  This paper is concerned with the channel estimation problem in Millimeter
wave (mmWave) wireless systems with large antenna arrays. By exploiting the
inherent sparse nature of the mmWave channel, we first propose a fast channel
estimation (FCE) algorithm based on a novel overlapped beam pattern design,
which can increase the amount of information carried by each channel
measurement and thus reduce the required channel estimation time compared to
the existing non-overlapped designs. We develop a maximum likelihood (ML)
estimator to optimally extract the path information from the channel
measurements. Then, we propose a novel rate-adaptive channel estimation (RACE)
algorithm, which can dynamically adjust the number of channel measurements
based on the expected probability of estimation error (PEE). The performance of
both proposed algorithms is analyzed. For the FCE algorithm, an approximate
closed-form expression for the PEE is derived. For the RACE algorithm, a lower
bound for the minimum signal energy-to-noise ratio required for a given number
of channel measurements is developed based on the Shannon-Hartley theorem.
Simulation results show that the FCE algorithm significantly reduces the number
of channel estimation measurements compared to the existing algorithms using
non-overlapped beam patterns. By adopting the RACE algorithm, we can achieve up
to a 6dB gain in signal energy-to-noise ratio for the same PEE compared to the
existing algorithms.
