Abstract
Downlink beamforming is a key technology for cellular networks. However, computing beamformers that maximize the weighted sum rate (WSR) subject to a power constraint is an NP-hard problem. The popular weighted minimum mean square error (WMMSE) algorithm converges to a local optimum but still exhibits considerable complexity. In order to address this trade-off between complexity and performance, we propose to apply deep unfolding to the WMMSE algorithm for a MU-MISO downlink channel. The main idea consists of mapping a fixed number of iterations of the WMMSE into trainable neural network layers. However, the formulation of the WMMSE algorithm, as provided in Shi <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , involves matrix inversions, eigendecompositions, and bisection searches. These operations are hard to implement as standard network layers. Therefore, we present a variant of the WMMSE algorithm i) that circumvents these operations by applying a projected gradient descent and ii) that, as a result, involves only operations that can be efficiently computed in parallel on hardware platforms designed for deep learning. We demonstrate that our variant of the WMMSE algorithm convergences to a stationary point of the WSR maximization problem and we accelerate its convergence by incorporating Nesterov acceleration and a generalization thereof as learnable structures. By means of simulations, we show that the proposed network architecture i) performs on par with the WMMSE algorithm truncated to the same number of iterations, yet at a lower complexity, and ii) generalizes well to changes in the channel distribution.
Highlights
Downlink beamforming is a pivotal technology in the fourth and fifth generation cellular communication systems [1]
We address the complexity versus performance trade-off by applying a machine-learning-based technique, called deep unfolding, to the weighted minimum mean square error (WMMSE) algorithm [16] for a multi-user multiple-input single-output (MU-MISO) downlink channel
Contrasting the iterative algorithm induced deep-unfolding neural network (IAIDNN) with the unfoldable WMMSE algorithm proposed by us, our solution i) is truly matrixinverse-free, which brings substantial benefits in terms of hardware implementation, ii) presents significantly fewer learnable parameters, as the dimension of the trainable parameter space does not scale with the problem dimension, and iii) achieves a higher weighted sum rate (WSR) in the fully loaded scenario, i.e., with an equal number of users and transmit antennas at the base station
Summary
Downlink beamforming is a pivotal technology in the fourth and fifth generation cellular communication systems [1]. The common underlying idea consists of replacing the well-performing, yet expensive and high-latency, iterative algorithms with neural networks These approaches [32]–[34] are based on end-toend learning, i.e., neural networks take as input the wireless channel and directly predict the beamformer weights. Contrasting the IAIDNN with the unfoldable WMMSE algorithm proposed by us, our solution i) is truly matrixinverse-free, which brings substantial benefits in terms of hardware implementation, ii) presents significantly fewer learnable parameters, as the dimension of the trainable parameter space does not scale with the problem dimension, and iii) achieves a higher WSR in the fully loaded scenario, i.e., with an equal number of users and transmit antennas at the base station (see Section VIII-C).
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