Statistically Robust Beamforming Design for Joint Target Detection and Communications

The detection probability of radar, as a widely used sensing metric used by the integrated sensing and communication (ISAC) beamforming design, typically relies on the true sensing parameters which can hardly be achieved. In this work, we present a statistically robust ISAC beamforming design to combat the performance degradation caused by the random sensing parameter estimation errors and the imperfect channel state information (CSI). Specifically, we first maximize the expectation of radar output signal-to-interference-plus-noise ratio (SINR) over both the angle and the reflection coefficient estimation errors, while guaranteeing the communication users’ SINR requirements. To address the challenging stochastic optimization problem, we first derive a tractable deterministic reformulation and then develop an efficient majorization-minimization (MM) based algorithm, where the solutions to the base station (BS) transmit beamformer and the BS receive beamformer in each MM iteration are obtained via the alternating direction method of multipliers (ADMM) and the generalized Rayleigh quotient in a closed form, respectively. For the single communication user case, a semi-closed-form solution to the transmit beamformer can be achieved in each MM iteration. In addition, we also consider the imperfect CSI by introducing outage SINR constraints. Although the resultant problem is more difficult, we can still obtain a high-quality solution based on the algorithm developed for the previous problem. Simulation results indicate that, given the same communication constraints, the proposed MM-based robust design achieves better target detection performance than the traditional non-robust designs and can even approach the clairvoyant scheme with known parameters.