Fundamental Limits of ISAC for Vehicular Lane Identification: A Rate-Distortion Approach

Integrated Sensing and Communication (ISAC) is a key technology for 6G, with safety-critical applications in Vehicle-to-Everything (V2X) networks. A fundamental challenge is to characterize the tradeoff between sensing accuracy and communication data rate. This is particularly difficult for discrete sensing tasks, such as identifying a target vehicle’s lane, where classical estimation bounds like the Cramér-Rao bound are not applicable. In this paper, we establish a novel converse bound on the performance of an ISAC system tasked with vehicular lane identification. By leveraging rate-distortion theory, we derive an outer bound on the achievable region of sensing error probability versus communication rate. Our framework is general and robust, requiring no regularity conditions on the channel statistics. We formulate a waveform optimization problem to determine an outer bound to the ISAC region and provide numerical results for the case of minimizing lane identification error rate and maximizing the ergodic communication rate, offering a performance benchmark for the design of future V2X systems.