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To perform multi-user multiple-input and multiple-output transmission inmillimeter-wave(mmWave) cellular systems, the high-dimensional channels need tobe estimated for designing the multi-user precoder. Conventional grid-basedcompressed sensing (CS) methods for mmWave channel estimation suffer from thebasis mismatch problem, which prevents accurate channel reconstruction anddegrades the precoding performance. This paper formulates mmWave channelestimation as an Atomic Norm Minimization (ANM) problem. In contrast togrid-based CS methods which use discrete dictionaries, ANM uses a continuousdictionary for representing the mmWave channel. We consider a continuousdictionary based on sub-sampling in the antenna domain via a small number ofradio frequency chains. We show that mmWave channel estimation using ANM can beformulated as a semidefinite programming (SDP) problem, and the user channelcan be accurately estimated via off-the-shelf SDP solvers in polynomial time.Simulation results indicate that ANM can achieve much better estimationaccuracy compared to grid-based CS, and significantly improves the spectralefficiency provided by multi-user precoding.

MmWave Channel Estimation via Atomic Norm Minimization for Multi-User Hybrid Precoding