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Deep unfolding of the weighted MMSE beamforming algorithm

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Document pages: 9 pages

Abstract: Downlink beamforming is a key technology for cellular networks. However,computing the transmit beamformer that maximizes the weighted sum rate subjectto a power constraint is an NP-hard problem. As a result, iterative algorithmsthat converge to a local optimum are used in practice. Among them, the weightedminimum mean square error (WMMSE) algorithm has gained popularity, but itscomputational complexity and consequent latency has motivated the need forlower-complexity approximations at the expense of performance. Motivated by therecent success of deep unfolding in the trade-off between complexity andperformance, we propose the novel application of deep unfolding to the WMMSEalgorithm for a MISO downlink channel. The main idea consists of mapping afixed number of iterations of the WMMSE algorithm into trainable neural networklayers, whose architecture reflects the structure of the original algorithm.With respect to traditional end-to-end learning, deep unfolding naturallyincorporates expert knowledge, with the benefits of immediate and well-groundedarchitecture selection, fewer trainable parameters, and better explainability.However, the formulation of the WMMSE algorithm, as described in Shi et al., isnot amenable to be unfolded due to a matrix inversion, an eigendecomposition,and a bisection search performed at each iteration. Therefore, we present analternative formulation that circumvents these operations by resorting toprojected gradient descent. By means of simulations, we show that, in most ofthe settings, the unfolded WMMSE outperforms or performs equally to the WMMSEfor a fixed number of iterations, with the advantage of a lower computationalload.

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