Robust Beamforming Design Based On Matrix Shrinkage Estimation

Beamforming has wide applications in wireless communications,radar,sonar,and other array systems.Digital beamforming is usually designed based on the array response and the estimation of the covariance matrix of the received signal.Due to the error of antenna gain,phase,direction of arrival(DOA),and covariance matrix estimation,the steering vector(SV)produces model mismatch,and this model mismatch leads to a decrease in beamforming performance.In practice,model mismatch is ubiquitous,but its severity may be unknown.The adaptive selection of beamformer solutions may be a meaningful research direction in the future.This thesis aims to study the robustness of several beamformer designs based on covariance or precision matrix shrinkage,interference-plus-noise covariance matrix reconstruction,diagonal loading,condition number regularization and eigensubspace,in the presence of model mismatch.We also study the combinations of the different strategies in beamformer design.These methods have different requirements for array response knowledge.The output signal and noise plus interference ratio(SINR)is adopted as the design criterion.Numerical studies show that knowledge of the DOA of SOI and array geometry significantly affects the performance.The interference plus noise covariance reconstruction method relies on knowledge of the array response of different DOA,and achieves superior performance when this knowledge is accurate.However,it seems to be the most sensitive to mismatch in array geometry.In contrast,methods based on covariance and exact matrix shrinkage do not utilize the array geometry and DOA of SOI.When such knowledge is accurate,they are clearly suboptimal,but their performance is more robust when model mismatches exist.