Integrated sensing and communication is regarded as a key enabler for next-generation wireless networks. To optimize the transmitted waveform for both sensing and communication, various performance metrics must be considered. This work focuses on sensing, and specifically on the mean square error (MSE) of channel estimation. Given the complexity of deriving the MSE, the Bayesian Cramer-Rao Bound (BCRB) is commonly recognized as a lower bound on the minimum MSE. However, the BCRB is not applicable to channels with discrete or mixed distributions. To address this limitation, a new lower bound based on a Poincar\'e inequality is proposed and applied to fading MIMO AWGN channels with blockage probability, and the behavior of the lower bound at high SNR is precisely characterized.

翻译：集成感知与通信被视为下一代无线网络的关键使能技术。为同时优化感知与通信的发射波形，需综合考虑多种性能指标。本文聚焦于感知领域，具体研究信道估计的均方误差。鉴于推导均方误差的复杂性，贝叶斯克拉美-罗界通常被视为最小均方误差的下界。然而，该界不适用于具有离散或混合分布的信道。为突破此限制，本文提出一种基于泊松不等式的新下界，并将其应用于具有阻塞概率的衰落MIMO加性高斯白噪声信道，同时精确刻画了该下界在高信噪比条件下的渐近特性。