Optimization of ISAC Trade-Off via Covariance Matrix Allocation in Multi-User Systems

Integrated Sensing and Communication (ISAC) is envisioned as a foundational technology for future wireless networks, enabling simultaneous wireless communication and environmental sensing using shared resources. A key challenge in ISAC systems lies in managing the trade-off between communication data rate and sensing accuracy, especially in multi-user scenarios. In this work, we investigate the joint design of transmit signal covariance matrices to optimize the sum data rate while ensuring certain sensing performance. Specifically, we formulate a constrained optimization problem where the transmit covariance matrix is allocated to maximize the communication sum-rate under sensing-related constraints. These constraints condition the design of the transmit signal's covariance matrix, impacting both the sensing channel estimation error and the sum data rate. Our proposed method leverages convex optimization tools to achieve a principled balance between communication and sensing. Numerical results demonstrate that the proposed approach effectively manages the ISAC trade-off, achieving near-optimal communication performance while satisfying sensing requirements.