Research On Robust Adaptive Beamforming Algorithm Under Angle Mismatch

Array signal processing is an important research branch in the field of signal processing,and useful information can be obtained after processing spatial signal received by the spatially distributed sensor array.Adaptive array processing is a technique to adjust the weight vector adaptively,and form spatial directivity in the direction of interest after processing the received data.It has been widely used in radar,communication,navigation,medical use and other fields.However,there will be a variety of complex errors in practical environment,such as observation direction error,array element calibration error,channel amplitude-phase error and other factors,resulting in the angle error of the direction of arrival.And the output signal to interference plus noise ratio(SINR)of the beamforming algorithm will be greatly reduced.Therefore,how to improve the output performance of adaptive beamforming algorithm under the condition of angle mismatch has been concerned and studied by many scholars in recent years.A series of robust beamforming algorithms have been proposed in succession,however,there are still some problems in these algorithms which should be solved urgently.Under the research background,this paper will focus on the robust beamforming algorithms under the condition of angle mismatch.The details are as follows:Firstly,the basic theory and method of adaptive beamforming algorithm are expounded.The mathematical model of far-field narrowband signal with uniform linear array,the three optimization criteria of beamforming algorithm,and the related evaluation of algorithm performance are introduced in detail.Then the paper introduces several traditional beamforming algorithms,including the conventional beamforming algorithm,minimum variance distortionless response algorithm and sample matrix inverse algorithm.For each algorithm,the mathematical model of formula is deduced in detail and simulation is carried out by using MATLAB software.The algorithms are summarized with different experimental parameters and relevant simulations.Then the influence of steering vector mismatching and the robustness of covariance matrix mismatching algorithm are analyzed.Several classical robust algorithms with steering vector mismatch in recent years are introduced emphatically.Experimental analysis shows that it is difficult to determine the loading factor of RAB algorithm based on diagonal loading.When the number of snapshots is low,the performance of RAB algorithm based on eigenvalue subspace division decreases sharply.With large error range of direction vector,the RAB algorithm modeled by the uncertainty has a poor performance.To deal with the mentioned problems,this paper proposes the improved method in the scenarios of limited snapshots and existing large angle error.Next,an improved SMI algorithm based on unitary transform is studied in this paper,aiming at the defects of SMI algorithm with high sidelobe and main beam distortion with low number of snapshots.SMI algorithm is the actual implementation of MVDR beamformers.The finite snapshots result in the mismatch of sample covariance matrix,and the eigenvalue of noise is not stable enough.It leads to the increase of sidelobe of beam response in SMI algorithm.The improved algorithm proposed in this paper processes the received data through unitary transformation,and the number of snapshots can be expanded.Meanwhile,the data is transformed from complex-value numbers to real-value numbers.Simulation results show that the proposed algorithm has faster convergence and better output performance with low snapshots.Then,in the view of angle mismatch caused by various factors in the actual environment,the robust algorithm of amplitude constraint of incoming signals has been widely used,but the sidelobe gain of such algorithm is often relatively high.In the process of obtaining the weight vector,if the received data contains signal components,even if the direction vector is only slightly mismatched,the algorithm performance will be greatly reduced.Therefore,an amplitude constraint algorithm based on covariance matrix reconstruction is proposed in this paper.The algorithm constraints the signal amplitude of an area which is close to the desired signal direction.At the same time,applying the subspace theory to evaluate the direction vector,then using the evaluation vector and real guidance vector,finding the covariance matrix of the desired signal steering vector and the corresponding signal eigenvalues,and replacing the eigenvalues by average noise eigenvalues,the influence of desired signal is eliminated.Finally,the performance evaluation of the algorithm is verified and analyzed with MATLAB simulation software,and the results show that the proposed improved algorithm has good robustness.