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 "probing 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 probing bandwidth grows as O N/(log N)², assuming a linear Minimum Mean Square Error channel estimator, and the achievable rate increases as O (log log N) per user, where N is the number of available subchannels. In contrast, if the users are pre-assigned nonoverlapping subchannels 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.