A Fractional Programming Approach for the Joint Optimization of Communication Performance and Detection Probability

This paper investigates the beamforming design for a multi-user, multi-target integrated sensing and communication (ISAC) system. Our objective is to maximize the radar detection probability, subject to constraints on the total transmit power of the base station (BS) and the communication quality of service (QoS) requirement for each user. The formulated optimization problem is non-convex, presenting a significant analytical challenge. For handling this, we propose a novel optimization framework that leverages the principles of fractional programming (FP), offering an alternative to prevalent methods like semidefinite relaxation or successive convex approximation. By utilizing the quadratic transform, a key technique within the FP framework, the original non-convex problem is equivalently reformulated as a group of more tractable convex subproblems. Numerical results validate the efficiency and feasibility of the proposed algorithm in solving the considered optimization problem.