Integrated sensing and communications (ISAC) is recognized as a key enabling technology for future wireless networks. To shed light on the fundamental performance limits of ISAC systems, this paper studies the deterministic-random tradeoff between sensing and communications (S\&C) from a rate-distortion perspective under Gaussian ISAC channels. We model the ISAC signal as a random matrix that carries information, whose realization is perfectly known to the sensing receiver, but is unknown to the communication receiver. We characterize the sensing mutual information conditioned on the random ISAC signal, and show that it provides a universal lower bound for distortion metrics of sensing. Furthermore, we prove that the distortion lower bound is minimized if the sample covariance matrix of the ISAC signal is deterministic. We then offer our understanding of the main results by interpreting wireless sensing as non-cooperative source-channel coding. Finally, we provide sufficient conditions for the achievability of the distortion lower bound by analyzing a specific example of target response matrix estimation.

翻译：综合遥感和通信(ISAC)被认为是未来无线网络的关键赋能技术。为了阐明ISAC系统的基本性能限制,本文件从高斯国际空间通信频道下的速率扭曲角度研究遥感和通信之间的确定-随机权衡(S ⁇ C),我们把ISAC信号模拟成一个随机矩阵,传递信息,感测接收者完全了解其实现情况,但通信接收者却不知道。我们用随机ISAC信号来描述相互的感测信息,并表明它为扭曲感测指标提供了普遍较低的约束。此外,我们证明,如果ISAC信号的样本共变式矩阵具有确定性,则将扭曲程度降低到最低程度。我们随后通过将无线遥感解释为不合作源电网的编码,对主要结果提供了理解。最后,我们通过分析目标响应矩阵评估的具体实例,为扭曲程度较低的约束提供了足够的条件。