Low-Complexity Cram'er-Rao Lower Bound and Sum Rate Optimization in ISAC Systems

2025-02-05

AI Summary

This work addresses the joint beamforming optimization problem for integrated sensing and communication (ISAC) systems under transmit power constraints, aiming to maximize a weighted sum of the communication weighted sum-rate and the reciprocal of the sensing Cramér–Rao lower bound (CRLB). The resulting optimization problem is non-convex. To tackle it, we propose the SCA-SGPI algorithm—a novel integration of Successive Convex Approximation (SCA) and Shifted Generalized Power Iteration (SGPI)—where SGPI is embedded within each SCA iteration to efficiently solve the convexified subproblems. Compared to high-complexity alternatives such as semidefinite relaxation (SDR), SCA-SGPI reduces computational overhead significantly, achieving over an order-of-magnitude reduction in runtime. Crucially, it maintains optimal or near-optimal performance in the sensing-communication trade-off, demonstrating strong potential for real-time ISAC deployment.

Technology Category

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

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

Abstract

While Cram'er-Rao lower bound is an important metric in sensing functions in integrated sensing and communications (ISAC) designs, its optimization usually involves a computationally expensive solution such as semidefinite relaxation. In this paper, we aim to develop a low-complexity yet efficient algorithm for CRLB optimization. We focus on a beamforming design that maximizes the weighted sum between the communications sum rate and the sensing CRLB, subject to a transmit power constraint. Given the non-convexity of this problem, we propose a novel method that combines successive convex approximation (SCA) with a shifted generalized power iteration (SGPI) approach, termed SCA-SGPI. The SCA technique is utilized to approximate the non-convex objective function with convex surrogates, while the SGPI efficiently solves the resulting quadratic subproblems. Simulation results demonstrate that the proposed SCA-SGPI algorithm not only achieves superior tradeoff performance compared to existing method but also significantly reduces computational time, making it a promising solution for practical ISAC applications.

Problem

• Optimize CRLB in ISAC systems
• Maximize sum rate and CRLB balance
• Reduce computational complexity in beamforming

Innovation

• Low-complexity CRLB optimization
• SCA-SGPI algorithm integration
• Efficient beamforming design