Hybrid Beamforming Design for Integrated Sensing and Communication Exploiting Prior Information

In this paper, we investigate the hybrid beamforming design for a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system, where a multi-antenna base station (BS) with hybrid analog-digital transmit antenna arrays sends dual-functional signals to communicate with a multi-antenna user and simultaneously sense the location information of a point target based on the reflected echo signals. Specifically, we aim to sense the target's unknown and random angle information by exploiting its prior distribution information, with posterior Cram\'{e}r-Rao bound (PCRB) employed as the sensing performance metric. First, we consider a sensing-only case and study the hybrid beamforming optimization to minimize the sensing PCRB. We analytically prove that hybrid beamforming can achieve the same performance as the optimized digital beamforming as long as the number of radio frequency (RF) chains is larger than 1. Then, we propose a convex relaxation based algorithm for the hybrid beamforming design with a single RF chain. Next, we study the hybrid beamforming optimization to minimize the PCRB subject to a communication rate target. Due to the intractability of the exact PCRB expression, we replace it with a tight upper bound. Although this problem is still non-convex and challenging to solve, we propose an alternating optimization (AO) algorithm for finding a high-quality suboptimal solution based on the feasible point pursuit successive convex approximation (FPP-SCA) method. Numerical results validate the effectiveness of our proposed hybrid beamforming design.