A Design Method of Adaptive Spatial Filter with Stopband Response Constraint

Abstract

The present invention proposes a design method for a stopband response-constrained adaptive spatial domain filter, belonging to the technical field of array signal processing. The present invention constrains the stopband response and minimizes the sum of the filter output signal norm and the overall response error of the filter passband. This filter design method solves three technical problems: First, this method can control the overall error of target signals in all directions in the passband by adjusting the passband response coefficients; Second, this method can control the overall suppression ability of the filter against omnidirectional interference in the stopband by adjusting the stopband response constraint value; Third, this method has high design efficiency and is conducive to real-time signal processing.

Description

Technical Field

[0001] The present invention belongs to the technical field of array signal processing, and relates to a design method of an adaptive spatial domain filter with a stopband response constraint and an adjustable passband response coefficient. Background Art

[0002] Target detection based on a sensor array is an important means to improve the accuracy of target orientation and positioning. However, the data received by the sensor array often contains strong far-field or near-field interference. Affected by the strong far-field and near-field interference, the accuracy of target orientation and positioning based on the sensor array decreases, and the target reconnaissance and recognition ability is reduced.

[0003] The spatial domain matrix filtering technology designs the passband and stopband of the detection spatial domain and adopts an appropriate filter design method to achieve the desired response effect of the spatial domain filter on the passband and stopband. The filter matrix is multiplied by the array data received by the sensor to achieve spatial domain filtering. Through spatial domain filtering, the stopband interference can be suppressed, and the useful signals in the passband can be retained.

[0004] The conventional spatial domain filter design technology mainly generates specific filtering response effects on the passband and stopband through fixed passband and stopband divisions. When the intensity of the interference in the spatial domain changes, the conventional spatial domain filter cannot adaptively adjust the suppression ability of the interference spatial domain according to the energy level of the interference. The prior art document 1 "Spatial Domain Matrix Filtering and Its Applications" (Han Dong, Zhang Haiyong, Science Press, April 2016) elaborates in detail on the designs of discrete, weighted discrete, and continuous filters, and their design methods are all conventional spatial domain filter design methods.

[0005] Prior art document 2, "Adaptive Spatial Matrix Filter Design and Target Azimuth Estimation", by Feng Jie, Yang Yixin, Sun Chao, Journal of System Simulation, 2007, 19(20): 4798 - 4802; and prior art document 3, "Convex OptimizationBased Beam-Space Preprocessing With Improved Robustness Against Out-of-SectorSources", by Hassanien A, Elkader S A, Gershman AB, etc., IEEE Trans. Signal Processing, 2006, 54(5): 1587 - 1595, designed an adaptive spatial filter design method to constrain the response error in each azimuth of the passband and the response in specific azimuths of the stopband. The passband and stopband settings in both are based on the model of a far-field plane wave signal incident on the array. That is, the target signal to be detected is in the spatial passband of the far-field plane wave model, and the interference signal is in the stopband of the far-field plane wave model. The main disadvantages of this method are twofold: First, the incident model of the interference signal is restricted to plane wave incidence, and its applicability is not wide. This model does not consider the complexity of signal propagation. When the noise is a near-field interference incident model or a model after multi-path incidence, 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 amount of computation is large, and the timeliness is poor. The design method needs to be converted into a second-order cone programming solution, and it cannot give a concise optimal solution expression, which in turn affects the practicality of this technology. Summary of the Invention

[0006] The object of the present invention is to provide an adaptive spatial filter design method with stopband response constraint and adjustable passband coefficients, and directly give the optimal solution of the filter. This filter design method solves three technical problems: First, this method can control the overall error of target signals in each azimuth of the passband by adjusting the passband response coefficients; Second, this method can control the overall suppression ability of the filter against omnidirectional interference in the stopband by adjusting the stopband response constraint values; Third, this method has high design efficiency and is conducive to real-time signal processing.

[0007] The technical solution of the present invention is as follows:

[0008] Assume that the array receives plane wave signals, s1(t) is the passband target signal, s0(t) is the stopband interference signal, and n(t) is the additive noise; the model of the array received data x(t) is as follows:

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

[0010] where is the array manifold matrix composed of the passband direction vectors, and V P = [a(θ1), …, a(θ p ), …, a(θ P ), 1 ≤ p ≤ P, θ p ∈ Θ P , where Θ P represents the passband region where the direction vectors are located, and a(θ p ) is the p-th direction vector after passband discretization, and P corresponds to the number of direction vectors after passband region discretization. is the array manifold matrix composed of the stopband response vectors, and V S = [v1, …, v s , …, v S , 1 ≤ s ≤ S, where S is the number of stopband interferences, and v s 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 other azimuth interference, or interference signal incident on the array after multipath superposition.

[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] Design the adaptive spatial filter H. Constrain the overall stopband response, and under this condition, minimize the sum of the filter output signal norm and the filter passband overall response error. This adaptive spatial filter corresponds to the optimization problem:

[0014]

[0015]

[0016] where k is an adjustable coefficient, and ε ≥ 0 is the stopband response constraint value.

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

[0018]

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

[0020]

[0021] Advantages of the present invention: The design method adopted by the present invention can directly give the optimal solution of the filter by using the received array data and the spatial domain passband array manifold where the target signal is located, improving the filter design efficiency. Moreover, since the objective function of the filter design optimization problem includes the overall passband response error, the overall distortion of the passband signal can be adjusted by the coefficient k. Description of the Drawings

[0022] Figure 1(a) - Figure 1(b) Shows the effect of the adaptive spatial filter, with the adjustment coefficient being 10 -3 , and the stopband response constraint value is 10 -5 , the passband range is set to [-15°, 15°], and the stopband range is set to [-90°, -18°] ∪ [18°, 90°]. Among them, Fig. 1(a) is the filter response, and Fig. 1(b) is the filter response error. Detailed Implementation Manner

[0023] The following specifically describes the embodiments of the present invention in detail in combination with the content of the invention and the drawings.

[0024] A method for designing a stopband response constraint adaptive spatial filter includes the following steps:

[0025] Step 1: Select the passband detection region Θ to be retained P , and discretize the passband detection region Θ P into P directions to obtain the corresponding plane wave incident azimuth angles θ p , p = 1, …, P. Use the signal incident model to find its corresponding direction vector a(θ p ) and the array manifold matrix V P = [a(θ1), …, a(θ p ), …, a(θ P ), 1 ≤ p ≤ P, and calculate

[0026] Step 2: Select the interference signals to be suppressed. Determine the number S of stopband interferences and the array response vector v of the interference signals s ; generate the array manifold matrix V S composed of the stopband array response vectors = [v1, …, v s , …, v S , 1 ≤ s ≤ S, and calculate

[0027] Step 3: Set the stopband response constraint value ε and the adjustable coefficient k.

[0028] Step 4: Calculate the covariance matrix C using the received array data x(t) x= x(t)x H (t).

[0029] Step 5: Use the formula to calculate and obtain the optimal solution of the adaptive spatial domain filter where is determined by Equation .

Claims

1. A design method for a stopband response-constrained adaptive spatial domain filter, characterized in that The method includes the following steps: Step 1: Select the passband detection region Θ to be retained P , discretize the passband detection region Θ P into P directions to obtain the corresponding incident azimuth angles θ of plane waves p , p = 1, …, P; use the signal incident model to find its corresponding direction vector a(θ p ) and the array manifold matrix V P = [a(θ1), …, a(θ p ), …, a(θ P )], and calculate Step 2: Select the interference signals to be suppressed; determine the number S of stopband interferences and the array response vector v of the interference signals s ; Generate the array manifold matrix V composed of the stopband array response vectors S = [v1, …, v s , …, v S , 1 ≤ s ≤ S, and calculate Step 3: Set the stopband response constraint value ε and the adjustable coefficient k; Step 4: Calculate the covariance matrix C using the received array data x(t) x = x(t)x H (t); Step 5: Use the formula to calculate and obtain the optimal solution of the adaptive spatial domain filter where is determined by Equation .

Images