This work proposes a mixed learning-based and optimization-based approach to the weighted-sum-rates beamforming problem in a multiple-input multiple-output (MIMO) wireless network. The conventional methods, i.e., the fractional programming (FP) method and the weighted minimum mean square error (WMMSE) algorithm, can be computationally demanding for two reasons: (i) they require inverting a sequence of matrices whose sizes are proportional to the number of antennas; (ii) they require tuning a set of Lagrange multipliers to account for the power constraints. The recently proposed method called the reduced WMMSE addresses the above two issues for a single cell. In contrast, for the multicell case, another recent method called the FastFP eliminates the large matrix inversion and the Lagrange multipliers by using an improved FP technique, but the update stepsize in the FastFP can be difficult to decide. As such, we propose integrating the deep unfolding network into the FastFP for the stepsize optimization. Numerical experiments show that the proposed method is much more efficient than the learning method based on the WMMSE algorithm.

翻译：本文针对多输入多输出（MIMO）无线网络中的加权和速率波束成形问题，提出了一种基于学习与优化相结合的混合方法。传统方法，即分式规划（FP）方法和加权最小均方误差（WMMSE）算法，在计算上可能较为耗时，原因有二：（i）它们需要对一系列尺寸与天线数量成比例的矩阵进行求逆；（ii）它们需要调整一组拉格朗日乘子以满足功率约束。最近提出的方法——简化WMMSE（reduced WMMSE）——在单小区场景中解决了上述两个问题。相比之下，对于多小区场景，另一种近期方法——快速分式规划（FastFP）——通过改进的分式规划技术消除了大规模矩阵求逆和拉格朗日乘子，但FastFP中的更新步长难以确定。为此，我们提出将深度展开网络集成到FastFP中以优化步长。数值实验表明，所提方法比基于WMMSE算法的学习方法高效得多。