Sensing performance is typically evaluated by classical metrics, such as Cramer-Rao bound and signal-to-clutter-plus-noise ratio. The recent development of the integrated sensing and communication (ISAC) framework motivated the efforts to unify the metric for sensing and communication, where researchers have proposed to utilize mutual information (MI) to measure the sensing performance with deterministic signals. However, the need to communicate in ISAC systems necessitates the use of random signals for sensing applications and the closed-form evaluation for the sensing mutual information (SMI) with random signals is not yet available in the literature. This paper investigates the achievable performance and precoder design for sensing applications with random signals. For that purpose, we first derive the closed-form expression for the SMI with random signals by utilizing random matrix theory. The result reveals some interesting physical insights regarding the relation between the SMI with deterministic and random signals. The derived SMI is then utilized to optimize the precoder by leveraging a manifold-based optimization approach. The effectiveness of the proposed methods is validated by simulation results.

翻译：感知性能通常通过经典指标（如克拉美罗界和信杂噪比）进行评估。集成感知与通信（ISAC）框架的最新发展推动了统一感知与通信指标的探索，研究人员已提出利用互信息（MI）以确定性信号衡量感知性能。然而，ISAC系统中的通信需求迫使感知应用采用随机信号，而现有文献尚未给出随机信号下感知互信息（SMI）的闭式评估方法。本文研究了随机信号在感知应用中的可达性能及预编码器设计。为此，我们首先利用随机矩阵理论推导了随机信号下SMI的闭式表达式，该结果揭示了关于确定性信号与随机信号下SMI之间关系的重要物理洞察。进而通过基于流形的优化方法，利用所推导的SMI对预编码器进行优化。仿真结果验证了所提方法的有效性。