Optimal Precoding Toward Random ISAC Signals

This paper introduces a new sensing performance metric, namely, ergodic least-squares error (ELSE), to characterize the average sensing performance under random integrated sensing and communications (ISAC) signaling. First, we propose a pair of novel precoding methods with their closed-form solutions to minimize the ELSE, termed as data-dependent precoding (DDP) and data-independent precoding (DIP), respectively. Second, we theoretically describe the performance degradation of random signals as compared with utilizing classical deterministic training signals. Moreover, we extend the proposed DDP and DIP methods into ISAC scenarios by explicitly constraining the achievable communication rate for ELSE minimization problems. Finally, we provide numerical results to demonstrate the effectiveness of our proposed DDP and DIP methods.