The recent emergence of the integrated sensing and communication (ISAC) framework has sparked significant interest in quantifying the sensing capabilities inherent in communication signals. However, existing literature has mainly focused on scenarios involving either purely random or purely deterministic waveforms. This overlooks a critical reality: operational communication standards invariably utilize a hybrid structure comprising both deterministic pilots for channel estimation and random payloads for data transmission. To bridge this gap, this paper investigates the sensing mutual information (SMI) and precoding design specifically for ISAC systems employing communication signals with both pilots and data payloads. First, by utilizing random matrix theory (RMT), we derive a tractable closed-form expression for the SMI that accurately accounts for the statistical properties of the hybrid signal. Building upon this theoretical foundation, we formulate a precoding optimization problem to maximize SMI with constraints on the transmit power and communication rate, which is solved via an efficient alternating direction method of multipliers framework. Simulation results validate the accuracy of the theoretical results and demonstrate the superiority of the proposed precoding design over conventional benchmarks.

翻译：近期兴起的集成感知与通信（ISAC）框架引发了学界对量化通信信号固有感知能力的广泛关注。然而，现有文献主要集中于研究纯随机或纯确定性波形场景，忽视了一个关键现实：实际运行的通信标准始终采用混合结构，即包含用于信道估计的确定性导频和用于数据传输的随机载荷。为弥补这一空白，本文针对采用导频与数据载荷混合通信信号的ISAC系统，深入研究了其感知互信息（SMI）与预编码设计。首先，通过运用随机矩阵理论（RMT），我们推导出可处理的SMI闭式表达式，该表达式精确刻画了混合信号的统计特性。基于此理论框架，我们构建了在发射功率与通信速率约束下最大化SMI的预编码优化问题，并通过高效的交替方向乘子法框架进行求解。仿真结果验证了理论推导的准确性，并证明了所提预编码设计方案相较于传统基准方法的优越性。