Beamspace ESPRIT for mmWave Channel Sensing: Performance Analysis and Beamformer Design

In this paper, we consider the beamspace ESPRIT algorithm for Millimeter-Wave (mmWave) channel sensing. We provide a non-asymptotic analysis of the beamspace ESPRIT algorithm. We derive a deterministic upper bound for the matching distance error between the true angle of arrival (AoA) of the channel paths and the estimated AoA considering a bounded noise model. Additionally, we leverage the insight obtained from our theoretical analysis to propose a novel max-min criterion for beamformer design which can enhance the performance of mmWave channel estimation algorithms, including beamspace ESPRIT. We consider a family of multi-resolution beamformers which can be implemented using phase shifters and introduce a design scheme for the optimal beamformers from this family with respect to the proposed max-min criteria. We can guarantee a minimum beamforming gain uniformly over a region of possible multipath directions, which can lead to more robust channel estimation. We provide several numerical experiments to verify our theoretical claims and demonstrate the superior performance of the proposed beamformers compared to existing beamformer design criteria.