A "Decision and Re-Solving" Beamformer for the PAM Communication System

Minimum variance distortionless response (MVDR) beamforming is known to degrade due to effects of imprecise knowledge about the steering vector and finite sample size. However, the theoretical reasons for these have not been well investigated yet. In this paper, we propose a new mathematical model about beamforming. In the new model, beamforming is posed as ill-conditioned linear equations. The new model can clearly explain why the MVDR method suffers significant performance degradation when the knowledge about the steering vector is imprecise and the sample size is finite. Using the new model, we also propose a new beamformer for the PAM communication, which is termed as "decision and resolving beamformer". Numerical experiments have shown the robustness of the proposed beamformer against imprecise knowledge on the steering vector and/or against the finite signal length effect.