  The fact that the millimeter-wave (mmWave) multiple-input multiple-output
(MIMO) channel has sparse support in the spatial domain has motivated recent
compressed sensing (CS)-based mmWave channel estimation methods, where the
angles of arrivals (AoAs) and angles of departures (AoDs) are quantized using
angle dictionary matrices. However, the existing CS-based methods usually
obtain the estimation result through one-stage channel sounding that have two
limitations: (i) the requirement of large-dimensional dictionary and (ii)
unresolvable quantization error. These two drawbacks are irreconcilable;
improvement of the one implies deterioration of the other. To address these
challenges, we propose, in this paper, a two-stage method to estimate the AoAs
and AoDs of mmWave channels. In the proposed method, the channel estimation
task is divided into two stages, Stage I and Stage II. Specifically, in Stage
I, the AoAs are estimated by solving a multiple measurement vectors (MMV)
problem. In Stage II, based on the estimated AoAs, the receive sounders are
designed to estimate AoDs. The dimension of the angle dictionary in each stage
can be reduced, which in turn reduces the computational complexity
substantially. We then analyze the successful recovery probability (SRP) of the
proposed method, revealing the superiority of the proposed framework over the
existing one-stage CS-based methods. We further enhance the reconstruction
performance by performing resource allocation between the two stages. We also
overcome the unresolvable quantization error issue present in the prior
techniques by applying the atomic norm minimization method to each stage of the
proposed two-stage approach. The simulation results illustrate the
substantially improved performance with low complexity of the proposed
two-stage method.
