Efficient channel estimation for massive MIMO systems via truncated two-dimensional atomic norm minimization

In millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems, channel estimation in the presence of sparse multipath fading boils down to two-dimensional (2D) direction-of-arrival (DOA) estimation followed by path gain estimation. To achieve super-resolution angle estimation at affordable complexity, this paper develops an efficient channel estimation approach by applying a truncated atomic norm minimization (T-ANM) technique, which is implemented via partial antenna activation during training-based channel estimation. This technique makes use of a key observation that the sparse scattering characteristics of mmWave MIMO channel gives rise to a low-rank two-level Toeplitz structure in the angular domain. Because of the low-rank property, only a subset of the transceiver antennas needs to be activated to save training resources. Meanwhile, the Toeplitz structure enables ANM-based gridless 2D DOA estimation via reduced-size semidefinite programming. Simulation results show that the proposed reduced-size method can achieve comparable spectral efficiency as the full-size benchmark method at much lower computational complexity and shorter sensing time.