Channel Estimation for Switch-Based Millimeter-Wave Communications via Atomic Norm

Channel estimation is a challenging issue in millimeter-wave massive multiple-input-multiple-output (MIMO) communication systems due to the large number of antennas in the transceiver. Existing methods are usually based on phase shifters which may not be a simple circuit at mmWave band. In this paper, we construct a switch-based architecture for analog processors from the coarray point of view and then propose an atomic ℓ0-norm minimization problem. We then propose an efficient algorithm to solve this problem based on Wirtinger projection. Since the proposed method requires no angle discretization, it does not suffer from grid mismatch effect that greatly deteriorates the estimation performance of grid-based channel estimation methods. Compared to the atomic norm minimization (ANM) method, our method does not involve vectorization of the channel matrix and hence the dimensionality of the problem is much less than that of ANM. We show that our method is able to provide comparable estimation performance to ANM but with much less computational time. Extensive simulations are carried out to verify the effectiveness of our proposed method.