Joint Cramér-Rao Bound and Communication Rate Optimization for Dual-Functional Radar-Communication Systems with Target DoA Estimation Errors

In dual-functional radar-communication (DFRC) systems, to achieve desirable performance in both direction-of-arrival (DoA) estimation for sensing targets and wireless communication for user equipments (UEs), the Cramér-Rao bound (CRB) for DoA estimation and the communication rates of UEs should be jointly optimized through beamforming design. However, the CRB function is inherently dependent on prior knowledge of DoA, which may only be obtained through existing estimators that introduce unavoidable estimation errors. Such errors inevitably degrade the optimization performance. To address this issue, we propose novel optimization methodologies for CRB minimization and communication rate guarantees, which effectively reduce the adverse impact of target DoA estimation errors. Specifically, considering a bounded DoA error model and a statistical DoA error model, two optimization problems are formulated to optimize the worst-case CRB and the statistical mean of CRB over the DoA error regions, while ensuring that the communication rates of multiple UEs exceed predefined thresholds. To tackle the first problem, we propose a semidefinite relaxation (SDR)-based iterative entropic regularization (SDR-IER) method, acquiring approximate solutions via alternating outer minimization and inner maximization. For the second problem, we develop a vectorial space analysis (VSA)-based projected stochastic gradient descent (VSA-PSGD) approach, featuring closed-form projections per iteration for single-user cases, and successive convex approximation (SCA)-based projections for multi-user cases. Simulation results demonstrate that our proposed methods exhibit enhanced robustness against target DoA estimation errors, compared with the existing benchmarks that do not take these errors into account.