Beamforming Optimization for Integrated Sensing and Communication Systems with SCNR Consideration

Integrated sensing and communication (ISAC) is acknowledged as a crucial facilitator for the advancement of future wireless communication technologies. This study introduces a combined communication and radar beamforming framework aimed at optimizing overall spectral efficiency (SE) that guarantees required radar performance, even with imperfect channel state information (CSI), in multi-user multi-target ISAC environments. To achieve this goal, we set a radar performance constraint to a receive signal-to-clutter-plus-noise ratio (SCNR) for the sum SE optimization. To address non-convexity and imperfect CSI issues, we reframe the optimization problem and derive the Karush-Kuhn-Tucker (KKT) stationarity conditions for the combined radar and communication precoding vector. By converting the condition into a nonlinear eigenvalue problem with eigenvector dependency (NEPv), we devise an alternating approach that identifies the joint precoder using power iteration and determines a Lagrangian multiplier via binary tree search. The proposed framework integrates radar and communication metrics and maintains robustness against channel estimation errors, featuring low complexity. Simulations show the effectiveness of the proposed methods.