Optimal Hybrid Transmit Beamforming for mm-Wave Integrated Sensing and Communication

A hybrid beamformer (HBF) is designed for integrated sensing and communication (ISAC)-aided millimeter wave (mmWave) systems. The ISAC base station (BS), relying on a limited number of radio frequency (RF) chains, supports multiple communication users (CUs) and simultaneously detects the radar target (RT). To maximize the probability of detection (PD) of the RT, and achieve rate fairness among the CUs, we formulate two problems for the optimization of the RF and baseband (BB) transmit precoders (TPCs): PD-maximization (PD-max) and geometric mean rate-maximization (GMR-max), while ensuring the quality of services (QoS) of the RT and CUs. Both problems are highly non-convex due to the intractable expressions of the PD and GMR and also due to the non-convex unity magnitude constraints imposed on each element of the RF TPC. To solve these problems, we first transform the intractable expressions into their tractable counterparts and propose a power-efficient bisection search and majorization and minimization-based alternating algorithms for the PD-max and GMR-max problems, respectively. Furthermore, both algorithms optimize the BB TPC and RF TPCs in an alternating fashion via the successive convex approximation (SCA) and penalty-based Riemannian conjugate gradient (PRCG) techniques, respectively. Specifically, in the PRCG method, we initially add all the constraints except for the unity magnitude constraint to the objective function as a penalty term and subsequently employ the RCG method for optimizing the RF TPC. Finally, we present our simulation results and compare them to the benchmarks for demonstrating the efficacy of the proposed algorithms.