Optical ISAC: Fundamental Performance Limits and Transceiver Design

2024-08-21

arXiv.org

AI Summary

This work investigates the fundamental capacity–distortion (C–D) trade-off limit for point-to-point integrated sensing and communication (ISAC) systems in the optical domain, under joint single-input single-output (SISO) communication and single-input multiple-output (SIMO) sensing. Addressing the unique nonlinearity, non-Gaussianity, and non-conjugate prior characteristics of optical ISAC, we first derive a rate–Cramér–Rao bound (R–CRB) outer bound and prove it constitutes a tight upper bound on the C–D Pareto frontier. We design asymptotically optimal maximum a posteriori (MAP)/maximum likelihood (MLE) estimators tailored to non-conjugate priors. Furthermore, we propose a Blahut–Arimoto-type iterative algorithm and a closed-form optimal input distribution at high optical signal-to-noise ratio (O-SNR), drastically reducing computational complexity. Theoretically, we establish that the multi-antenna estimator converges to the Bayesian CRB, thereby extending the deterministic–random trade-off (DRT) framework to optical ISAC.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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 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.

Problem

• Characterizing optimal capacity-distortion tradeoff in optical ISAC
• Designing practical estimators for target distance in ISAC
• Proposing algorithms to optimize input distribution in ISAC

Innovation

• MAP and MLE estimators for target distance
• Iterative BAA-type and CF algorithms
• Deterministic-random tradeoff adaptation