written as follows:

[0154] a = a 1+ δ

[0155] in a 1 represents a real DSDV; a random, undefined set of DSDV mismatches can be derived from...

[0156]

[0157] in δ The norm is It is in It is randomly generated. δ The coordinates are in the range [0, 2π]. The u-th independent run generates the coordinates. . Figure 8 The diagram shows the simulated relationship between the input signal-to-noise ratio (SNR) and the output SINR. It is easy to see that the proposed beamformer achieves the best SINR across the entire input SNR range, proving the effectiveness of the algorithm in this embodiment. Furthermore, the proposed beamformer significantly outperforms other tested beamformers, indicating stronger robustness to random DSDV mismatches.

[0158] Example 2

[0159] This embodiment provides a robust adaptive beamforming device for coherent signals based on a virtual antenna array, including a physical array, and further comprising:

[0160] Memory; and

[0161] A processor coupled to the memory is configured to execute the coherent signal robust adaptive beamforming method based on a virtual antenna array as described in Example 1, based on instructions stored in the memory.

[0162] The memory may include, for example, system memory, fixed non-volatile storage media, etc. System memory may store, for example, the operating system, application programs, boot loader, and other programs.

[0163] Beamforming devices may also include input / output interfaces, network interfaces, and storage interfaces. These interfaces, as well as the memory and processor, can be connected via, for example, a bus. The input / output interfaces provide connection interfaces for input / output devices such as monitors, mice, keyboards, and touchscreens. The network interfaces provide connection interfaces for various networked devices. The storage interfaces provide connection interfaces for external storage devices such as SD cards and USB flash drives.

[0164] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-non-transitory readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer program code.

[0165] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0166] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0167] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0168] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A robust adaptive beamforming method for coherent signals based on a virtual antenna array, characterized in that, include: Construct a virtual antenna array that is symmetrical to the physical antenna array, and combine the physical antenna array and the virtual antenna array to construct a virtual antenna array model; The method for constructing a virtual antenna array model is as follows: Construct a virtual antenna array b that is rotationally conjugate symmetric to the physical antenna array a, wherein the virtual antenna array b consists of M+1 virtual antenna array elements; the virtual antenna array c is formed by combining the leftmost array element of the physical antenna array a and the rightmost array element of the virtual antenna array b as the intersection point. use v ( t Let ) represent the received signal of the virtual antenna array in b. According to the rotational conjugate symmetry relationship between a and b, we have v ( t )= I v x * ( t ),in, I v It is an inverse identity matrix of dimension M+1; The received signal of the constructed virtual antenna array c is represented as follows: x v ( t )= v ( t )∪ x ( t ); An observation vector is constructed by using a virtual antenna array and intermediate array elements, and then a new covariance matrix is ​​obtained by Toplitz reconstruction. The method for constructing observation vectors using a virtual antenna array and intermediate array elements, and then reconstructing them using Toplitz to obtain a new covariance matrix is ​​as follows: Based on the constructed virtual antenna array and its most central element, we have （1） in, r v ( g )express r v The element located at position g is represented as: （2） Since the first P signals are coherent and independent of other signals, the noise is independent of each other. The received signal and noise are also independent of each other. Formula (2) can be rewritten as: （3） in, , （4） Substituting formulas (3) and (4) into (1), we can... r v Represented as （5） in, ; n 0 consists of zeros, except that the element at position g=0 is 1; Due to the covariance matrix R d = r v r v H Not yet full rank, passed r v The constructed Toplitz matrix yields the covariance matrix of the received signal, where the newly constructed covariance matrix is ​​expressed as: in ； The DOA of the signal is estimated using the new covariance matrix obtained from the reconstruction using the ESPRIT-like algorithm. The method for estimating the DOA of a signal using the reconstructed covariance matrix via the ESPRIT-like algorithm is as follows: New covariance matrix R v Similar to the covariance matrix obtained by combining M+1 virtual antenna arrays and K signals, where the incident signals are independent and their powers are respectively... , R v The eigenvalue decomposition can be written as: in, λ i yes R v The eigenvalues ​​are arranged in descending order. e i It is the eigenvector corresponding to the eigenvalue, the signal subspace. U s =[ e 1, e 2, e 3,…, e K ], U N For the noise subspace, i =1,2,…,M+1; DOA estimation of the signal is obtained using the ESPRIT-like algorithm. , i =1,2,…, K ; Substitute the DOA estimation result into the direction vector of the i-th signal. a ( θ i The estimated direction vector of the signal is as follows: in, ; When performing DOA estimation of a signal, the following method is used to estimate the direction vector. Optimize: set up The corresponding feature vector is e sm , m =1,2,…, K ; Then the eigenvector e sm and direction vector The correlation coefficient is expressed as: （6） The signal subspace Us and the direction vector Substitute the obtained K eigenvectors into (6); The correlation coefficient reaches its maximum value when the direction vector corresponds to the eigenvector, from which we obtain... e sm and The corresponding relationship between them; Since the direction vectors of different signals are orthogonal to each other, and considering the norm constraint, we have Let the corrected direction vector be e sm Therefore, it exists. Then the desired direction vector is obtained. ； When performing DOA estimation of a signal, the following method is used to estimate the signal power. Make an estimate: The constructed new covariance matrix R v Rewritten as After transformation, we get （7） Will Substituting into formula (7), we get （8） Signal power is represented by the first K eigenvalues, and noise power corresponds to the remaining M+1-K eigenvalues. The noise power is estimated using the average value, which is: （9） By substituting formula (9) into formula (8), and considering that the fading coefficient is a complex number, we can obtain it by taking its modulus. Subtract the smaller eigenvalue corresponding to the noise power from the larger eigenvalue, then divide by... To estimate the power of the interference signal Because we cannot know accurately β and β j * The value of , therefore for The processing procedure is as follows: The range of signals received by a uniform linear array ULA is Therefore there is ,and ,get ； This also includes reconstructing the interference plus noise covariance matrix (INCM) to replace the sample covariance matrix for subsequent signal processing. Replace the estimated power and direction vector with the original interference plus noise covariance matrix INCM. in, σ i 2 This represents the power of the i-th signal. σ n 2 The power representing the noise. This represents the identity matrix with 1s on the main diagonal; The reconstructed interference plus noise covariance matrix INCM is: Finally, the desired signal direction vector a sm and reconstructed Substitute into MVDR beamformer ω opt The weight vector of the algorithm is obtained as follows 。 2. A robust adaptive beamforming device for coherent signals based on a virtual antenna array, comprising a physical array, characterized in that, Also includes: Memory; as well as A processor coupled to the memory is configured to execute the coherent signal robust adaptive beamforming method based on a virtual antenna array as described in claim 1, based on instructions stored in the memory.

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