Researches On Numerical Algorithms For Robust Adaptive Beamforming And The Related Theory

The array processing as an important branch of the signal processing domain is applied for many areas such as radar,sonar,communication and biomedical testing. Beamforming is a vital task for array signal processing.Beamforming which is independent of data includes the delay-sum method and all kinds of weight vector methods which are based on sidelobe control.The adaptive ben.reforming makes the optimum performance of the bcamformer by choosing weight vector,which is the function of data,under some constraint conditions.Compared with the beamformer which is independent of data,the adaptive beamformer has better resolution and ability to suppress the interference.However,the adaptive beamformer is more sensitive to errors than the one that is independent of data.Therefore,in real applications,the errors in the system always severely affect the performance of the array signal processing.So many researchers are trying to study robust array signal processing algorithms in the past thirty years.Various methods related to robust beamforming arise gradually,which include controlling the norm of the weight vector,and using the information about the variation in the steering vector to improve the robustness.By nature,these methods are modifications of the M-VDR beamforming which is presented by Capon.Recently,Yan and Ma study these beamforming methods under the frame of second-order cone programming, and solve these robust beamformers by currently available SeDuMi software pack,and give satisfying results.This paper studies several existing robust beamformers under the frame of least squares(LS) with constraints,improves some algorithms and puts forward updating algorithms for robust beamforming.It is more favorable to enhance computation efficiency, update robust beamformers effectively,and analyze their sensitivity using the algorithms of LS with constraints than using second-order cone programming.Firstly,we reduce miscellaneous robust beamformers to LS problems with constraints. In order to avoid solving the secular equation,we deduce the approximate formula for computing the optimum loading factor to improve some existing algorithms. Simulation examples show that compared with second-order cone programming ap- proach,the computation efficiency of the improved algorithm is increased,and the results in accuracy and robustness of robust beamformers are satisfying.Secondly,based on the LS updating algorithm,the fourth section concerns itself on updating and downdating algorithms for robust beamformers.The proposed algorithms have a computational advantage in the on-line mode,where it can be used to update the robust beamformer weights with computational complexity O(M~2)per updating step.Up to date,by second-order cone programming,the weight vector of the robust beamformer cannot be easily updated but has to be recomputed in each step.Lastly,we analyze the sensitivity of robust beamformers and derive some instructive conclusions for designing robust beamformers.