  The scaling of coherent and non-coherent channel capacity is studied in a
single-input multiple-output (SIMO) block Rayleigh fading channel as both the
bandwidth and the number of receiver antennas go to infinity jointly with the
transmit power fixed. The transmitter has no channel state information (CSI),
while the receiver may have genie-provided CSI (coherent receiver), or the
channel statistics only (non-coherent receiver). Our results show that if the
available bandwidth is smaller than a threshold bandwidth which is proportional
(up to leading order terms) to the square root of the number of antennas, there
is no gap between the coherent capacity and the non-coherent capacity in terms
of capacity scaling behavior. On the other hand, when the bandwidth is larger
than this threshold, there is a capacity scaling gap. Since achievable rates
using pilot symbols for channel estimation are subject to the non-coherent
capacity bound, this work reveals that pilot-assisted coherent receivers in
systems with a large number of receive antennas are unable to exploit excess
spectrum above a given threshold for capacity gain.
