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

TL;DR

This paper introduces a low-complexity, efficient algorithm for optimizing the Cramér-Rao lower bound in integrated sensing and communications systems, balancing sensing accuracy and data rate.

Contribution

It develops a novel SCA-SGPI method combining convex approximation and power iteration for CRLB optimization in ISAC beamforming.

Findings

Achieves better tradeoff between sum rate and sensing CRLB.

Reduces computational complexity compared to existing methods.

Demonstrates superior performance in simulations.

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.