  This work studies the capacity of multipath fading channels. A noncoherent
channel model is considered, where neither the transmitter nor the receiver is
cognizant of the realization of the path gains, but both are cognizant of their
statistics. It is shown that if the delay spread is large in the sense that the
variances of the path gains decay exponentially or slower, then capacity is
bounded in the signal-to-noise ratio (SNR). For such channels, capacity does
not tend to infinity as the SNR tends to infinity. In contrast, if the
variances of the path gains decay faster than exponentially, then capacity is
unbounded in the SNR. It is further demonstrated that if the number of paths is
finite, then at high SNR capacity grows double-logarithmically with the SNR,
and the capacity pre-loglog, defined as the limiting ratio of capacity to
log(log(SNR)) as SNR tends to infinity, is 1 irrespective of the number of
paths.
