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We study the problem of optimal power allocation in a single-hop ad hocwireless network. In solving this problem, we depart from classical purelymodel-based approaches and propose a hybrid method that retains key modelingelements in conjunction with data-driven components. More precisely, we putforth a neural network architecture inspired by the algorithmic unfolding ofthe iterative weighted minimum mean squared error (WMMSE) method, that wedenote by unfolded WMMSE (UWMMSE). The learnable weights within UWMMSE areparameterized using graph neural networks (GNNs), where the time-varyingunderlying graphs are given by the fading interference coefficients in thewireless network. These GNNs are trained through a gradient descent approachbased on multiple instances of the power allocation problem. We show that theproposed architecture is permutation equivariant, thus facilitatinggeneralizability across network topologies. Comprehensive numerical experimentsillustrate the performance attained by UWMMSE along with its robustness tohyper-parameter selection and generalizability to unseen scenarios such asdifferent network densities and network sizes.

Unfolding WMMSE using Graph Neural Networks for Efficient Power Allocation