  This paper proposes and analyzes a mmWave sparse channel estimation technique
for OFDM systems that uses the Orthogonal Matching Pursuit (OMP) algorithm.
This greedy algorithm retrieves one additional multipath component (MPC) per
iteration until a stop condition is met. We obtain an analytical approximation
for the OMP estimation error variance that grows with the number of retrieved
MPCs (iterations). The OMP channel estimator error variance outperforms a
classic maximum-likelihood (ML) non-sparse channel estimator by a factor of
approximately $2\hat{L}/M$ where $\hat{L}$ is the number of retrieved MPCs
(iterations) and $M$ the number of taps of the Discrete Equivalent Channel.
When the MPC amplitude distribution is heavy-tailed, the channel power is
concentrated in a subset of dominant MPCs. In this case OMP performs fewer
iterations as it retrieves only these dominant large MPCs. Hence for this MPC
amplitude distribution the estimation error advantage of OMP over ML is
improved. In particular, for channels with MPCs that have
lognormally-distributed amplitudes, the OMP estimator recovers approximately
5-15 dominant MPCs in typical mmWave channels, with 15-45 weak MPCs that remain
undetected.
