A Poincaré Lower Bound Approach for Performance Trade-offs in MIMO ISAC Systems with Blockage

TL;DR

This paper addresses the sensing–communication trade-off in a MIMO ISAC system with blockage by replacing the inapplicable Bayesian Cramér–Rao bound with a Poincaré-type lower bound on the sensing MSE. It derives an achievable sensing–rate region and an outer bound, and proposes signaling strategies that are asymptotically optimal for sensing at high sensing SNR, along with a capacity-based comms strategy via short-term power constraints. The analysis reveals that, in the limit of large coherence time $T$, the corner points converge and the region becomes effectively rectangular, with the sensing-optimal and communication-optimal points collapsing; finite-$T$ effects and nonlinear-channel extensions remain open for future work.

Abstract

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 Cramér-Rao Bound to channels with discrete or mixed distributions, this work proposes a Poincaré 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.

Figures (1)

• Figure 1: Inner bound and outer bound of the sensing-rate region for the task of target response matrix estimation, where both communication and sensing channel are subject to uncorrelated Rayleigh fading and blockage probabilities $1-\alpha_{\rm c} = 0$ and $1-\alpha_{\rm s} = 0.6$.