ADMM-Based Outage Constrained MIMO-ISAC Hybrid Beamforming Design

This paper considers the problem of robust hybrid beamforming design for multiple-input multiple-output (MIMO) integrated sensing and communications (ISAC) systems in the presence of channel state information (CSI) error. Specifically, the analog and digital hybrid beamformer at the transmitter is designed with imperfect CSI, through synthesizing a desired transmit power pattern for radar sensing under the outage probability constraints on the signal-to-interference-plus-noise ratio (SINR) of each user. The formulated nonconvex problem is addressed by taking advantage of the Cantelli's Inequality and the Alternating Direction Method of Multipliers (ADMM) frame- work, and deriving the solution of each subproblem involved in the algorithm. Numerical experiments are carried out to show the effectiveness and robustness of the proposed MIMO-ISAC hybrid beamforming design.