The problem of channel estimation for millimeter wave (mmWave) systems employing few-bit ADCs is studied. Since the mmWave channel is usually characterized by a geometric channel model, which is low rank and sparse in angular domains, utilizing the low-rank structure along with the sparsity improves the channel estimation performance. Specifically, this paper develops a two stage approach for mmWave channel estimation, namely, a low rank matrix recovery stage and a gridless angle recovery stage. At the first stage, because the low rank matrix undergoes a linear transform followed by a componentwise nonlinear transform, three modules named sparse Bayesian learning, linear minimum mean squared error (LMMSE) module, MMSE module are designed respectively for the signal recovery. At the second stage, utilizing the recovered low rank matrix along with the subspace, MUSIC is adopted to recover the angular information, which further improves the channel estimation performance. Numerical experiments are conducted to show the effectiveness of the proposed approach.

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