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The millimeter-wave (mmWave) full-dimensional (FD) MIMO system employs planar arrays at both the base station and user equipment and can simultaneously support both azimuth and elevation beamforming. In this paper, we propose atomic-norm-based methods for mmWave FD-MIMO channel estimation under both uniform planar arrays (UPA) and non-uniform planar arrays (NUPA). Unlike existing algorithms such as compressive sensing (CS) or subspace methods, the atomic-norm-based algorithms do not require to discretize the angle spaces of the angle of arrival (AoA) and angle of departure (AoD) into grids, thus provide much better accuracy in estimation. In the UPA case, to reduce the computational complexity, the original largescale 4D atomic norm minimization problem is approximately reformulated as a semi-definite program (SDP) containing two decoupled two-level Toeplitz matrices. The SDP is then solved via the alternating direction method of multipliers (ADMM) where each iteration involves only closed-form computations. In the NUPA case, the atomic-norm-based formulation for channel estimation becomes nonconvex and a gradient-decentbased algorithm is proposed to solve the problem. Simulation results show that the proposed algorithms achieve better performance than the CS-based and subspace-based algorithms.

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