Deep unfolding of the weighted MMSE beamforming algorithm

Abstract

Downlink beamforming is a key technology for cellular networks. However, computing the transmit beamformer that maximizes the weighted sum rate subject to a power constraint is an NP-hard problem. As a result, iterative algorithms that converge to a local optimum are used in practice. Among them, the weighted minimum mean square error (WMMSE) algorithm has gained popularity, but its computational complexity and consequent latency has motivated the need for lower-complexity approximations at the expense of performance.Motivated by the recent success of deep unfolding in the tradeoff between complexity and performance, we propose the novel application of deep unfolding to the WMMSE algorithm for a MISO downlink channel. The main idea consists of mapping a fixed number of iterations of the WMMSE algorithm into trainable neural network layers, whose architecture reflects the structure of the original algorithm. With respect to traditional end-to-end learning, deep unfolding naturally incorporates expert knowledge, with the benefits of immediate and well-grounded architecture selection, fewer trainable parameters, and better explainability. However, the formulation of the WMMSE algorithm, as described in Shi et al., is not amenable to be unfolded due to a matrix inversion, an eigendecomposition, and a bisection search performed at each iteration. Therefore, we present an alternative formulation that circumvents these operations by resorting to projected gradient descent. By means of simulations, we show that, in most of the settings, the unfolded WMMSE outperforms or performs equally to the WMMSE for a fixed number of iterations, with the advantage of a lower computational load.

Meta-learning Based Beamforming Design for MISO Downlink

“…The unfolded WMMSE algorithm follows the original mathematical model of the WSR optimization problem, and designs a specific network structure to map the variables and the parameters in the original problem; therefore, the optimization of the WSR problem is converted into the optimization of the designed neural network. However, the performance of the aforementioned approaches [8], [9], [11], [12] do not surpass the WMMSE algorithm.…”

“…These approaches convert the original model-based problem into a data-driven learning-based problem, and the performance depends on the the network architecture. Alternatively, more recent works in [11], [12] propose unfolding the WMMSE algorithm in order to design a model-inspired computational structure for the neural network, and learn specific parameters of the original model by training on a set of channel samples. The unfolded WMMSE algorithm follows the original mathematical model of the WSR optimization problem, and designs a specific network structure to map the variables and the parameters in the original problem; therefore, the optimization of the WSR problem is converted into the optimization of the designed neural network.…”

Graph-based Algorithm Unfolding for Energy-aware Power Allocation in Wireless Networks

“…Deep neural networks (DNNs) have shown promising success in wireless power allocation and other communication problems [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. Most of these approaches are model-free, meaning that they parameterize some function of interest with established multi-purpose architectures such as multi-layer perceptrons (MLPs) [32][33][34], convolutional neural networks (CNNs) [35,36], recurrent neural networks [37], and graph neural networks (GNNs) [38,40].…”

“…Related work. The application of deep learning to wireless power allocation is an active area of research [32][33][34][35][36][37][38][39][40][41][42][43][44][45]. However, only a limited subset of these works utilize graph-based learning methods [38,40,43] or algorithm unfolding [41,[43][44][45].…”

“…The application of deep learning to wireless power allocation is an active area of research [32][33][34][35][36][37][38][39][40][41][42][43][44][45]. However, only a limited subset of these works utilize graph-based learning methods [38,40,43] or algorithm unfolding [41,[43][44][45]. The only prior work within power allocation that lives at the intersection (like our proposed approach) is [43,50], which unfolds the iterative weighted minimum mean squared error (WMMSE) method for sum-rate maximization.…”