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 vector Gaussian 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, and reveal the deterministic-random tradeoff of S&C for ISAC systems. Finally, we provide sufficient conditions for the achievability of the distortion 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,本文件从矢量高斯频道下的速率扭曲角度研究遥感和通信(S&C)之间的确定-随机权衡。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。我们根据ISAC随机信号来描述相互遥感信息,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信号的抽样共变矩阵具有确定性,那么扭曲程度就会降低。我们随后通过将无线遥感解释为不合作源-电道编码,并揭示ISAC系统S&C的确定-随机交易。最后,我们通过分析一个目标响应矩阵估计的具体例子,为扭曲约束提供了充分的条件。我们通过分析一个目标响应矩阵估计的可实现性能。