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Characterizing the performance trade-offs between sensing and communication subsystems is essential for enabling integrated sensing and communication systems. Various metrics exist for each subsystem; however, this study focuses on the ergodic capacity of the communication subsystem. Due to the complexity of deriving the sensing mean square error (MSE) and the inapplicability of the Bayesian Cram\'er-Rao Bound to channels with discrete or mixed distributions, this work proposes a Poincar\'e lower bound on the sensing MSE to address these issues. An achievable inner bound for the rate-sensing trade-off in a fading multiple-input multiple-output channel with additive white Gaussian noise and blockage probability is established. In addition, a strategy that is asymptotically optimal for sensing is provided., Comment: 5 pages, 1 figure, 1 table, submitted to IEEE International Symposium on Information Theory (ISIT) 2025 Ann Arbor (Michigan), USA

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., Comment: Submitted to IEEE WCNC 2025