\begin{abstract}
We consider a multiple access, doubly-selective block Rayleigh
fading channel in which the users coordinate spectrum sharing
through a limited feedback scheme. Each user probes a random set of
sub-channels, known to the receiver, by sending a pilot sequence at
the beginning of each coherence block. Multiple users may probe the
same sub-channel, causing interference. The receiver assigns each
sub-channel to the user with the highest estimated sub-channel gain
(via limited feedback), provided that this gain exceeds a
predetermined threshold. Our problem is to optimize the number of
channels to probe, or ``spreading bandwidth'', for each user. We
maximize a lower bound on the ergodic capacity, and consider a large
system limit in which the system bandwidth and number of users scale
linearly with the coherence time. We show that the optimal spreading
bandwidth grows as order N/(log N)^2, assuming a linear Minimum Mean
Square Error channel estimator, and the achievable rate increases as
 order log(log N) per user, where N is the number of available
sub-channels. In contrast, if the users are pre-assigned
nonoverlapping sub-channels on which they probe and transmit, then
the capacity per user converges to a constant as N becomes large.
Additionally, the optimal training length and training power are
computed and the effect of system load (number of users per unit
coherence time) on the achievable rate is studied.
\end{abstract}