论文标题
MU-MIMO WMMSE波束成形算法的无基质内实现
A matrix-inverse-free implementation of the MU-MIMO WMMSE beamforming algorithm
论文作者
论文摘要
WMMSE波束形成算法是一种解决NP - 硬加权总和（WSR）最大化边界成形问题的流行方法。尽管它有效地找到了局部最佳，但它需要矩阵倒置，特征组合和二分搜索，对于实时实现而言是有问题的操作。 在以前的工作中，我们考虑了MU-MISO案例，并通过诉诸一阶方法来有效地取代了此类操作。在这里，我们考虑了更笼统和具有挑战性的MU-MIMO案例。我们较早的方法不会推广到这种情况，也不能应用于替换MU-Mimo情况中出现的所有难以合行的操作。因此，我们建议利用Hu等人给出的辅助WMMSE功能的重新制定。通过应用梯度下降和Schulz迭代，我们制定了适用于MU-MIMO案例的WMMSE算法的第一个变体，该变体无基质倒置和其他串行操作，因此可用于实时实现和深入展开。从理论上的角度来看，我们将其收敛到WSR最大化问题的固定点。从实际的角度来看，我们表明，在基于深度的实现中，无矩阵内的WMMSE算法在固定的迭代次数中获得与原始WMMSE算法相当的WSR，可以将其截断为相同数量的迭代，但具有相同数量的迭代，但具有相同的实现，并且在并行的实时执行方面具有显着的实现。
The WMMSE beamforming algorithm is a popular approach to address the NP-hard weighted sum rate (WSR) maximization beamforming problem. Although it efficiently finds a local optimum, it requires matrix inverses, eigendecompositions, and bisection searches, operations that are problematic for real-time implementation. In our previous work, we considered the MU-MISO case and effectively replaced such operations by resorting to a first-order method. Here, we consider the more general and challenging MU-MIMO case. Our earlier approach does not generalize to this scenario and cannot be applied to replace all the hard-to-parallelize operations that appear in the MU-MIMO case. Thus, we propose to leverage a reformulation of the auxiliary WMMSE function given by Hu et al. By applying gradient descent and Schulz iterations, we formulate the first variant of the WMMSE algorithm applicable to the MU-MIMO case that is free from matrix inverses and other serial operations and hence amenable to both real-time implementation and deep unfolding. From a theoretical viewpoint, we establish its convergence to a stationary point of the WSR maximization problem. From a practical viewpoint, we show that in a deep-unfolding-based implementation, the matrix-inverse-free WMMSE algorithm attains, within a fixed number of iterations, a WSR comparable to the original WMMSE algorithm truncated to the same number of iterations, yet with significant implementation advantages in terms of parallelizability and real-time execution.
