  A great increase in wireless access rates might be attainable by using the
large amount of spectrum available in the millimeter wave (mmWave, 30 - 300
GHz) band. However, due to higher propagation losses inherent in these
frequencies, to use wider bandwidth for transmission at ranges beyond 100
meters or in non-line-of-sight (NLOS) settings may be ineffective or even
counterproductive when the penalty for estimating the channel is taken into
account. In this work we quantify the maximum beneficial bandwidth for mmWave
transmission in some typical deployment scenarios which use pilot-based channel
estimation and assume a minimum mean square error (MMSE) channel estimator at
the receiver. We find that for an I.I.D. block fading model with coherence time
$T_c$ and coherence bandwidth $B_c$, for transmitters and receivers equipped
with a single antenna, the optimal (rate-maximizing) signal-to-noise-ratio is a
constant that only depends on the product $B_cT_c$, which measures the channel
coherence and equals the average number of orthogonal symbols per each
independent channel coefficient. That is, for fixed channel coherence, the
optimal bandwidth scales linearly with the received signal power. Under some
typical deployment scenarios with both transmit and receive side beamforming, 1
GHz bandwidth can be too much.
