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We study the problem of optimal power allocation in a single-hop ad hocwireless network. In solving this problem, we propose a hybrid neuralarchitecture inspired by the algorithmic unfolding of the iterative weightedminimum mean squared error (WMMSE) method, that we denote as unfolded WMMSE(UWMMSE). The learnable weights within UWMMSE are parameterized using graphneural networks (GNNs), where the time-varying underlying graphs are given bythe fading interference coefficients in the wireless network. These GNNs aretrained through a gradient descent approach based on multiple instances of thepower allocation problem. Once trained, UWMMSE achieves performance comparableto that of WMMSE while significantly reducing the computational complexity.This phenomenon is illustrated through numerical experiments along with therobustness and generalization to wireless networks of different densities andsizes.

Efficient power allocation using graph neural networks and deep algorithm unfolding