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

TL;DR

The paper develops a unified information-theoretic framework for memoryless ISAC systems by modeling a state-dependent DMC with side information and optional feedback, enabling joint data communication and channel-state estimation. It derives capacity–distortion trade-offs for point-to-point and degraded broadcast channels across strictly causal, causal, and noncausal SIT, and introduces a proximal block coordinate descent algorithm with convergence guarantees to compute the CD regions. The framework encompasses monostatic and bistatic radar interpretations and provides special-case insights that connect to existing results such as Wyner–Ziv rate-splitting and Ahmadipour’s ISAC analyses. Through representative examples, the work demonstrates the practical viability of the approach and offers a versatile tool for exploring ISAC design trade-offs in memoryless and potential memory-bearing extensions.

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.

Figures (8)

• Figure 1: Channel model for point-to-point isac system.
• Figure 2: An example of cd functions for all scenarios.
• Figure 3: The sddmbc model for isac system.
• Figure 4: The equivalent model for the isac system inahmadipour2022information.
• Figure 5: Optimization results of $R(\mathcal{P}^{\mathrm{SC}}_{D})$, $R(\mathcal{P}^{\mathrm{C}}_{D})$ and $R(\mathcal{P}^{\mathrm{NC}}_{D})$ for the simo system.

Theorems & Definitions (36)

• Lemma 1: Conditional Typicality Lemmael2011networkkramer2008topics
• Lemma 2: Covering Lemmael2011network
• Lemma 3: Packing Lemmael2011network
• Lemma 4: Support Lemmael2011networkcsiszar2011information
• Lemma 5
• proof
• Lemma 6
• proof
• Definition 1
• Lemma 7