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

TL;DR

The paper addresses the fundamental limit of channel capacity for FMCW-based optical wireless ISAC under a sensing constraint implemented as a harmonic-mean on the signal envelope. It develops an information-theoretic framework, derives a max-entropy lower bound and regime-specific upper bounds, and obtains tight asymptotic results in both low and high SNR. Guided by these bounds, it proposes PAM-based envelope designs that approach capacity-achieving distributions, and validates the designs with numerical results and a realistic sensing performance assessment. The findings provide principled guidance for simultaneous communication and sensing in OW-ISAC, balancing envelope constraints, capacity, and practical waveform design.

Abstract

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.

Figures (8)

• Figure 1: System model for FMCW-based OW-ISAC. The abbreviations APD, BPD, CCR, LPF, MZM, and TIA stand for avalanche photodetector, balanced photodetector, corner-cube reflector, low-pass filter, Mach-Zehnder modulator, and transimpedance amplifier, respectively.
• Figure 2: CDFs of the max-entropy distribution and PAM-based envelopes. (a) $10\%$ NSP with $A=0.10,B=1.00,\varsigma=1.156$. (b) $90\%$ NSP with $A=0.10,B=1.00,\varsigma=2.406$.
• Figure 3: Capacity bounds and achievable data rates of PAM-based envelopes. (a) $10\%$ NSP with $A=0.10,B=1.00,\varsigma=1.156$. (b) $90\%$ NSP with $A=0.10,B=1.00,\varsigma=2.406$.
• Figure 4: MSE of beat signal recovery with different NSPs.
• Figure 5: RMSE of target distance and velocity estimation with different NSPs.