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Optical ISAC: Fundamental Performance Limits and Transceiver Design

Alireza Ghazavi Khorasgani, Mahtab Mirmohseni, Ahmed Elzanaty

TL;DR

This work analyzes the capacity-distortion tradeoffs in optical ISAC for a point-to-point link with SISO communication and SIMO sensing. It develops MAP and MLE estimators for target distance under nonlinear sensing and non-conjugate priors, and proves that these estimators converge to the Bayesian Cramér-Rao bound as the number of sensing antennas grows. It establishes the $R$-$ ext{CRB}$ bound as an outer bound for the asymptotic C-D region and provides two input-distribution design methods—a BA-type algorithm and a memory-efficient closed-form approach—for tracing the Pareto boundary, along with an adaptation of the deterministic-random tradeoff to optical ISAC. Numerical results show convergence of MAP/MLE to the BCRB with increasing $n_s$, validate the BCRB as an outer bound, and demonstrate that high-O-SNR inputs follow an exponential family form, enabling practical transceiver design for optical ISAC applications in V2X and beyond.

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.

Optical ISAC: Fundamental Performance Limits and Transceiver Design

TL;DR

This work analyzes the capacity-distortion tradeoffs in optical ISAC for a point-to-point link with SISO communication and SIMO sensing. It develops MAP and MLE estimators for target distance under nonlinear sensing and non-conjugate priors, and proves that these estimators converge to the Bayesian Cramér-Rao bound as the number of sensing antennas grows. It establishes the - bound as an outer bound for the asymptotic C-D region and provides two input-distribution design methods—a BA-type algorithm and a memory-efficient closed-form approach—for tracing the Pareto boundary, along with an adaptation of the deterministic-random tradeoff to optical ISAC. Numerical results show convergence of MAP/MLE to the BCRB with increasing , validate the BCRB as an outer bound, and demonstrate that high-O-SNR inputs follow an exponential family form, enabling practical transceiver design for optical ISAC applications in V2X and beyond.

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.
Paper Structure (14 sections, 15 theorems, 15 equations, 3 figures, 3 tables)

This paper contains 14 sections, 15 theorems, 15 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. Main Result
  4. MAP-Based Achievable ISAC C-D Region
  5. MLE-Based ISAC C-D Region
  6. BCRB-Based Approach: OB
  7. Numerical Results
  8. Proof of Lemma
  9. Numerical Methods for Solving
  10. Proof of Lemma
  11. Proof of Theorem
  12. Proof of Lemma
  13. Complexity Comparison of BAA and CFA
  14. Complexity Comparison of MAP and MLE

Key Result

Lemma 1

The deterministic MMSE estimator $\hat{r_\textrm{s}}$, which minimises the expected distortion, depends on $x$ and $\boldsymbol{y}_{\textrm{s}} \triangleq \text{vec}\{y_{\textrm{s},j}\}_{j=1}^{n_{\textrm{s}}}$ and is given by The distortion $\Delta^{(n)}$ is minimised by the estimator, regardless of the encoding and decoding functions: The estimation cost for each input symbol $x \in \mathcal{X}

Figures (3)

  • Figure 1: O-ISAC system with memoryless channels.
  • Figure 2: Average BCRB, and variance and MSE of MAP and MLE for $\lambda=0.3$ and $0.5$ versus $x$ ($n_s=64$).
  • Figure 3: (left) optimised CDF for several modes, (right) C-D Region ($n_{\textrm{s}}=64$).

Theorems & Definitions (35)

  • Definition 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Remark 1
  • Lemma 4
  • proof
  • ...and 25 more