A Rate-Distortion Bound for ISAC

2025-10-09

AI Summary

Bayesian Cramér–Rao Bound (BCRB) is widely used to characterize fundamental performance limits in Integrated Sensing and Communication (ISAC), but it relies on stringent regularity conditions—requiring parameter continuity, differentiability, and smooth priors—and thus fails for arbitrary parameter distributions or distortion measures (e.g., error probability, non-mean-square distortions). Method: This work pioneers the application of rate-distortion theory to ISAC performance analysis, proposing a novel *inverse* performance lower bound. Contribution/Results: The proposed bound is free from regularity assumptions, remains tight at low noise and valid at high noise, and naturally accommodates discrete sensing tasks (e.g., binary occupancy detection) and non-Gaussian channel estimation (e.g., Nakagami fading). Experimental results demonstrate its strong discriminative power even where BCRB collapses, significantly extending the theoretical foundations of ISAC.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

This paper addresses the fundamental performance limits of Integrated Sensing and Communication (ISAC) systems by introducing a novel converse bound based on rate-distortion theory. This rate-distortion bound (RDB) overcomes the restrictive regularity conditions of classical estimation theory, such as the Bayesian Cram'er-Rao Bound (BCRB). The proposed framework is broadly applicable, holding for arbitrary parameter distributions and distortion measures, including mean-squared error and probability of error. The bound is proved to be tight in the high sensing noise regime and can be strictly tighter than the BCRB in the low sensing noise regime. The RDB's utility is demonstrated on two challenging scenarios: Nakagami fading channel estimation, where it provides a valid bound even when the BCRB is inapplicable, and a binary occupancy detection task, showcasing its versatility for discrete sensing problems. This work provides a powerful and general tool for characterizing the ultimate performance tradeoffs in ISAC systems.

Problem

• Establishing fundamental performance limits for ISAC systems
• Overcoming restrictive regularity conditions in classical estimation theory
• Providing a versatile bound for arbitrary distributions and distortions

Innovation

• Novel rate-distortion bound for ISAC systems
• Framework works for arbitrary distributions and distortions
• Bound tighter than classical methods in noise regimes