  We study the problem of optimal power allocation in a single-hop ad hoc
wireless network. In solving this problem, we depart from classical purely
model-based approaches and propose a hybrid method that retains key modeling
elements in conjunction with data-driven components. More precisely, we put
forth a neural network architecture inspired by the algorithmic unfolding of
the iterative weighted minimum mean squared error (WMMSE) method, that we
denote by 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. We show that the
proposed architecture is permutation equivariant, thus facilitating
generalizability across network topologies. Comprehensive numerical experiments
illustrate the performance attained by UWMMSE along with its robustness to
hyper-parameter selection and generalizability to unseen scenarios such as
different network densities and network sizes.
