Passband response constrained adaptive spatial filter design method

Abstract

The application provides a passband response constrained adaptive spatial filter design method, and belongs to the technical field of array signal processing.The application constrains the passband response error and minimizes the output array data norm, and can directly give an optimal solution of the filter.The filter design method solves two technical problems: on the one hand, the target signal of a required detection passband can be reserved, the passband target signal error is controllable, and other interference signals can be effectively suppressed; on the other hand, the design efficiency is high, and is beneficial to real-time signal processing.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology and relates to an adaptive spatial filter design method with passband response error constraints. Background Technology

[0002] Target detection using sensor arrays is an important means of improving target orientation and positioning accuracy. However, the data received by sensor arrays often contains strong far-field or near-field interference. This interference reduces the target orientation and positioning accuracy based on sensor arrays, thus lowering the target reconnaissance and identification capabilities.

[0003] Spatial matrix filtering technology achieves the desired response of a spatial filter to the passband and stopband by designing the passband and stopband of the probe space and employing appropriate filter design methods. Spatial filtering is achieved by multiplying the filter matrix by the array data received by the sensor. This spatial filtering process suppresses stopband interference while preserving useful signals in the passband.

[0004] Conventional spatial filter design techniques primarily utilize fixed passband and stopband divisions to produce specific filtering responses for each passband and stopband. However, when the intensity of interference in the spatial domain changes, conventional spatial filters cannot adaptively adjust their suppression capability based on the interference's energy level. Existing literature 1, "Spatial Matrix Filtering and Its Applications" (Han Dong, Zhang Haiyong, Science Press, 2016.4), elaborates on the design of discrete, weighted discrete, and continuous filters, all employing conventional spatial filter design methods.

[0005] Existing technical literature 2, “Adaptive Spatial Matrix Filter Design and Target Azimuth Estimation”, Feng Jie, Yang Yixin, Sun Chao, Journal of System Simulation, 2007, 19(20):4798-4802; and existing technical literature 3, “Convex OptimizationBased Beam-Space Preprocessing With Improved Robustness Against Out-of-Sector Sources”, Hassanien A, Elkader SA, Gershman AB, et al., IEEE Trans. Signal Processing, 2006, 54(5):1587-1595, designed an adaptive spatial filter design method, which constrains the response error of each azimuth in the passband and the response of a specific azimuth in the stopband. The passband and stopband settings are based on the model of far-field plane wave signals incident on the array. That is, the target signal to be detected is located in the spatial passband of the far-field plane wave model, and the interference signal is located in the stopband of the far-field plane wave model. The main drawbacks of this method are twofold: First, the incident model of the interference signal is limited to plane wave incidence, resulting in limited applicability. This model does not consider the complexity of signal propagation. When the noise is a near-field interference incident model or a model after multipath incident, the stopband design should be adapted to the spatial incident response vector of the interference, rather than the plane wave direction vector. Second, the solution efficiency is low, the computational load is high, and the timeliness is poor. The design method needs to be converted to a second-order cone programming solution, which cannot provide a concise optimal solution expression, thus affecting the practicality of the technique. Summary of the Invention

[0006] The purpose of this invention is to provide a passband response-constrained adaptive spatial filter design method and directly provide the optimal solution for the filter. This filter design method solves two technical problems: firstly, it can retain the target signal in the desired detection passband, making the passband target signal error controllable and effectively suppressing other interference signals; secondly, due to its high design efficiency, this method is beneficial for real-time signal processing.

[0007] The technical solution of this invention is:

[0008] Assuming s1(t) is the target signal via the passband, s0(t) is near-field interference, far-field interference from other directions, or interference signal superimposed by multipath interference, and n(t) is additive noise; the model for the array-received data x(t) is as follows:

[0009] x(t)=V P s1(t)+V S s0(t)+n(t)

[0010] In the formula, It is an array manifold matrix composed of passband direction vectors, V P =[a(θ1),…,a(θ)] p ),…,a(θ P )],1≤p≤P,θ p ∈Θ P Θ P a(θ) represents the passband region containing the direction vector. p ) is the p-th direction vector after the passband is discretized, and P corresponds to the number of direction vectors after the passband region is discretized. It is an array manifold matrix composed of stopband response vectors, V S =[v1,…,v s ,…,v S ], 1≤s≤S, where S is the number of stopband interferences, v s This is the array response vector of the interference signal. Here, the stopband array response vector can be the result of near-field interference, far-field interference from other directions, or interference signals superimposed by multiple paths incident on the array.

[0011] Design an N×N dimensional adaptive spatial filter H, and use this filter to filter the received array data to obtain the output filtered signal:

[0012] y(t)=Hx(t)=HV P s1(t)+HV S s0(t)+Hn(t)

[0013] Given a passband overall response error constraint, find the adaptive spatial filter that minimizes the data norm of the output array. This adaptive spatial filter corresponds to the optimization problem:

[0014]

[0015]

[0016] Where ξ is the passband response error constraint value.

[0017] The optimal solution for the adaptive spatial filter H is:

[0018]

[0019] In the formula C x =x(t)x H (t); The optimal Lagrange multiplier is determined by the following formula:

[0020]

[0021] The beneficial effects of this invention are as follows: The design method employed in this invention can directly provide the optimal solution for the filter using the spatial passband array manifold where the received array data and the target signal reside, thereby improving filter design efficiency. Furthermore, since the overall error of the passband response is limited during the filter design process, the distortion of the passband signal can be guaranteed to be controllable. Attached Figure Description

[0022] Figure 1 shows the effect of the adaptive spatial filter H, with the ξ value set to 10. -6 The passband region is [-10°, 15°]. Figure 1(a) shows the filter response, and Figure 1(b) shows the filter response error. Detailed Implementation

[0023] The specific embodiments of the present invention are described in detail below with reference to the invention description and accompanying drawings.

[0024] A passband response-constrained adaptive spatial filter design method includes the following steps:

[0025] Step 1: Select the passband detection area to be retained. P The passband detection area Θ P Discretize into P directions to obtain the corresponding plane wave incident azimuth angle θ p p = 1, ..., P. Using the signal incident model, find the corresponding direction vector a(θ). p and array manifold matrix V P =[a(θ1),…,a(θ)] p ),…,a(θ P Given that 1 ≤ p ≤ P, find the answer.

[0026] Step 2: Set the passband response error constraint value ξ.

[0027] Step 3: Calculate the covariance matrix C using the received array data x(t). x =x(t)x H (t).

[0028] Step 4: According to the formula Calculate the optimal solution for the adaptive spatial filter. Among them, the optimal Lagrange multiplier From the formula Sure.

[0029] The design method described in this invention has high design efficiency, can ensure that plane wave signals in the passband pass through with less distortion, and can effectively suppress other interference signals.

Claims

1. A method for designing a passband response-constrained adaptive spatial filter, characterized in that, The method includes the following steps: Step 1: Select the passband detection area to be retained. P The passband detection area Θ P Discretize into P directions to obtain the corresponding plane wave incident azimuth angle θ p p = 1, ..., P; use the signal incident model to find its corresponding direction vector a(θ) p and array manifold matrix V P =[a(θ1),…,a(θ)] p ),…,a(θ P ]], and find Step 2: Set the passband response error constraint value ξ; Step 3: Calculate the covariance matrix C using the received array data x(t). x =x(t)x H (t); Step 4: According to the formula Calculate the optimal solution for the adaptive spatial filter. Among them, the optimal Lagrange multiplier From the formula Sure.

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