KKT-Based Analysis of Capacity-Distortion Tradeoff in Integrated Sensing and Communication System

With the progression towards Beyond 5G and 6G, Integrated Sensing and Communication (ISAC) emerges as a key technology for high-precision sensing services. This paper addresses the challenges in ISAC research by proposing a theoretical framework that incorporates the Karush-Kuhn-Tucker (KKT) conditions to analyze the capacity-distortion tradeoff. We introduce a state-dependent ISAC channel model that captures the correlation between sensing and channel states. Utilizing this model, we characterize the optimal capacity-distortion tradeoff and demonstrate through illustrative examples the substantial benefits of employing the KKT conditions over traditional Lagrange multiplier methods. Our findings pave the way for more efficient ISAC system designs that can leverage the interplay between communication and sensing functionalities.