  The analysis of the channel capacity in the absence of prior channel
knowledge (noncoherent channel) has gained increasing interest in recent years,
but it is still unknown for the general case. In this paper we derive bounds on
the capacity of the noncoherent, underspread complex Gaussian, orthogonal
frequency division multiplexing (OFDM), wide sense stationary channel with
uncorrelated scattering (WSSUS), under a peak power constraint or a constraint
on the second and fourth moments of the transmitted signal. These bounds are
characterized only by the system signal-to-noise ratio (SNR) and by a newly
defined quantity termed effective coherence time. Analysis of the effective
coherence time reveals that it can be interpreted as the length of a block in
the block fading model in which a system with the same SNR will achieve the
same capacity as in the analyzed channel. Unlike commonly used coherence time
definitions, it is shown that the effective coherence time depends on the SNR,
and is a nonincreasing function of it. We show that for low SNR the capacity is
proportional to the effective coherence time, while for higher SNR the coherent
channel capacity can be achieved provided that the effective coherence time is
large enough.
