Spatial non-uniform sampling covariance matrix reconstruction method for robust adaptive dbf

Abstract

The application discloses a spatial non-uniform sampling covariance matrix reconstruction method for robust adaptive DBF, according to the actual directivity pattern shape, the whole space is divided into a main lobe area and a side lobe area, the non-uniform integral of the interference noise covariance matrix in the side lobe area is reconstructed by using the Capon power spectrum weighted steering vector space, and the optimal weight vector is obtained by adopting a linear constraint minimum variance criterion optimization. Specifically, the Capon power spectrum of the side lobe area is calculated by large-angle stepping, the first L maximum values and corresponding angles theta are found; M small-angle stepping points are uniformly arranged near the angles corresponding to the L maximum values, and the Capon power spectrum of the M interpolation points is calculated; the Capon power spectrum weighted side lobe area integral directivity vector space is calculated by using the large-angle stepping and small-angle stepping angles; and the optimal weight coefficient is calculated by adopting the LCMV criterion. The application has the characteristics of robust main lobe shape preserving ability, side lobe null depth and null width, and significantly improves the side lobe interference suppression ability of the adaptive array antenna.

Description

Technical Field

[0001] This invention belongs to the field of spatial anti-interference technology for array antennas, and in particular relates to a method for reconstructing the spatial non-uniform sampling covariance matrix for robust adaptive DBF. Background Technology

[0002] A significant advantage of adaptive digital beamforming technology lies in its ability to adaptively generate nulls in the interference direction while ensuring that the main lobe of the antenna pattern points to the desired signal. Minimum Variance Distortionless Response (MVDR) and Linear Constraint Minimum Variance (LCMV) criteria are commonly used adaptive algorithm criteria. The LCMV beamformer, in particular, adds a series of linear constraints while minimizing the beamformer's output power; its objective function is:

[0003]

[0004] Where C is the constraint matrix and f is the constraint vector. Let w be the signal sampling covariance matrix. The optimal weight vector w can be expressed using the Lagrange multiplier method as follows:

[0005]

[0006] When the received signal contains the desired signal, especially when the desired signal deviates from the beam pointing direction, a "self-zeroing" phenomenon occurs. That is, the LCMV adaptive beamformer will form a depression in the main lobe region of the radiation pattern, resulting in problems such as distortion of the main lobe radiation pattern shape and increased side lobe level, which severely limits the performance of adaptive beamforming technology in angle measurement and target tracking.

[0007] Feature projection preprocessing algorithms find the eigenvectors corresponding to main lobe interference through eigenvalue decomposition and construct a feature projection matrix to eliminate main lobe interference. However, they suffer from errors in estimating the main lobe interference eigenvectors. Eigenvalue replacement covariance matrix reconstruction methods replace the eigenvalues ​​corresponding to the desired signal with the average values ​​of the noise eigenvalues ​​to reconstruct the covariance matrix, eliminating the influence of the desired signal on the adaptive weights. However, the eigenvalue correspondence is difficult to determine, and good performance is only achieved under specific conditions. The robustness of existing methods needs further improvement. Summary of the Invention

[0008] The purpose of this invention is to solve the problems mentioned in the background art. By using the Capon power spectrum non-uniform weighted reconstruction interference plus noise covariance matrix method, the desired signal component in the received signal is removed, and the suppression of side lobe interference is adaptively enhanced while keeping the main lobe beam shape unchanged.

[0009] To achieve the objective of this invention, a method for reconstructing the spatial non-uniform sampling covariance matrix for robust adaptive DBF is disclosed, comprising the following steps:

[0010] Step 1: Divide the entire airspace into the main lobe region and the side lobe region. Calculate the Capon power spectrum of the side lobe region with a large angle step, find the peak position of the power spectrum, and calculate the Capon power spectrum of the region with a small angle step at the angle close to the peak.

[0011] Step 2: Simultaneously construct the weighted steering vector space of the sidelobe region using the Capon power spectra corresponding to all large and small angle steps, and reconstruct the interference plus noise covariance matrix using non-uniform angle integration.

[0012] Step 3: Calculate the optimal weighting coefficients Where C is the constraint matrix and f is the constraint vector, which is optimized and selected according to the requirements of main lobe and side lobe shape preservation.

[0013] Furthermore, a large-angle step refers to a step of ≥1°, while a small-angle step refers to a step of <1°.

[0014] Furthermore, step 1 specifically includes:

[0015] Step 1-1: Calculate the Capon power spectrum of the sidelobe region using large-angle steps;

[0016] The entire airspace is divided into the main lobe region Θ and the side lobe region. With large angle step Δθ r Calculate the sidelobe region

[0017]

[0018] in The sampled covariance matrix of the received signal, a(θ) i ) is θ i The corresponding guiding vector, θ0 is the sampling start angle of the sidelobe region, and Q is the number of sampling points.

[0019] Steps 1-2: Locate the peak position of the power spectrum;

[0020] Sort the Capon power spectrum obtained in step 1-1 in descending order, and find the top L maximum values ​​and their corresponding angles θ. l, l=0,…,L-1, where L is the maximum number of sidelobe interferences.

[0021] Steps 1-3: Step at θ with small angles l ±Δθ r Sampling points are set within the range;

[0022] At θ l Nearby, take small steps Δθ a Evenly distributed Calculate the Capon power spectrum corresponding to small-angle step angles at each angle point.

[0023]

[0024] Furthermore, step 2 specifically involves: using all the large-angle step angles θ from step 1. i and all small-angle step angles θ lm The sidelobe steering vector space is calculated using Capon power spectrum weighting, i.e., the interference plus noise covariance matrix is ​​reconstructed using non-uniform angular integration. The calculation method is as follows:

[0025]

[0026] Compared with the prior art, the significant advancements of this invention are: 1) It can maintain the robust main lobe shape and generate deeper and wider nulls to resist interference when the received signal contains the desired signal and the main lobe beam pointing deviates from the desired signal at a certain angle; 2) By non-uniformly selecting sampling angle points in the sidelobe region at different angle steps, the steering vector space of the corresponding Capon power spectrum weighted sidelobe region is calculated, thereby realizing the characteristics of null deepening and broadening; 3) This invention only requires prior knowledge of the desired static radiation pattern or weighting coefficients, without requiring prior information on interference, and can achieve robust adaptive interference resistance for radiation patterns of arbitrary shapes, thus having universal applicability.

[0027] To more clearly illustrate the functional characteristics and structural parameters of the present invention, further explanation is provided below in conjunction with the accompanying drawings and specific embodiments. Attached Figure Description

[0028] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0029] Figure 1 This is a flowchart of the algorithm implementation of the present invention;

[0030] Figure 2The high-gain adaptive point beam adaptive normalization pattern is the desired signal with an incoming wave direction of 0° and a signal-to-noise ratio of 10dB in a 32-element half-wavelength uniform linear array in Example 1, and two sidelobe interferences with incoming wave directions of -35° and -60° and interference-to-noise ratios of 40dB.

[0031] Figure 3 This is a graph showing the variation of the high-gain adaptive spot beam output signal-to-interference-plus-noise ratio (SIR / NOR) under different conditions, in Example 1, with a desired signal having an arrival direction of 0° and a SIR / NOR of 10dB, and two sidelobe interferences having arrival directions of -35° and -60°, both with an INR / NOR of 40dB.

[0032] Figure 4 This is the static radiation pattern of the desired main lobe-shaped wide beam in Example 2.

[0033] Figure 5 In Example 2, the adaptive normalized pattern of the main lobe-shaped beam is obtained when there is a desired signal with an arrival direction of 0° and a signal-to-noise ratio of 10dB in a 32-element half-wavelength uniform linear array, and two sidelobe interferences with arrival directions of -35° and -60° and interference-to-noise ratios of 40dB.

[0034] Figure 6 This is a graph showing the output signal-to-interference-plus-noise ratio (SNR) of the main lobe shaped beam under different conditions, given the presence of a desired signal with an arrival direction of 0° and a SNR of 10dB, and two sidelobe interferences with arrival directions of -35° and -60°, both with an SNR of 40dB. Detailed Implementation

[0035] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] Combination Figure 1 A method for reconstructing the spatial non-uniform sampling covariance matrix for robust adaptive DBF includes the following steps:

[0037] Step 1: Divide the entire airspace into main lobe region and side lobe region. Calculate the Capon power spectrum of the side lobe region with large angle steps, find the peak position of the power spectrum, and calculate the Capon power spectrum of the region with small angle steps near the peak. Specifically:

[0038] Step 1-1: Calculate the Capon power spectrum in the sidelobe region using large-angle steps;

[0039] The entire airspace is divided into the main lobe region Θ and the side lobe region. With large angle step Δθ r Calculate the Capon power spectrum in the sidelobe region in The sample covariance matrix for the received signal is given, where θ0 is the sampling start angle of the sidelobe region and Q is the number of sampling points.

[0040] Steps 1-2: Locate the peak position of the power spectrum;

[0041] Sort the Capon power spectrum obtained in step 1-1 in descending order, and find the top L maximum values ​​and their corresponding angles θ. l , l=0,…,L-1, where L is the maximum number of sidelobe interferences.

[0042] Steps 1-3, advance at small angles in θ l ±Δθ r Set sampling points within the specified range;

[0043] At θ l Nearby, take small steps Δθ a Evenly distributed Calculate the Capon power spectrum corresponding to small-angle step angles at each angle point:

[0044]

[0045] Step 2, use all the large-angle step angles θ from Step 1. i and all small-angle step angles θ lm The sidelobe steering vector space is calculated using Capon power spectrum weighting, i.e., the interference plus noise covariance matrix is ​​reconstructed using non-uniform angular integration. The calculation method is as follows:

[0046]

[0047] Step 3, calculate the optimal weighting coefficients. Where C is the constraint matrix and f is the constraint vector, which needs to be optimized and selected according to the requirements of main lobe and side lobe shape preservation.

[0048] The present invention will now be described in detail with reference to specific embodiments.

[0049] Example 1

[0050] This invention proposes a spatial non-uniform sampling covariance matrix reconstruction method for robust adaptive deep beamforming (DBF), which possesses main lobe beamform preservation capability while adaptively suppressing side lobe interference. See the flowchart for the method. Figure 1This example uses a 32-element, half-wavelength, equally spaced, uniform linear array. The element antennas are isotropic omnidirectional antennas, and element coupling is not considered. The desired signal originates from the 0° direction, with an element signal-to-noise ratio (SNR) of 10 dB. The two sidelobe interferences originate at angles of -60° and -35°, respectively, with an element interference-to-noise ratio (INR) of 40 dB for both. The noise is unit additive white Gaussian noise, and the interference and signal are spatially and temporally uncorrelated. The static radiation pattern shows the main lobe region Θ = [-3.5°, 3.5°], and the sidelobe region...

[0051] The implementation of this robust adaptive DBF algorithm based on spatial non-uniform sampling covariance matrix reconstruction under this 32-element uniform linear matrix includes the following steps:

[0052] Step 1: Based on the static radiation pattern, the main lobe region Θ = [-3.5°, 3.5°], and the side lobe region... With large angle step Δθ r =1° Calculation of Capon power spectrum in sidelobe region in The covariance matrix of the received signal is sampled. (Search) The first two maximum values ​​and their corresponding angles θ1 and θ2 are identified. Small angle steps Δθ are then taken near θ1 and θ2, respectively. α =0.1°, uniformly set M=20 angle points, and calculate the Capon power spectrum corresponding to small angle step angles.

[0053]

[0054] Step 2: Use all the large-angle step angles θ from Step 1 i and all small-angle step angles θ lm The sidelobe steering vector space is calculated using Capon power spectrum weighting, i.e., the interference plus noise covariance matrix is ​​reconstructed using non-uniform angular integration. The calculation method is as follows:

[0055]

[0056] Step 3: Calculate the optimal weighting coefficients Let C = a(θ0), f = 1, and a(θ0) be the steering vector of the desired signal.

[0057] For this embodiment, Figure 2The adaptive radiation pattern of the array antenna under the given signal and interference conditions is presented. The simulation covariance matrix was constructed with 512 sampling snapshots, and 200 Monte Carlo independent experiments were conducted. It can be seen that the main lobe beam shape of the adaptive radiation pattern remains unchanged, while deep nulls are generated at the locations of the two side lobe interferences. The null depths are all below -100dB, and the width of the nulls below -60dB is approximately 4°, indicating that the present invention can robustly achieve main lobe beamform preservation, side lobe adaptive anti-interference, and null broadening characteristics. Figures (a), (b), and (c) show the changes in output signal-to-interference plus noise ratio (SINR) with input SNR, number of interference sampling snapshots, and input INR, respectively. Figure (a) shows that the output SINR is not affected by the input SNR and almost matches the optimal output SINR curve, indicating that the algorithm is stable and unaffected by the desired signal. Figure (b) shows that the output SINR tends to stabilize when the number of snapshots is close to the number of array elements. As can be seen from Figure (c), the output SINR is independent of the input INR and is close to the optimal output SINR. This patented algorithm, based on robust point beamform preservation, can effectively suppress sidelobe interference.

[0058] Example 2

[0059] This example uses a 32-element, half-wavelength, equally spaced, uniform linear array. The element antennas are isotropic omnidirectional antennas, and element coupling is not considered. The desired signal originates from the 0° direction, with an element SNR of 10dB. Two sidelobe interferences originate from the -60° and -35° directions, respectively, with an element INR of 40dB for both. The noise is unit additive white Gaussian noise, and the interference and signal are spatially and temporally uncorrelated. The desired static radiation pattern is that the main lobe region satisfies the cosecant squared radiation pattern characteristics, with the main lobe region Θ = [-5°, 35°], and the sidelobe region... The sidelobe level is approximately -30dB. This statically shaped beam can be obtained using pattern synthesis algorithms such as alternating projection, with the static weight vector being w. q Static radiation pattern as Figure 4 As shown, the corresponding weighting coefficients are shown in Table 1.

[0060] Table 1 Static weights w q

[0061]

[0062] The implementation of this robust adaptive DBF algorithm based on spatial non-uniform sampling covariance matrix reconstruction under this 32-element uniform linear matrix includes the following steps:

[0063] Step 1: Based on the static radiation pattern, the main lobe region Θ = [-5°, 35°], and the side lobe region... With large angle step Δθ r =1° Calculation of Capon power spectrum in sidelobe region in The covariance matrix of the received signal is sampled. (Search) The first two maximum values ​​and their corresponding angles θ1 and θ2 are identified. Small angle steps Δθ are then taken near θ1 and θ2, respectively. α =0.1°, uniformly set M=20 angle points, and calculate the Capon power spectrum corresponding to small angle step angles.

[0064]

[0065] Step 2: Use all the large-angle step angles θ from Step 1 i and all small-angle step angles θ lm The sidelobe steering vector space is calculated using Capon power spectrum weighting, i.e., the interference plus noise covariance matrix is ​​reconstructed using non-uniform angular integration. The calculation method is as follows:

[0066]

[0067] Step 3: Select 300 angles θ evenly within the main lobe region. q (j=1,2,...,300), according to the formula Calculate the main lobe covariance matrix R Θ ,a(θ q ) is the array guidance vector. For R Θ Perform eigenvalue decomposition, and arrange the eigenvalues ​​in descending order, λ n For R Θ The nth eigenvalue, u n The corresponding normalized feature vectors are used; the first M feature vectors are taken to form the main lobe subspace U. Θ =[u1,u2,...,u M ], with U Θ Let C = U as the main lobe region constraint matrix. Θ , Calculate the optimal weight coefficient

[0068] For this embodiment, Figure 4 The synthesized static radiation pattern shape is given. The corresponding weighting coefficients are shown in Table 1. The simulation covariance matrix was constructed using 512 sampling snapshots and 200 Monte Carlo independent experiments. Figure 5The adaptive normalized beam pattern of the main lobe shaped beam is presented under the following conditions: a desired signal with an arrival direction of 0° and a signal-to-noise ratio (SNR) of 10dB; and two sidelobe interferences with arrival directions of -35° and -60°, and an SNR of 40dB each. It can be seen that the main lobe beam shape remains unchanged in the adaptive beam pattern, the sidelobe gain is below -30dB, and deep nulls are generated at the locations of both sidelobe interferences, with null depths below -100dB. Furthermore, the nulls below -60dB have a certain width, indicating that the present invention can robustly achieve main lobe beamform preservation, adaptive sidelobe anti-interference, and null broadening characteristics. Figures (d), (e), and (f) show the variation of SINR with input SNR, number of sampling snapshots, and input INR, respectively. Figure (d) shows that the output SINR is unaffected by the input SNR and is almost equal to the optimal output SINR, indicating that the algorithm has stable performance and is unaffected by the main lobe signal. Figure (e) shows that as the number of snapshots increases, the output SINR tends to stabilize when the number of snapshots is close to the number of array elements. As can be seen from Figure (f), the output SINR is independent of the input INR and approaches the optimal output SINR. This further illustrates that the algorithm of this patent can suppress sidelobe interference with high performance while maintaining the shape of the main lobe of the robust shaped wide beam.

[0069] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0070] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for reconstructing the covariance matrix of spatial non-uniform sampling for robust adaptive DBF, characterized in that, Includes the following steps: Step 1: Divide the entire airspace into the main lobe region and the side lobe region. Calculate the Capon power spectrum of the side lobe region with a large angle step, find the peak position of the power spectrum, and calculate the Capon power spectrum of the region with a small angle step at the angle close to the peak. Step 2: Simultaneously construct the weighted steering vector space of the sidelobe region using the Capon power spectra corresponding to all large and small angle steps, and reconstruct the interference plus noise covariance matrix using non-uniform angle integration. ; Step 3: Calculate the optimal weighting coefficients Where C is the constraint matrix and f is the constraint vector, which is optimized and selected according to the requirements of main lobe and side lobe shape preservation. Step 1 is as follows: Step 1-1: Calculate the Capon power spectrum of the sidelobe region using large-angle steps; The entire airspace is divided into the main lobe region Θ and the side lobe region. Taking large steps Calculate the Capon power spectrum in the sidelobe region ,in To sample the covariance matrix of the received signal, yes The corresponding guiding vector, It is the sampling start angle of the side lobe region, and Q is the number of sampling points; Steps 1-2: Locate the peak position of the power spectrum; Sort the Capon power spectrum obtained in step 1-1 in descending order, and find the top L maximum values ​​and their corresponding angles. , l=0,…,L-1, where L is the maximum number of sidelobe interferences; Steps 1-3: Advance at small angles in... Sampling points are set within the range; In respectively Take small steps nearby Uniformly set M= Calculate the Capon power spectrum corresponding to small-angle step angles at each angle point. ； Step 2 specifically involves: using all the large-angle step angles from Step 1. and all small-angle step angles The sidelobe steering vector space is calculated using Capon power spectrum weighting, i.e., the interference plus noise covariance matrix is ​​reconstructed using non-uniform angular integration. The calculation method is as follows: 。 2. The method for reconstructing the spatial non-uniform sampling covariance matrix for robust adaptive DBF according to claim 1, characterized in that, The large-angle step refers to a step of ≥1°, and the small-angle step refers to a step of <1°.

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