Channel Capacity for FMCW-based Optical Wireless Integrated Sensing and Communication: Asymptotic Analysis and Envelope Design

Optical wireless integrated sensing and communication (OW-ISAC) is rapidly burgeoning as a complement and augmentation to its radio-frequency counterpart. In this paper, the channel capacity is analyzed to guide the design of a coherent OW-ISAC system based on frequency-modulated continuous wave (FMCW). Firstly, the system model of FMCW-based OW-ISAC is recast into an information-theoretic formulation, where an additional harmonic-mean constraint is imposed to ensure the sensing performance. Subsequently, both lower and upper bounds for channel capacity are derived under the imposed sensing constraint, based on which asymptotic expressions for channel capacity are presented for both low and high signal-to-noise-ratio regions. Moreover, the analysis of channel capacity provides guidance for the envelope design based on pulse amplitude modulation, whose capacity-achieving capabilities are demonstrated by numerical results. Furthermore, simulations reveal the trade-off between communication and sensing functionalities. In summary, the analysis of channel capacity under the sensing constraint provides insights into both the optimality and the practicality of OW-ISAC design.