Fundamental channel coupling effects for integrated sensing and communication systems

Integrated sensing and communication (ISAC) has emerged as a promising solution to achieve high-rate communication and ultra-precise sensing for next-generation technologies. Existing studies primarily focus on trade-offs arising from communication and sensing (C&S) functions competing for shared system resources, while often overlooking coupling effects due to the co-location of communication users, sensing targets, and the base station, along with joint channel characteristics. To bridge this gap, we establish a novel framework for analyzing uplink and downlink ISAC performance, accounting for both trade-offs and coupling constraints. Specifically, we first investigate trade-offs through C&S performance regions between the channel estimation error and the successful detection probability in the uplink process, as well as between the transmission rate and Cram´er-Rao lower bound in the downlink process. We derive theoretical formulations for these metrics and explore their scaling laws, asymptotic behaviors, and monotonicity properties. Additionally, the fundamental coupling effects can be examined by the joint ISAC coverage probability using stochastic geometry, which evaluates the likelihood of C&S simultaneously meeting performance thresholds. Our theoretical results provide innovative union bounds for ISAC systems, offering deep insights into the best achievable performance of one function under the coupling constraints inherently imposed by the other function. Finally, numerical results verify the accuracy of all theoretical derivations, and highlight the impact of trade-offs and coupling constraints on C&S performance regions.