  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 large-scale 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-decent-based 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.
