  In this paper, channel estimation for millimeter wave (mmWave) massive
multiple-input multiple-output (MIMO) systems with one-bit analog-to-digital
converters (ADCs) is considered. In the mmWave band, the number of propagation
paths is small, which results in sparse virtual channels. To estimate sparse
virtual channels based on the maximum a posteriori (MAP) criterion,
sparsity-constrained optimization comes into play. In general, optimizing
objective functions with sparsity constraints is NP-hard because of their
combinatorial complexity. Furthermore, the coarse quantization of one-bit ADCs
makes channel estimation a challenging task. In the field of compressed sensing
(CS), the gradient support pursuit (GraSP) and gradient hard thresholding
pursuit (GraHTP) algorithms were proposed to approximately solve
sparsity-constrained optimization problems iteratively by pursuing the gradient
of the objective function via hard thresholding. The accuracy guarantee of
these algorithms, however, breaks down when the objective function is
ill-conditioned, which frequently occurs in the mmWave band. To prevent the
breakdown of gradient pursuit-based algorithms, the band maximum selecting
(BMS) technique, which is a hard thresholder selecting only the "band maxima,"
is applied to GraSP and GraHTP to propose the BMSGraSP and BMSGraHTP algorithms
in this paper.
