  This paper studies the capacity of discrete-time multipath fading channels.
It is assumed that the number of paths is finite, i.e., that the channel output
is influenced by the present and by the L previous channel inputs. A
noncoherent channel model is considered where neither transmitter nor receiver
are cognizant of the fading's realization, but both are aware of its statistic.
The focus is on capacity at high signal-to-noise ratios (SNR). In particular,
the capacity pre-loglog - defined as the limiting ratio of the capacity to
loglog SNR as SNR tends to infinity - is studied. It is shown that,
irrespective of the number paths L, the capacity pre-loglog is 1.
