Beamforming Design and Subcarrier Allocation for Multicarrier Multiuser MIMO ISAC
This paper investigates joint beamforming design and subcarrier allocation in a multicarrier integrated sensing and communications (ISAC) system that operates as a monostatic multiple-input multiple-output (MIMO) radar while simultaneously providing downlink communications services to multiple users. The main objective is to jointly optimize the beamforming and subcarrier allocation to maximize the minimum radar signal-to-interference-plus-noise ratio (SINR), subject to communications SINR and total power constraints. To address the resulting mixed-integer nonconvex optimization problem, we first derive a closed-form solution for the radar receive filter using the well-known minimum variance distortionless response (MVDR) beamforming scheme, and then employ an alternating optimization (AO) framework to decompose the original problem into two subproblems: beamforming design and subcarrier allocation. For the beamforming design, we propose an efficient approach that combines fractional programming (FP) and successive convex approximation (SCA) techniques. Furthermore, by leveraging the block-diagonal form of the matrices in the radar SINR formulation, we derive a simplified expression for the radar SINR, which significantly reduces the computational complexity and memory usage of the proposed method. Numerical results validate the convergence and effectiveness of the proposed algorithm and illustrate the trade-off between sensing and communications performances. The results show that the proposed method performs close to the radar-only benchmark under moderate communications SINR requirements and achieves substantial performance gains compared with a beampattern-mismatch-driven baseline scheme.