The millimeter-wave (mmWave) full-dimensional (FD) MIMO system employs planararrays at both the base station and user equipment and can simultaneouslysupport both azimuth and elevation beamforming. In this paper, we proposeatomic-norm-based methods for mmWave FD-MIMO channel estimation under bothuniform planar arrays (UPA) and non-uniform planar arrays (NUPA). Unlikeexisting algorithms such as compressive sensing (CS) or subspace methods, theatomic-norm-based algorithms do not require to discretize the angle spaces ofthe angle of arrival (AoA) and angle of departure (AoD) into grids, thusprovide much better accuracy in estimation. In the UPA case, to reduce thecomputational complexity, the original large-scale 4D atomic norm minimizationproblem is approximately reformulated as a semi-definite program (SDP)containing two decoupled two-level Toeplitz matrices. The SDP is then solvedvia the alternating direction method of multipliers (ADMM) where each iterationinvolves only closed-form computations. In the NUPA case, the atomic-norm-basedformulation for channel estimation becomes nonconvex and agradient-decent-based algorithm is proposed to solve the problem. Simulationresults show that the proposed algorithms achieve better performance than theCS-based and subspace-based algorithms.
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