Deep Channel Estimation

We consider the problem of channel estimation from a single noisy snapshot. We use a typical hierarchical channel model, where the channel is zero-mean, complex Gaussian distributed given the covariance matrix. The covariance matrix is unknown and depends on underlying random hyperparameters such as the angles of the propagation paths. For this model we derive the MMSE estimator and then exploit the structure of the channel model to arrive at a low-complexity, approximate MMSE estimator for a specific channel model with only one hyperparameter. We use the structure of this low-complexity estimator as a blueprint to design the architecture of a neural network which we then apply to general channel models. Simulation results demonstrate the effectiveness of our approach.