Optimal Solutions for Joint Beamforming and Antenna Selection: From Branch and Bound to Graph Neural Imitation Learning
Optimal Solutions for Joint Beamforming and Antenna Selection: From Branch and Bound to Graph Neural Imitation Learning
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DOI：
10.1109/tsp.2023.3244096
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发表时间：
2022-06
影响因子：
5.4
通讯作者：
S. Shrestha;Xiao Fu;Mingyi Hong
中科院分区：
文献类型：
--
作者：
S. Shrestha;Xiao Fu;Mingyi Hong
本文研究了联合波束形成(BF)和天线选择(AS)问题及其在非理想信道状态信息(CSI)下的稳健波束形成(RBF)问题。这些问题是由各种原因引起的，例如射频(RF)链的昂贵性质和能源/资源节约方面的考虑。联合(R)BF&AS问题是一个混合的整数和非线性规划，因此寻找最优解往往是昂贵的。以前的大多数工作都是使用连续逼近、贪婪方法和有监督的机器学习等技术来解决这些问题，但这些方法并不能确保解的最优性，甚至不能确保解的可行性。这项工作的主要贡献有三个方面。首先，针对所考虑的问题提出了一个有效的分支定界(B&B)框架，该框架通过利用现有的BF和RBF求解器来保证全局最优性。其次，为了加速可能代价高昂的B&B算法，提出了一种基于机器学习(ML)的方案来帮助跳过B&B搜索树的中间状态。学习模型以基于图神经网络(GNN)的设计为特征，该设计对无线通信中常见的挑战具有弹性，即，跨训练和测试阶段的问题大小(例如，用户数量)的变化。第三，给出了综合的性能表征，结果表明，在合理的条件下，基于GNN的方法保持了B&B的全局最优性，且复杂度明显降低。数值模拟还表明，基于ML的加速通常可以获得相对于B&B的数量级的加速比。
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.