The worst-case performance optimal robust beamforming method

Abstract

This invention provides a novel method for worst-case performance-optimal robust beamforming. First, through analysis, the following important conclusions are obtained: In the design of a worst-case performance-optimal beamformer, the constraint of the uncertainty set can be given by the Capon spectrum search grid spacing. Based on this, and combined with a method for reconstructing the interference noise covariance matrix, the novel robust beamforming method of this invention is obtained. Because the interference noise covariance matrix is ​​reconstructed, the target signal component is removed, and the constraint of the uncertainty set for worst-case performance is determined based on the analysis, the novel method of this invention can ensure the design of an optimal beamformer under worst-case performance conditions. Furthermore, for the uncertainty set constraint method in robust adaptive beamforming technology, the novel method of this invention also provides a general and universal method for calculating the uncertainty set constraint, which is of great significance.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and relates to a signal processing technology for transmitting and receiving radio waves or sound waves via directional signals, specifically to a worst-case performance robust beamforming method. Background Technology

[0002] Adaptive beamforming, as a key array signal processing technique, has been widely applied in radar, sonar, communication, navigation, radio astronomy, medical imaging, and other fields (see references 1 and 2). Among them, the Capon beamformer, by minimizing interference and noise in the array output, has become a widely used optimal beamformer (see references 1-3). However, this optimal beamformer lacks robustness when there are errors in the prior information of the target signal steering vector, and / or when the statistical characteristics of the received data are not stable (see references 4-10). Therefore, robust adaptive beamforming technology has been extensively studied.

[0003] Generally, robust adaptive beamforming techniques include the following: diagonal loading method (see references 4-9), characteristic space projection method (see references 10-12), uncertainty set constraint method (see references 16, 17), and interference plus noise covariance matrix reconstruction method (see references 15-25). Among these, the diagonal loading method is the most classic. However, its main drawback is that it is difficult to find a general loading factor to adapt to all possible situations; in other words, finding a suitable loading factor is itself a difficult task (see reference 15). The characteristic space projection method suffers severe performance degradation when the signal-to-noise ratio (SNR) is low (see reference 3). Although the uncertainty set constraint method can optimize beamformer design under worst-case performance, a general method for constraining its uncertainty set has not yet been found (see reference 21). Furthermore, when the target signal component exists in the sample covariance matrix, the performance loss of the designed beamformer may be very severe (see reference 16).

[0004] To eliminate the target signal component in the sample covariance, many methods for reconstructing the interference-plus-noise covariance matrix have been developed in recent years. For example, Reference 15 presents a method for removing the target signal component covariance from the sample covariance by utilizing the Capon spectrum of the target signal in the possible prior angular sectors of a Uniform Linear Array (ULA). Reference 21 proposes a simple method for reconstructing the interference-plus-noise covariance. This method first obtains the steering vector of the interference signal through Capon spectrum search. Then, it uses the largest eigenvalue of the sample covariance matrix as the power of the interference signal, and reconstructs the interference covariance based on them. Adding the noise power, considered as the smallest eigenvalue, yields the reconstructed interference-plus-noise covariance matrix without the target signal. Thus, beamformers designed based on the reconstructed interference-plus-noise covariance matrix eliminate the potential influence of the target signal component in the sample covariance on beamformer design. At this point, although the robust beamformer designed does not have the optimal signal-to-interference-plus-noise rate (SINR), it can suppress potential interference to the greatest extent possible. However, when there is an estimation error in the target signal steering vector, or when there is an error between the direction of arrival (DOA) of the target signal incident array and its estimated DOA, the method in reference 21 still lacks robustness. Reference 25, based on reference 15, proposes a method for designing a robust beamformer to address array element position perturbations and improve Capon spectral resolution, thereby reconstructing the interference plus noise covariance matrix; however, its constraint on the uncertainty set is empirical. Reference 20 proposes a target signal steering vector estimation method based on uncertainty constraints, but it requires prior knowledge of the number of interferences and other priors to constrain the given uncertainty set. Furthermore, it does not discuss or analyze the potential impact of training snapshots containing the target signal on the performance of the designed beamformer.

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[0030]

[25] .L HUANG, J ZHANG,

[0031]

[26] .YANG Z,ZHANG C,XIE L.Robustly stable signal recovery incompressed sensing with structured matrix perturbation[J].IEEE Transactionson Signal Processing, 2012, 60(9):4658-4671. Summary of the Invention

[0032] This invention addresses the aforementioned problems and aims to provide a robust optimization design method for beamformers under conditions where training snapshots containing target signal components and steering vector estimation have errors. The invention employs the following technical solution:

[0033] This invention provides a novel worst-case performance robust beamforming method for beamforming N narrowband signals received by a ULA uniform linear array composed of M sensors. The N narrowband signals include a target signal and N-1 interfering noise signals. The method is characterized by a worst-case performance relationship between the estimated and actual steering vector of the target signal.

[0034] Step S1: Perform K quick-sampling operations on the N narrowband signals to obtain the sampled signal x(k) and its sampling covariance matrix.

[0035] Step S2: Perform Capon spectrum search. Perform grid search on the sampled signal x(k) with a predetermined grid spacing L to obtain the Capon spectrum of the target signal and the steering vector estimate a[θ(l)]. In the formula, θ is the observable angular range of the ULA uniform linear array, θ(l) = θ / L (l = 0, 1, 2, ..., L-1) are discrete grid points, and the steering vector estimate a[θ(l)] is constrained on the uncertainty set. The maximum deviation between the steering vector estimate a[θ(l)] and the actual value is the grid spacing.

[0036] Step S3: Reconstruct the interference noise cofactor based on the Capon spectrum of the target signal.

[0037] Difference matrix Remove the components of the target signal;

[0038] Step S4: Calculate the constraints of the uncertain set based on the grid spacing L.

[0039]

[0040] Step S5: Based on the constraints of the uncertain set and the reconstructed interference noise covariance matrix, solve for the weight vector w used to design the beamformer according to the following formula:

[0041]

[0042] The novel worst-case performance robust beamforming method provided by this invention may also have the following technical features, wherein step S3 specifically involves summing the interference grid points and noise grid points obtained from the Capon spectral search to obtain the reconstructed interference-noise covariance matrix:

[0043]

[0044] In the formula, Θ represents the observation corner sector of the array where the interference noise signal is located, and Θ represents the corner sector where the target signal is located.

[0045] It can be approximated by the following formula:

[0046]

[0047] In the formula, Q is the sum of the number of grid points occupied by the interference grid points and the noise grid points.

[0048] The novel worst-case performance robust beamforming method provided by this invention may also have the following technical features, wherein, in step S5, the weight vector w is solved using the Matlab convex optimization toolbox CVX.

[0049] Invention Function and Effect

[0050] The novel worst-case performance robust beamforming method of the present invention first yields the following important conclusions through analysis: In the design of a worst-case performance optimal beamformer, the constraint of the uncertainty set can be given by the grid spacing of the Capon spectrum search, aided by Capon spectral search. Based on this, and combined with the reconstruction method of the interference noise covariance matrix, the novel robust beamforming method of the present invention is obtained. Because the interference noise covariance matrix is ​​reconstructed, the target signal component is removed, and the constraint of the worst-case performance uncertainty set is determined based on the analysis, the novel method of the present invention can ensure the design of an optimal beamformer under worst-case performance conditions. Furthermore, for the uncertainty set constraint method in robust adaptive beamforming technology, the novel method of the present invention also provides a general and universal method for calculating the uncertainty set constraint, which is of great significance. Attached Figure Description

[0051] Figure 1 This is a flowchart of a novel method for worst-case robust beamforming in an embodiment of the present invention;

[0052] Figure 2 This is the performance intent of the beamformer in this embodiment of the invention when both the target and interfering DOAs are mismatched;

[0053] Figure 3 This is a schematic diagram illustrating the performance of an Optimal SINR beamformer in the prior art when both the target and interference DOAs are mismatched.

[0054] Figure 4 This is a schematic diagram of the performance of the beamformer in the prior art, as described in reference 21, when both the target and interference DOAs are mismatched.

[0055] Figure 5 This is a performance diagram of the beamformer that optimizes the worst-performing conventional beamformer in the prior art when both the target and interference DOAs are mismatched.

[0056] Figure 6 This is a schematic diagram illustrating the performance of an existing SMI beamformer when both the target and interference DOAs are mismatched.

[0057] Figure 7 This is a schematic diagram illustrating the performance of an RCB-like beamformer in the prior art when both the target and interference DOAs are mismatched.

[0058] Figure 8 This is a schematic diagram of the performance of the beamformer in reference 15 of the prior art when both the target and interference DOAs are mismatched.

[0059] Figure 9 This is a line graph showing the performance of the beamformer in this embodiment of the invention as a function of the number of snapshots;

[0060] Figure 10 This is a line graph showing the performance of the Optimal SINR beamformer in the prior art as a function of the number of snapshots.

[0061] Figure 11 It is a line graph showing the performance of the beamformer in document 21 of the prior art as a function of the number of snapshots;

[0062] Figure 12 It is a line graph showing the performance of the beamformer with the worst performance in the existing technology as a function of the number of snapshots;

[0063] Figure 13 This is a line graph showing the performance of SMI beamformers in the prior art as a function of the number of snapshots.

[0064] Figure 14 This is a line graph showing the performance of RCB Like beamformers in the prior art as a function of the number of snapshots.

[0065] Figure 15 This is a line graph showing the performance of the beamformer in document 15 as a function of the number of snapshots in the prior art.

[0066] Figure 16 This is a line graph showing the performance of the beamformer according to an embodiment of the present invention as a function of grid spacing.

[0067] Figure 17 This is a line graph showing the performance of the Optimal SINR beamformer in the prior art as a function of grid spacing.

[0068] Figure 18 It is a line graph showing the performance of the beamformer in document 21 of the prior art as a function of grid spacing;

[0069] Figure 19 It is a line graph showing the performance of the beamformer with the worst performance in the existing technology as a function of grid spacing.

[0070] Figure 20 This is a line graph showing the performance of RCB Like beamformers in the prior art as a function of grid spacing.

[0071] Figure 21 It is a line graph showing the performance of the beamformer in document 15 as a function of grid spacing in the prior art;

[0072] Figure 22 This is a schematic diagram illustrating the performance of the beamformer in an embodiment of the present invention when coherent scattering is present.

[0073] Figure 23 This is a schematic diagram illustrating the performance of an Optimal SINR beamformer in the presence of coherent scattering.

[0074] Figure 24 This is a schematic diagram of the performance of the beamformer in the prior art, as described in document 21, when coherent scattering is present.

[0075] Figure 25 This is a performance diagram of the beamformer that optimizes the worst-performing conventional beamformer in the presence of coherent scattering.

[0076] Figure 26 This is a schematic diagram illustrating the performance of existing SMI beamformers in the presence of coherent scattering.

[0077] Figure 27 This is a schematic diagram illustrating the performance of an existing RCB-like beamformer in the presence of coherent scattering.

[0078] Figure 28 This is a schematic diagram of the performance of the beamformer in document 15 of the prior art when coherent scattering exists. Detailed Implementation

[0079] To make the technical means, creative features, objectives and effects of this invention easy to understand, the following describes in detail the new method of worst-case performance robust beamforming of this invention with reference to embodiments and accompanying drawings.

[0080] <Example>

[0081] This embodiment provides a novel worst-case performance robust beamforming method for robustly optimizing the beamformer under conditions where training snapshots containing target signal components and errors exist in their guide vector estimation.

[0082] To facilitate the description of the specific implementation of the method of the present invention, assume a ULA uniform linear array composed of M sensors receives N narrowband signals, one of which is the target signal and the remaining N-1 are interference noise signals. Then the array observation signal is represented as:

[0083]

[0084] In the formula, x s (k)∈C M×1 ,x i (k)∈C M×1 ,x n (k)∈C M×1 These are the target signal, the interference signal, and the signal with a mean of 0 and a variance of 1. The Gaussian noise signal mentioned above includes both interference signals and Gaussian noise signals.

[0085] Where x s (k)=a1s1(k), s i(k)(i=1,2,...,N) is the complex envelope of the target signal and the interference noise signal at time k, a i =a(θ) i )∈C M×1 It is the guide vector of ULA, where a1 is the target signal x. s The guiding vector. When the first element of the array is used as the reference element, its structure is as follows:

[0086]

[0087] In the formula, λ is the wavelength of the signal, and d is the spacing between array elements. The sample covariance matrix of x(k) in formula (1) can be expressed as:

[0088] R=E{x(k)x H (k)}=R s +R i+n (3)

[0089] In the formula, E{·} represents the expectation operation. This is the covariance matrix of the target signal. When the target signal and the interference noise signal are uncorrelated, the interference noise covariance matrix can be expressed as:

[0090]

[0091] In the formula, I is an M×M identity matrix. This represents the power of the i-th interference noise signal.

[0092] The output of a beamformer can be expressed as:

[0093] y(k)=w H x(k) (5)

[0094] In the formula, w = [w1,...,w M ] T ∈C M×1 is the weight vector of the beamformer to be designed. The optimal beamformer weight vector w in equation (5) can be designed by maximizing the following output SINR:

[0095]

[0096] In the formula, Let represent the target signal power. To maximize the SINR in equation (6), and to ensure the target signal passes through the designed beamformer without distortion while suppressing interference and noise as much as possible, maximizing equation (6) is mathematically equivalent to the following design problem for Minimum Variance Distortionless Response (MVDR) beamforming:

[0097]

[0098] The optimal solution w obtained by equation (7) is:

[0099]

[0100] Typically, R i+n Through the following sample covariance matrix To make an estimate:

[0101]

[0102] In the formula, K represents the number of snapshots. The beamformer designed using this method is also called a Sample Matrix Inversion (SMI) beamformer. When the number of snapshots K approaches infinity, Approximating the theoretical value R = R s +R i+n Even if equation (9) is close to the theoretical value, due to R in equation (9) s The existence of this will make the beamformer weight vector obtained by equation (8) not the optimal solution for maximizing SINR in equation (6). In the design of classical MVDR beamformers, it is generally believed that the interference plus noise covariance matrix without the target signal can be obtained through training with snapshots without the target signal. However, when the beamformer is designed to detect non-cooperative targets, it is almost impossible to obtain training snapshots without the target signal. Therefore, under the condition that the target signal exists, the above-mentioned references 15-25 have studied and reported many methods on how to reconstruct the interference plus noise covariance based on snapshots with the target signal. Even so, their performance is still limited by the estimation error of the steering vector of the target signal.

[0103] To reconstruct the interference plus noise covariance matrix required to obtain the optimal weight vector equation (8) from snapshots containing the target signal, the methods for reconstructing the interference plus noise covariance based on the Capon spectrum reported in recent years (15-21) can be divided into the following three categories:

[0104] The first type involves removing the target signal component covariance from the sample covariance matrix. In this case, the reconstructed interference noise covariance can be expressed as:

[0105]

[0106] In the formula, This represents the sample covariance matrix estimated according to equation (9). and These represent the power and steering vector of the target signal, respectively, estimated from the Capon spectrum. The Capon spectrum can be expressed as:

[0107]

[0108] The implementation of Equation (11) involves discretizing the observable angular range θ of the array into equally spaced grid points, for example, letting θ(l) = θ / L (l = 0, 1, 2, ..., L-1), and then using a Capon beamformer to perform a grid-by-grid search to obtain the Capon spectrum. Since the spectrum obtained by the Capon spectrum search is not an ideal line spectrum, and the spectrum of the target signal may not be exactly located on the discretized grid points, this means that the spectrum of the target signal will inevitably leak some of its energy to the grid points near its corresponding steering vector. In other words, the interference noise covariance reconstructed according to Equation (10) will also contain a portion of the target signal's energy. This will affect the performance of the beamformer designed using Equations (10) and (7).

[0109] The second type of method addresses the potential spectral leakage problem of the first type of method by summing the grid points of interference and noise obtained from the Capon spectral search, i.e.:

[0110]

[0111] In the formula, Θ is the observation sector of the array where interference and noise are located, and Θ is the sector where the target signal is located. Θ can generally be determined by the array configuration and a rough prior knowledge of the sector where the target signal is located. Together with Θ, they form the entire angular space region observed by the array. The integral of equation (12) can be approximated by the following equation:

[0112]

[0113] In the formula, Q is the sum of the number of grid points occupied by interference and noise.

[0114] The third type of method estimates the power of the interfering signal and then reconstructs the interference-noise covariance matrix based on the power of the interfering signal, which is expressed as:

[0115]

[0116] In the formula, and These are the power estimation of the interference signal and the estimation of its steering vector, respectively. It is an estimate of noise power.

[0117] The first type of method inevitably results in the leakage of the spectral energy of the target signal beyond the grid points occupied by its estimated steering vector, therefore, in equation (10) There will still be some target signal energy remaining, so at high SNR, the performance of the beamformer designed for it will decrease. The second type of method... When the range is relatively accurate, the problem of Capon spectrum leakage can be solved well. For the third type of method, reference 21 proposes a method that... The method uses the maximum eigenvalue as the power of the interfering signal. This allows for potentially greater suppression of any interference. While it performs well when the interference signal steering vector and its power are accurately estimated, if the grid spacing in the spectral search is large, the estimation error of the interference steering vector can cause a sharp decline in performance, resulting in a loss of necessary robustness.

[0118] Once R is obtained from equations (10), (13), or (14) i+n Then, as can be easily seen from equation (8), if the steering vector estimation of the target signal is inaccurate, it will also be impossible to obtain its optimal solution. Considering the steering vector estimation of the target signal... Inevitably, the value a1 will differ from the actual value. Therefore, this invention will address this issue by providing a steering vector estimation method for the target signal. A new approach to designing robust beamformers is proposed, which constrains the worst-case performance that the actual value a1 may have.

[0119] Figure 1 This is a flowchart of a novel robust beamforming method with the worst-case performance in this invention embodiment.

[0120] like Figure 1 As shown, in this embodiment, the novel method for worst-case performance robust beamforming specifically includes the following steps:

[0121] Step S1: Perform K quick-sampling operations on the N narrowband signals to obtain the sampled signal x(k) and its sampling covariance matrix.

[0122] Step S2: Perform Capon spectrum search. Perform grid search on the sampled signal x(k) with a predetermined grid spacing L to obtain the Capon spectrum of the target signal and the steering vector estimate a[θ(l)]. In the formula, θ is the observable angular range of the ULA uniform linear array, θ(l) = θ / L (l = 0, 1, 2, ..., L-1) are discrete grid points, and the steering vector estimate a[θ(l)] is constrained on the uncertainty set. The maximum deviation between the steering vector estimate a[θ(l)] and the actual value is the grid spacing.

[0123] The Capon spectrum is shown in equation (11). The grid point corresponding to the target signal spectrum estimate obtained through Capon spectrum search is θ(l), and the estimated steering vector of the target signal is a[θ(l)]. At this time, θ1 in the actual value a(θ1) of the target signal must satisfy the following equation:

[0124]

[0125] In the formula, θ is the angular range observed by the array, and Equation (15) shows that even if the target signal spectrum is not exactly located on the discretized grid point (l), it must be at some angle within a grid spacing centered on the grid point (l). Otherwise, the searched target signal spectrum will definitely not appear on the grid point (l). This is because the spectrum obtained by Capon spectrum search is not an ideal line spectrum, so most of its energy will leak to the nearest grid point, see reference 26 above.

[0126] Step S3: Reconstruct the interference noise covariance matrix based on the Capon spectrum of the target signal. Remove the components of the target signal.

[0127] In step S3, the interference noise covariance can be reconstructed using the second type of method described above, that is, obtained according to equation (13).

[0128] Step S4: Calculate the constraints of the uncertain set based on the grid spacing L.

[0129]

[0130] As mentioned above, if the target signal spectrum is not exactly located at the discretized grid point θ(l), then it must also be at some angle within a grid spacing centered at grid point θ(l). This means that the relationship between the steering vector estimate a[θ(l)] and the actual value a(θ1) can be described using an uncertainty set, i.e.:

[0131] ||a(θ1)-a[θ(l)]||2≤ε (16)

[0132] In the formula, ε represents the constraint of the uncertain set. From equation (15), ε can be further expressed as:

[0133]

[0134] Step S5: Based on the constraints of the uncertain set and the reconstructed interference noise covariance matrix, solve for the weight vector w used to design the beamformer according to the following formula:

[0135]

[0136] According to equation (17), the actual value a(θ1) will belong to the following uncertain set:

[0137]

[0138] Thus, the cost function (7) can be rewritten as:

[0139]

[0140] Equation (19) can also be expressed as:

[0141]

[0142] stw H a[θ(l)]≥εw+1

[0143] Im{w H a[θ(l)]}=0

[0144] It can be seen that the difference between equations (19) and (20) and the traditional worst-case performance optimization beamformer design method in reference

[16] is that the objective function of equations (19) and (20) replaces the original sample covariance matrix with the interference plus noise covariance matrix. This means that they can not only design beamformers using snapshots containing target signals, but also design beamformers using training snapshots without target signals. Most importantly, in the traditional worst-case performance optimization beamformer design, how to determine its uncertainty set is an unfinished task. However, the value of the uncertainty constraint in equations (19) and (20) can be conveniently determined by equation (17) by means of the grid division in equation (11). In addition, the optimization of equation (20) belongs to the second-order cone programming problem, which can be solved by Matlab convex optimization toolbox CVX.

[0145] As described above, through steps S1-S5, the weight vector w used to design the beamformer is obtained, and a robust beamformer can be designed based on the weight vector w.

[0146] Parameter settings

[0147] In this embodiment, simulation experiment parameters were set according to the above method. A uniform linear array of ULA consisting of M=10 omnidirectional antennas was used, with the element spacing being half a wavelength and the first element located at the origin of the coordinate system serving as the reference element. In all simulation experiments, 500 independent Monte Carlo simulations were performed for each simulation, and their average results were reported. It was assumed that the target signal DOA was 5°, and the approximate prior angular sector was [1°, 9°]. The grid point corresponding to the Capon spectrum search peak within this angular sector was selected as the estimated value of the target signal DOA. The DOAs of the three interference signals were -50°, -20°, and 30°, respectively. The Interference to Noise Rate (INR) was 30dB, the noise variance was 1, the number of snapshots was 30, and unless otherwise specified, the grid point angle increment, i.e., the interval, was set to 1°. Through simulation experiments using the above parameters, experimental data of the beamformer in this embodiment were obtained.

[0148] Simulation Experiment 1

[0149] Simulation Experiment 1 considers the case where there are errors between the estimated and actual values ​​of the target signal's steering vector and those of the interference noise signal. It is assumed that the random steering vector errors are uniformly distributed between [-4°, 4°]. That is, the target signal's DOA is uniformly distributed between [1°, 9°], and the three interference signals' DOAs are uniformly distributed within [-54°, ​​-46°], [-24°, -16°], and [26°, 34°], respectively.

[0150] Figure 2-8 The following diagram illustrates the performance (output signal-to-interference-plus-noise ratio as a function of signal-to-noise ratio) of various beamformers obtained through simulation experiment 1. Figure 2 This is a schematic diagram illustrating the performance of a beamformer according to an embodiment of the present invention.

[0151] like Figure 2-8 As shown, the beamformer in this embodiment performs significantly better than the conventional worst-case optimal and SMI beamformers. This is because the sample covariance estimation used in the design of the conventional worst-case optimal and SMI beamformers contains the target signal component, so they minimize not only the energy of noise and interference, but also the energy of the target signal. Therefore, when SNR>0, the performance of both degrades significantly.

[0152] Furthermore, the beamformer of this embodiment outperforms the beamformers designed in References 15 and 21, which also proves that the method of the present invention has accurate and effective constraints on the steering vector estimation of the target signal.

[0153] Figure 9-15Line graphs showing the performance of various beamformers as a function of snapshot number, obtained through simulation experiments, are shown. Figure 9 This is a line graph of the beamformer according to an embodiment of the present invention.

[0154] like Figure 9-15 As shown, when the number of snapshots is small, the performance of the beamformer in this embodiment is slightly better than that of the beamformers designed in References 15 and 21, which also shows that the method of the present invention is easier to converge.

[0155] Simulation Experiment 2

[0156] Building upon Simulation Experiment 1, Simulation Experiment 2 will verify the impact of selecting constraints based on grid spacing on performance.

[0157] The signal-to-noise ratio is fixed at 20dB, and the grid spacing is selected as [0.1°, 0.5°, 1°, 1.5°, 2°, 2.5°, 3°]. The larger the grid spacing, the greater the corresponding steering vector error. Figure 16-21 The following is a line graph showing the performance (output signal-to-interference-plus-noise ratio) of various beamformers as a function of grid spacing, obtained from simulation experiment 2. Figure 16 This is a line graph of the beamformer according to an embodiment of the present invention.

[0158] Figure 16 This demonstrates that the constraint on the uncertainty set of the steering vector based on a grid spacing, as presented in this paper, remains effective for beamformer design, and its performance outperforms existing methods when the grid spacing in the Capon spectral search is greater than 10. Furthermore, Figure 16-21 It also shows that when the Capon spectrum search grid spacing is less than 0.50 and the target signal DOA estimation error is less than one grid spacing, the target and interference DOA estimation errors are relatively small, which leads to their corresponding steering vector errors being smaller. At this time, the beamformers designed in references

[15] and

[21] also have a certain robustness to the target signal steering vector estimation error. When the error is large, this is more robust than them.

[0159] Simulation Experiment 3

[0160] Based on Simulation Experiment 1, Simulation Experiment 3 considers the influence of coherent scattering on the steering vector estimation of the target signal. This influence can be expressed as:

[0161]

[0162] In the formula, p represents the direct path, and a(θ) p (p=1,2,3,4) represents the corresponding correlated scattering path. Angle θ p(p=1,2,3,4) are independently and uniformly distributed in [θ0-4°,θ0+4°] in each experiment, with phase parameter ψ p In each experiment, they are independently and uniformly distributed in [0, 2π].

[0163] like Figure 22-28 As shown, the beamformer designed in this embodiment performs slightly better than that in Reference 15, and significantly better than the beamformers designed by other comparative methods.

[0164] Functions and effects of the embodiments

[0165] Based on the novel worst-case performance robust beamforming method provided in this embodiment, the following important conclusions were first obtained through analysis: In the design of a worst-case performance optimal beamformer, the constraint of the uncertainty set can be given by the grid spacing of the Capon spectrum search, aided by Capon spectral search. Based on this, and combined with the reconstruction method of the interference noise covariance matrix, the novel robust beamforming method of this embodiment was obtained. Since the interference noise covariance matrix was reconstructed, the target signal component was removed, and the constraint of the worst-case performance uncertainty set was determined based on the analysis, the method of this embodiment can ensure the design of an optimal beamformer under worst-case performance conditions.

[0166] Furthermore, for the uncertainty set constraint method in robust adaptive beamforming technology, the method of this invention also provides a general and universal method for calculating the uncertainty set constraint, which is of great significance.

[0167] The simulation experiments and comparative analysis of the implementation data also show that when the Capon spectrum search grid spacing is greater than 0.5° and the DOA estimation error of the target signal is less than one grid spacing, the robustness and performance of the beamformer designed in this embodiment are better than the methods reported in the literature in the present technology.

[0168] The above embodiments are only used to illustrate specific implementations of the present invention, and the present invention is not limited to the scope of the description of the above embodiments.

Claims

1. A worst-case performance robust beamforming method for beamforming N narrowband signals received by a ULA uniform linear array composed of M sensors, wherein the N narrowband signals include a target signal and N-1 interference noise signals, characterized in that, The worst performance exists between the steering vector estimation of the target signal and the actual value, and the method comprises: Step S1, K times of fast sampling of the N narrowband signals are performed to obtain a sampling signal x(k) and a sampling covariance matrix In step S2, Capon spectrum search is performed to search the sampling signal x(k) at predetermined grid point spacing L to obtain the Capon spectrum of the target signal and the steering vector estimation a[θ(l)], wherein θ is the angle range that can be observed by the ULA uniform linear array, θ(l)=θ / L (l=0, 1, 2,..., L-1) is a discrete grid point, wherein the steering vector estimation a[θ(l)] is constrained on an uncertainty set, and the maximum deviation of the steering vector estimation a[θ(l)] from the actual value is the grid point spacing; Step S3, reconstructing an interference noise covariance matrix based on the Capon spectrum of the target signal remove the component of the target signal therein; In step S4, the constraint of the uncertainty set is calculated according to the grid point spacing L: In step S5, the weight vector w for designing the beamformer is solved according to the following formula based on the constraint of the uncertainty set and the reconstructed interference noise covariance matrix:

2. The worst performance optimal robust beamforming method according to claim 1, wherein: wherein In step S3, the interference grid points and the noise grid points obtained by the Capon spectrum search are summed to obtain the reconstructed interference noise covariance matrix: wherein is the angular sector of array observation where the interference noise signal is located, and Θ is the angular sector where the target signal is located. And can be approximated by the following formula: Wherein Q is the sum of the grid points occupied by the interference grid points and the noise grid points.

3. The worst performance optimal robust beamforming method according to claim 1, wherein: wherein In step S5, the weight vector w is solved by using the Matlab convex optimization toolbox CVX.

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