Abstract
This paper characterizes the optimal Capacity-Distortion (C-D) tradeoff in an optical point-to-point system with Single-Input Single-Output (SISO) for communication and Single-Input Multiple-Output (SIMO) for sensing within an Integrated Sensing and Communication (ISAC) framework. We consider the optimal Rate-Distortion (R-D) region and explore several Inner (IB) and Outer Bounds (OB). We introduce practical, asymptotically optimal Maximum A Posteriori (MAP) and Maximum Likelihood Estimators (MLE) for target distance, addressing nonlinear measurement-to-state relationships and non-conjugate priors. As the number of sensing antennas increases, these estimators converge to the Bayesian Cramér-Rao Bound (BCRB). We also establish that the achievable Rate-Cramér-Rao Bound (R-CRB) serves as an OB for the optimal C-D region, valid for both unbiased estimators and asymptotically large numbers of receive antennas. To clarify that the input distribution determines the tradeoff across the Pareto boundary of the C-D region, we propose two algorithms: i) an iterative Blahut-Arimoto Algorithm (BAA)-type method, and ii) a memory-efficient Closed-Form (CF) approach. The CF approach includes a CF optimal distribution for high Optical Signal-to-Noise Ratio (O-SNR) conditions. Additionally, we adapt and refine the Deterministic-Random Tradeoff (DRT) to this optical ISAC context.