An Analysis of Capacity-Distortion Trade-Offs in Memoryless ISAC Systems

TL;DR

This paper explores the fundamental limits of integrated sensing and communication systems, analyzing the trade-off between data rate and channel estimation accuracy using information theory and proposing an optimization algorithm.

Contribution

It introduces a comprehensive framework for modeling and analyzing the capacity-distortion trade-off in ISAC systems with various side information scenarios and develops a convergent optimization method.

Findings

Characterized the capacity-distortion trade-off across different side information causality levels.

Derived a tight achievable capacity-distortion region for the two-user degraded broadcast channel.

Proposed a proximal BCD algorithm with proven convergence for optimizing the trade-off.

Abstract

This manuscript investigates the information-theoretic limits of integrated sensing and communications (ISAC), aiming for simultaneous reliable communication and precise channel state estimation. We model such a system with a state-dependent discrete memoryless channel (SD-DMC) with present or absent channel feedback and generalized side information at the transmitter and the receiver, where the joint task of message decoding and state estimation is performed at the receiver. The relationship between the achievable communication rate and estimation error, the capacity-distortion (C-D) trade-off, is characterized across different causality levels of the side information. This framework is shown to be capable of modeling various practical scenarios by assigning the side information with different meanings, including monostatic and bistatic radar systems. The analysis is then extended to the two-user degraded broadcast channel, and we derive an achievable C-D region that is tight under certain conditions. To solve the optimization problem arising in the computation of C-D functions/regions, we propose a proximal block coordinate descent (BCD) method, prove its convergence to a stationary point, and derive a stopping criterion. Finally, several representative examples are studied to demonstrate the versatility of our framework and the effectiveness of the proposed algorithm.