Globally Optimal Beamforming Design for Integrated Sensing and Communication Systems

TL;DR

This paper introduces a globally optimal beamforming design for integrated radar sensing and multi-user communication systems, using a novel branch-and-bound algorithm to solve a complex NP-hard optimization problem.

Contribution

It develops a global optimization algorithm based on branch-and-bound, McCormick envelope, and semidefinite relaxation, providing a benchmark for existing suboptimal methods.

Findings

The algorithm guarantees finding the global optimum.

It effectively balances radar sensing and communication performance.

Provides a benchmark for evaluating other algorithms.

Abstract

In this paper, we propose a multi-input multi-output beamforming transmit optimization model for joint radar sensing and multi-user communications, where the design of the beamformers is formulated as an optimization problem whose objective is a weighted combination of the sum rate and the Cram\'{e}r-Rao bound, subject to the transmit power budget constraint. Obtaining a global solution for the formulated problem is a challenging task, because the sum rate maximization problem itself (even without considering the sensing metric) is known to be NP-hard. In this paper, we propose an efficient global branch-and-bound algorithm for solving the formulated problem based on the McCormick envelope relaxation and the semidefinite relaxation technique. The proposed algorithm is guaranteed to find the global solution for the considered problem, and thus serves as an important benchmark for performance evaluation of the existing local or suboptimal algorithms for solving the same problem.