TY - JOUR
T1 - Optimal Solutions for Joint Beamforming and Antenna Selection
T2 - From Branch and Bound to Graph Neural Imitation Learning
AU - Shrestha, Sagar
AU - Fu, Xiao
AU - Hong, Mingyi
N1 - Publisher Copyright:
© 1991-2012 IEEE.
PY - 2023
Y1 - 2023
N2 - This work revisits the joint beamforming (BF) and antenna selection (AS) problem, as well as its robust beamforming (RBF) version under imperfect channel state information (CSI). Such problems arise due to various reasons, e.g., the costly nature of the radio frequency (RF) chains and energy/resource-saving considerations. The joint (R)BF&AS problem is a mixed integer and nonlinear program, and thus finding optimal solutions is often costly. The vast majority of the prior works tackled these problems using techniques such as continuous approximations, greedy methods, and supervised machine learning - yet these approaches do not ensure optimality or even feasibility of the solutions. The main contribution of this work is threefold. First, an effective branch and bound (B&B) framework is proposed for the considered problem that guarantees global optimality by leveraging existing BF and RBF solvers. Second, to expedite the potentially costly B&B algorithm, a machine learning (ML)-based scheme is proposed to help skip intermediate states of the B&B search tree. The learning model features a graph neural network (GNN)-based design that is resilient to a commonly encountered challenge in wireless communications, namely, the change of problem size (e.g., the number of users) across the training and test stages. Third, comprehensive performance characterizations are presented, showing that the GNN-based method retains the global optimality of B&B with provably reduced complexity, under reasonable conditions. Numerical simulations also show that the ML-based acceleration can often achieve an order-of-magnitude speedup relative to B&B.
AB - This work revisits the joint beamforming (BF) and antenna selection (AS) problem, as well as its robust beamforming (RBF) version under imperfect channel state information (CSI). Such problems arise due to various reasons, e.g., the costly nature of the radio frequency (RF) chains and energy/resource-saving considerations. The joint (R)BF&AS problem is a mixed integer and nonlinear program, and thus finding optimal solutions is often costly. The vast majority of the prior works tackled these problems using techniques such as continuous approximations, greedy methods, and supervised machine learning - yet these approaches do not ensure optimality or even feasibility of the solutions. The main contribution of this work is threefold. First, an effective branch and bound (B&B) framework is proposed for the considered problem that guarantees global optimality by leveraging existing BF and RBF solvers. Second, to expedite the potentially costly B&B algorithm, a machine learning (ML)-based scheme is proposed to help skip intermediate states of the B&B search tree. The learning model features a graph neural network (GNN)-based design that is resilient to a commonly encountered challenge in wireless communications, namely, the change of problem size (e.g., the number of users) across the training and test stages. Third, comprehensive performance characterizations are presented, showing that the GNN-based method retains the global optimality of B&B with provably reduced complexity, under reasonable conditions. Numerical simulations also show that the ML-based acceleration can often achieve an order-of-magnitude speedup relative to B&B.
KW - Beamforming
KW - antenna selection
KW - global optimum
KW - graph neural networks
KW - machine learning
UR - http://www.scopus.com/inward/record.url?scp=85149420857&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85149420857&partnerID=8YFLogxK
U2 - 10.1109/TSP.2023.3244096
DO - 10.1109/TSP.2023.3244096
M3 - Article
AN - SCOPUS:85149420857
SN - 1053-587X
VL - 71
SP - 831
EP - 846
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
ER -