Robust adaptive beamforming method and system based on improved householder transformation

Abstract

The application provides a robust adaptive beamforming method and system based on Householder transformation and improved array manifold prior knowledge, relates to the technical field of radars, communications and sensor networks, and converts a WCPO problem containing a nonlinear constraint into an unconstrained optimization problem, realizes fast convergence in combination with a least mean square (LMS) algorithm, and solves the problems of high calculation complexity and poor real-time performance in the prior art.

Description

Technical Field

[0001] This invention relates to the fields of radar, communication and sensor network technology, and more particularly to a robust adaptive beamforming method and system for geometric perturbation of sensor arrays or antenna arrays and suppression of interference signals. Background Technology

[0002] Existing adaptive beamforming techniques (such as MVDR and SMI) exhibit significant performance degradation when there is signal steering vector (SV) mismatch or covariance matrix estimation error. Traditional diagonal loading (DL) techniques require manual setting of the loading factor, resulting in insufficient flexibility; while the second-order cone programming (SOCP) algorithm can optimize worst-case performance (WCPO), its computational complexity is high. This approach is insufficient to meet the real-time application requirements of radar, broadband communications, and other applications. Therefore, a robust beamforming method that combines high performance with low computational complexity is urgently needed. Summary of the Invention

[0003] In response to the technical problems mentioned in the background section, this invention provides a robust adaptive beamforming method and system based on an improved Householder transform. This invention offers a robust adaptive beamforming method and system improved based on Householder transform and prior knowledge of the array manifold. By transforming the WCPO problem with nonlinear constraints into an unconstrained optimization problem, and combining it with the Least Mean Square (LMS) algorithm to achieve fast convergence, it solves the problems of high computational complexity and poor real-time performance in existing technologies.

[0004] The technical means employed in this invention are as follows: A robust adaptive beamforming method based on an improved Householder transform is characterized by designing a beamforming spatial filter using prior knowledge of the sensor array manifold and the desired signal direction angle information, transforming the objective optimization problem with array perturbation uncertainty constraints into an unconstrained objective optimization problem using a variable substitution method, and combining stochastic gradient optimization techniques to achieve parameter estimation of the beamforming spatial filter, including the following steps: Step 1: Construct an N-order Householder matrix G from the sensor array manifold; extract the last N-1 column vectors of G to form a construction matrix D; construct matrix [aD] = [ ] from the construction matrix D and the receiving array steering vector a; Step 2: Transform the worst-case performance optimization (WCPO) problem with constraints into a problem about... Unconstrained optimization problem; Step 3: Iteratively solve the unconstrained optimization problem using the Least Mean Square (LMS) algorithm to obtain the optimal array weights. .

[0005] Furthermore, in step 1, the beamformer Represents the normalized steering vector and the column vector of D Linear combinations with basis: ; in, Determined by the uncertainty set constraint equation; These are parameters to be optimized.

[0006] Furthermore, the construction of the improved Householder matrix Includes the following steps: Step 11: Define the normalized steering vector and unit vector ; Step 12: Construct the Householder matrix Extract the last N-1 columns of G to form a matrix. ; Step 13, the constructed matrix ,satisfy: as well as ; Then the beamforming vector Represented as: ; in, , This indicates the parameters to be optimized.

[0007] Furthermore, in step 2, the objective function of the unconstrained optimization problem is: ; in, , = , .

[0008] Furthermore, step 2 includes the following steps: Step 21: Transform the original constrained optimization problem into a matrix. Transformation into an unconstrained optimization problem: The original constraint optimization problem is: ; Step 22: Derive the results using constraints The expression: ; Step 23: The objective function is transformed into a function about Unconstrained optimization problem:

[0009] in, , , All are constant parameters.

[0010] Furthermore, in step 3, the LMS algorithm iterates using the following formula: ; in, This represents the gradient of the objective function.

[0011] The present invention also includes a robust adaptive beamforming system based on an improved Householder transform, comprising: The matrix construction module is used to generate the improved Householder matrix. ; The optimization problem transformation module is used to transform constrained optimization problems into unconstrained optimization problems; The LMS iterative module is used to adaptively solve for the optimal array weights. Compared with the prior art, this invention has the following advantages: Compared with the traditional SOCP algorithm, the method of this invention has comparable performance in terms of signal-to-noise ratio (SNR), number of samples, convergence speed and number of array units, and effectively suppresses the performance degradation caused by signal mismatch.

[0012] The computational complexity of the method of this invention is (Parameter initialization phase) + (LMS iteration phase) significantly lower than the traditional SOCP algorithm The average CPU time is only 1 / 295 of that of traditional SOCP. (Refer to Table 1) Table 1. Comparison of computation time (time / second) using the method of this invention and commonly used second-order cone optimization methods.

[0013] The method of this invention can converge in about 15 iterations (average of 100 Monte Carlo experiments) using the LMS algorithm (see Table 2), and is suitable for scenarios with high real-time requirements such as radar and broadband communication.

[0014] Table 2. Number of convergence iterations using the method of this invention (average of 100 Monte Carlo experiments) Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of the overall process of the present invention.

[0017] Figure 2 This is a schematic diagram comparing the performance of the present invention with existing methods when the drying ratio is 30 dB for a 16-element uniform linear array.

[0018] Figure 3 This is a schematic diagram comparing the beam patterns of the 16-element uniform linear array of the present invention with those of existing methods.

[0019] Figure 4 This is a schematic diagram showing the relationship between the array output signal-to-interference-plus-noise ratio (SNR) and the number of snapshots (signal samples) when the interference-to-noise ratio (INR) is 30 dB and the signal-to-noise ratio (SNR) is 10 dB.

[0020] Figure 5 This diagram illustrates a comparison of the time taken by the present invention and the time taken by the second-order cone method when achieving the same performance.

[0021] Figure 6 This shows the relationship between the time consumption of the method of the present invention and the time consumption of the second-order cone method and the number of array sensors. Detailed Implementation

[0022] To enable those skilled in the art to better understand the present invention, 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 should fall within the scope of protection of the present invention.

[0023] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0024] like Figure 1-6 As shown, this invention provides a robust adaptive beamforming method based on an improved Householder transform. Its key feature is that it designs a beamforming spatial filter using prior knowledge of the sensor array manifold and the desired signal direction angle information. It transforms the objective optimization problem with array perturbation uncertainty constraints into an unconstrained objective optimization problem using a variable substitution method, and combines stochastic gradient optimization techniques to achieve parameter estimation of the beamforming spatial filter. The method includes the following steps: Step 1: Construct an N-order Householder matrix G from the sensor array manifold; extract the N-1 column vectors from G to form a construction matrix D; construct matrix [aD] = [] from the construction matrix D and the receiving array steering vector a; in Step 1, the beamformer... Represents the normalized steering vector and the column vector of D Linear combinations with basis: ; in, Determined by the uncertainty set constraint equation; These are parameters to be optimized.

[0025] In this application, an improved Householder matrix is ​​constructed. Includes the following steps: Step 11: Define the normalized steering vector and unit vector ; Step 12: Construct the Householder matrix Extract the last N-1 columns of G to form a matrix. ; Step 13, the constructed matrix ,satisfy: as well as ; Then the beamforming vector Represented as: ; in, , This indicates the parameters to be optimized.

[0026] Step 2: Transform the worst-case performance optimization (WCPO) problem with constraints into a problem about... The unconstrained optimization problem; in step 2, the objective function of the unconstrained optimization problem is: ; in, , = , .

[0027] In a preferred embodiment, step 2 in this application includes the following steps: Step 21: Transform the original constrained optimization problem into a matrix. Transformation into an unconstrained optimization problem: The original constraint optimization problem is: ; Step 22: Derive the results using constraints The expression: ; Step 23: The objective function is transformed into a function about Unconstrained optimization problem:

[0028] in, , , All are constant parameters.

[0029] Step 3: Iteratively solve the unconstrained optimization problem using the Least Mean Square (LMS) algorithm to obtain the optimal array weights. In step 3, the LMS algorithm iterates, and the formula is: ; in, This represents the gradient of the objective function.

[0030] In this application, the present invention also includes a robust adaptive beamforming system based on an improved Householder transform, comprising: The matrix construction module is used to generate the improved Householder matrix. ; The optimization problem transformation module is used to transform constrained optimization problems into unconstrained optimization problems; The LMS iterative module is used to adaptively solve for the optimal array weights.

[0031] Example 1 Parameter initialization: Set the number of array cells Error bound , guide vector Corresponding target direction The incident angles of the interfering signals are -20 degrees and 30 degrees, and the interference-to-noise ratio is 30 dB. The signal of interest and the interfering signal are simulated using Gaussian distributed random numbers. Initial parameters are calculated. and improved Householder matrix .

[0032] Covariance matrix estimation: Estimating the covariance matrix using 100 sample snapshots .

[0033] Gradient calculation of objective function:

[0034] Approximation using LMS iterative calculation Set the convergence threshold Maximum number of iterations: 2000. Updated iteratively. This continues until the relative error is less than the threshold.

[0035] Beamforming weight calculation: based on the optimized Calculate array weights This enables the enhancement of the target signal and the suppression of interference.

[0036] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0037] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0038] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For instance, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling, direct coupling, or communication connection may be through some interfaces; the indirect coupling or communication connection between units or modules may be electrical or other forms.

[0039] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0040] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0041] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0042] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A robust adaptive beamforming method based on an improved Householder transform, characterized in that, A beamforming spatial filter is designed using prior knowledge of the sensor array manifold and the desired signal direction angle information. A variable substitution method is employed to transform the objective optimization problem with array perturbation uncertainty constraints into an unconstrained objective optimization problem. Combined with stochastic gradient optimization, the parameters of the beamforming spatial filter are estimated, including the following steps: Step 1: Construct an N-order Householder matrix G from the sensor array manifold; extract the last N-1 column vectors of G to form a construction matrix D; construct matrix [aD] from the construction matrix D and the receiving array steering vector a; Step 2: Transform the worst-case performance optimization (WCPO) problem with constraints into a problem concerning the parameters to be optimized. The unconstrained optimization problem; step 2 includes the following steps: Step 21: Transform the original constrained optimization problem into a matrix. Transformation into an unconstrained optimization problem: The original constraint optimization problem is: ； Step 22: Derive the results using constraints The expression: ； Step 23: The objective function is transformed into a function about Unconstrained optimization problem: in, , , All are constant parameters; among them, , = , ; Step 3: Use the Least Mean Square (LMS) algorithm to iteratively solve the unconstrained optimization problem and obtain the optimal array weights.

2. The robust adaptive beamforming method based on the improved Householder transform according to claim 1, characterized in that, In step 1, the beamformer Represented as a normalized steering vector and constructing matrices D column vectors Linear combinations with basis: ； in, Determined by the uncertainty set constraint equation; These are parameters to be optimized.

3. The robust adaptive beamforming method based on the improved Householder transform according to claim 1, characterized in that, Constructing an improved Householder construction matrix Includes the following steps: Step 11: Define the normalized steering vector and unit vector ; Step 12: Construct the Householder matrix Extract the last N-1 columns of G to construct the matrix. ; Step 13, the constructed matrix ,satisfy: as well as ; Beamformer Represented as: ； in, , This indicates the parameters to be optimized.

4. A robust adaptive beamforming method based on improved Householder transform according to claim 1, characterized in that, In step 3, the LMS algorithm iteratively uses the following formula: ； in, This represents the gradient of the objective function.

5. A robust adaptive beamforming system based on an improved Householder transform, employing the method described in any one of claims 1-4, characterized in that, include: The matrix construction module is used to generate the improved Householder construction matrix. ; The optimization problem transformation module is used to transform constrained optimization problems into unconstrained optimization problems; The LMS iterative module is used to adaptively solve for the optimal array weights.

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