  We propose super-resolution MIMO channel estimators for millimeter-wave
(mmWave) systems that employ hybrid analog and digital beamforming and
generalized spatial modulation, respectively. Exploiting the inherent sparsity
of mmWave channels, the channel estimation problem is formulated as an atomic
norm minimization that enhances sparsity in the continuous angles of departure
and arrival. Both pilot-assisted and data-aided channel estimators are
developed, with the former one formulated as a convex problem and the latter as
a non-convex problem. To solve these formulated channel estimation problems, we
develop a computationally efficient conjugate gradient descent method based on
non-convex factorization which restricts the search space to low-rank matrices.
Simulation results are presented to illustrate the superior channel estimation
performance of the proposed algorithms for both types of mmWave systems
compared to the existing compressed-sensing-based estimators with finely
quantized angle grids.
