A Low Complexity Channel Estimation for Millimeter Wave Massive MIMO Systems Based on Atomic Norm Minimization

Millimeter Wave (mmWave) systems will likely employ directional beamforming with large antenna arrays at both the transmitter and the receiver. However, Acquiring channel knowledge to design these beamformers is challenging due to the large antenna arrays and small signal-to-noise ratio before beamforming. In this paper we propose a downlink channel estimation for multi-user mmWave systems based on 2D Atomic Norm Minimization (2D-ANM). With the large number of antenna elements, computational cost grows in 2D-ANM because the angular information of the channel, namely AoAs and AoDs, are coded in the two-level Toeplitz matrix which has a huge complexity in the large scale arrays. So a low complexity solution is required. This paper introduces Decoupled Atomic Norm Minimization (DeANM) which express the original high-dimension problem by two decoupled Toeplitz matrices in one dimension. For further improvements, we reformulate the DeANM problem with Reweighted Atomic Norm Minimization (ReANM) to get Reweighted Decoupled Atomic Norm Minimization (ReDeANM) that exploits the sparsity of the channel to greatest extent. Simulation results verify the performance of the proposed methods.