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 Cram\'er-Rao Bound (BCRB). We also establish that the achievable Rate-Cram\'er-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.

翻译：本文在光通信感知一体化框架下，研究了采用单输入单输出通信与单输入多输出感知的光学点对点系统中最优容量-失真权衡特性。我们考察了最优速率-失真区域，并探讨了若干内界与外界。针对目标距离估计问题，我们提出了实用且渐近最优的最大后验估计器与最大似然估计器，解决了非线性测量-状态关系与非共轭先验的挑战。随着感知天线数量的增加，这些估计器收敛于贝叶斯克拉美-罗下界。我们同时证明了可达速率-克拉美-罗界可作为最优容量-失真区域的外界，该结论对无偏估计器及渐近多接收天线情形均成立。为阐明输入分布决定容量-失真区域帕累托边界的权衡特性，我们提出了两种算法：i) 基于迭代的Blahut-Arimoto型方法，ii) 内存高效的闭式求解方法。闭式方法包含适用于高光信噪比条件下的闭式最优分布。此外，我们将确定性-随机权衡理论适配并优化应用于光通信感知一体化场景。