Information-Theoretic Limits of Integrated Sensing and Communication with Finite Learning Capacity

2025-12-15

AI Summary

This paper addresses the fundamental constraint of limited representational capacity—termed “AI capacity budget”—in AI-assisted integrated sensing and communication (ISAC) systems. Method: We formally define the AI capacity budget and model finite learning capability as equivalent additive noise, establishing an information-theoretic trade-off framework between communication rate and sensing distortion. Leveraging information-theoretic analysis, MIMO matrix inequalities, and variational constrained training, we derive tight upper and lower bounds on the rate-distortion region. For Gaussian channels, we obtain closed-form capacity-distortion expressions. Results: We uncover quantitative scaling laws governing the co-design of model size, waveform, and hardware. Our work establishes theoretical performance limits and principled design guidelines for joint AI-communication-sensing optimization in ISAC systems.

Technology Category

• Machine Learning: Information Theory
• Multiagent Systems: Agent Communication
• Search and Optimization: Learning to Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Security and privacy of machine learning and AI applications
• Search and Retrieval-Augmented AI: Assisted, interactive, and conversational search

Abstract

This paper develops a unified information-theoretic framework for artificial-intelligence (AI)-aided integrated sensing and communication (ISAC), where a learning component with limited representational capacity is embedded within the transceiver loop. The study introduces the concept of an AI capacity budget to quantify how the finite ability of a learning model constrains joint communication and sensing performance. Under this framework, the paper derives both converse (upper) and achievability (lower) bounds that define the achievable rate-sensing region. For Gaussian channels, the effect of limited learning capacity is shown to behave as an equivalent additive noise, allowing simple analytical expressions for the resulting communication rate and sensing distortion. The theory is then extended to Rayleigh and Rician fading as well as to multiple-input multiple-output (MIMO) systems through new matrix inequalities and a constructive mapping between AI capacity and effective noise covariance. Resource allocation between sensing and communication is optimized under this learning constraint, yielding closed-form conditions in the Gaussian case. A general learning-information trade-off law is also established, linking the representational power of the learning module to the achievable performance frontier. Finally, a practical variational training procedure is proposed to enforce the capacity constraint and to guide empirical evaluation. The derived scaling laws provide quantitative insight for co-designing model size, waveform, and hardware in next-generation ISAC systems.

Problem

• Establishes an information-theoretic framework for AI-aided ISAC with limited learning capacity
• Quantifies how finite learning capacity constrains joint communication and sensing performance
• Derives achievable rate-sensing bounds and optimizes resource allocation under learning constraints

Innovation

• AI capacity budget quantifies learning constraints on ISAC performance
• Limited learning capacity modeled as equivalent additive noise in Gaussian channels
• Variational training enforces capacity constraint for practical ISAC implementation