Learning the MMSE Channel Estimator

We present an O(M logM) method for estimating M -dimensional structured channels that uses techniques from the field of machine learning. Our channel model is typical in communications: the channel vector is normal distributed given an unknown covariance matrix, which depends on random hyperparameters such as the angles of the propagation paths. If the channel model exhibits certain Toeplitz and shift-invariance structures, the complexity of the MMSE estimator can be reduced to O(M logM); otherwise, it is much higher. To obtain an O(M logM) estimator for the general case, we use the structure of this specific MMSE estimator as an informed guess for the architecture of a neural network. We discuss how this network can be efficiently trained with channel realizations to learn the MMSE estimator in the class of O(M logM) estimators.