Efficient Global Algorithms for Transmit Beamforming Design in ISAC Systems

In this paper, we propose a MIMO transmit beamforming 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 Cramér-Rao bound, subject to...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 72; pp. 4493 - 4508
Main Authors: Wu, Jiageng, Wang, Zhiguo, Liu, Ya-Feng, Liu, Fan
Format: Journal Article
Language:English
Published: IEEE 2024
Subjects:
Array signal processing
Branch and bound algorithm
global optimality
Interference
Machine learning algorithms
McCormick envelope relaxation
Measurement
Radar
Signal processing algorithms
Signal to noise ratio
sum-rate maximization
transmit beamforming
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:In this paper, we propose a MIMO transmit beamforming 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 Cramér-Rao bound, subject to the transmit power budget. Obtaining the global solution for the formulated nonconvex problem is a challenging task, since the sum-rate maximization problem itself (even without considering the sensing metric) is known to be NP-hard. The main contributions of this paper are threefold. Firstly, we derive an optimal closed-form solution to the formulated problem in the single-user case and the multi-user case where the channel vectors of different users are orthogonal. Secondly, for the general multi-user case, we propose a novel branch and bound (B&B) algorithm based on the McCormick envelope relaxation. The proposed algorithm is guaranteed to find the globally optimal solution to the formulated problem. Thirdly, we design a graph neural network (GNN) based pruning policy to determine irrelevant nodes that can be directly pruned in the proposed B&B algorithm, thereby significantly reducing the number of unnecessary enumerations therein and improving its computational efficiency. Simulation results show the efficiency of the proposed vanilla and GNN-based accelerated B&B algorithms.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2024.3457817