  This paper develops a channel estimation technique for millimeter wave
(mmWave) communication systems. Our method exploits the sparse structure in
mmWave channels for low training overhead and accounts for the phase errors in
the channel measurements due to phase noise at the oscillator. Specifically, in
IEEE 802.11ad/ay-based mmWave systems, the phase errors within a beam
refinement protocol packet are almost the same, while the errors across
different packets are substantially different. Consequently, standard
sparsity-aware algorithms, which ignore phase errors, fail when channel
measurements are acquired over multiple beam refinement protocol packets. We
present a novel algorithm called partially coherent matching pursuit for sparse
channel estimation under practical phase noise perturbations. Our method
iteratively detects the support of sparse signal and employs alternating
minimization to jointly estimate the signal and the phase errors. We
numerically show that our algorithm can reconstruct the channel accurately at a
lower complexity than the benchmarks.
