Group Sparsity via Implicit Regularization for MIMO Channel Estimation

To compensate for the path losses in millimeter wave (mmWave) communication, multiple-input-multiple-output (MIMO) systems leverage beamforming-based solutions to boost the received SNR. Since beamforming requires knowledge of the wireless channel, its performance is also closely tied with the channel estimation accuracy. In mmWave communication, wireless channels are known to have only a few dominant paths. Several channel estimation methods leverage this characteristic by either using low-rank methods or by modeling element-wise sparsity of channels in angular domain. In this work we propose that the channel in angular domain is better characterized as group sparse rather than element-wise sparse. We further leverage the recent advancements in implicit regularization with gradient descent to develop a non-convex formulation that implicitly enforces group sparsity without additional regularization terms. We further compare the performance of the proposed approach against existing low rank or sparsity based matrix completion methods for channel estimation.