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