Robust Beamforming for ISAC Systems via Probability of Detection Optimisation

ABSTRACT Due to the trade‐off between sensing and communication performance in the integrated sensing and communication (ISAC) systems, the sensing ability will inevitably be reduced for guaranteed communication performance. This degradation can severely compromise target detection performance. Existing methods fail to effectively address this issue. To address this, we propose a two‐step optimisation framework for robust beamforming design. First, we optimise the correlation matrix via manifold optimisation to maximise multi‐target detection probability without communication constraint. Second, we jointly design the beamforming matrix under communication SINR constraints by projecting the solution to a convex set that satisfies the communication SINR constraint and power constraint. This approach strategically distributes transmit energy across targets while strictly guaranteeing communication performance. The numerical results demonstrate that the proposed scheme outperforms the baselines, significantly improving the probability of detection without sacrificing communication quality.