Optimal ISAC Beamforming Structure and Efficient Algorithms for Sum Rate and CRLB Balancing

Integrated sensing and communications (ISAC) has emerged as a promising paradigm to unify wireless communications and radar sensing, enabling efficient spectrum and hardware utilization. A core challenge for realizing the gains of ISAC stems from dual-functional beamforming design where the key performance metrics, such as communications sum rate and sensing Cramér-Rao lower bound (CRLB), present highly non-convex formulations. In this paper, we propose a low-complexity structured approach to ISAC beamforming optimization to simultaneously enhance spectral efficiency and sensing accuracy. Specifically, we develop a successive convex approximation (SCA)-based algorithm that transforms the original non-convex problem into a sequence of convex subproblems ensuring convergence to a stationary point. Furthermore, leveraging the proposed SCA framework and Lagrange duality, we derive the optimal beamforming structure for CRLB minimization in ISAC systems. Our analysis reveals the maximum reduction in radar streams without affecting the sensing performance. This finding enables a dimensionality reduction that enhances computational efficiency. Numerical simulations validate that our approach achieves comparable or superior performance to the considered benchmarks while requiring significantly lower computational complexity. © 1991-2012 IEEE.