Active Uplink Sensing Beamformer Design via Bayesian Cramér-Rao Bound Dual Optimization

This paper presents a novel optimization framework for solving active sensing problems in wireless communications, in which a base station equipped with massive multiple-input multiple-output (MIMO) and a limited number of radio-frequency chains aims to estimate the channel parameters of a sensing target. Specifically, the receive beamforming matrix at the BS is designed sequentially through optimizing the Bayesian Cramér-Rao bound (B-CRB) metric at each sensing stage, while satisfying a rank constraint and that the receive beamformers must be implementable by analog phase shifters. The proposed approach tackles this B-CRB minimization problem in the Lagrangian dual domain. This dual optimization approach has the advantage of reducing the dimension of the search space from the number of antenna elements to the number of channel parameters, which is typically much smaller for sparse mmWave channels. We propose efficient numerical methods for obtaining the primal solution from the dual and subsequentially setting the phase shifts in each active sensing stage based on this approach. Finally, we demonstrate the benefits of the proposed approach as compared to existing beamforming strategies.