  We consider the problem of rate allocation in a fading Gaussian
multiple-access channel (MAC) with fixed transmission powers. Our goal is to
maximize a general concave utility function of transmission rates over the
throughput capacity region. In contrast to earlier works in this context that
propose solutions where a potentially complex optimization problem must be
solved in every decision instant, we propose a low-complexity approximate rate
allocation policy and analyze the effect of temporal channel variations on its
utility performance. To the best of our knowledge, this is the first work that
studies the tracking capabilities of an approximate rate allocation scheme
under fading channel conditions. We build on an earlier work to present a new
rate allocation policy for a fading MAC that implements a low-complexity
approximate gradient projection iteration for each channel measurement, and
explicitly characterize the effect of the speed of temporal channel variations
on the tracking neighborhood of our policy. We further improve our results by
proposing an alternative rate allocation policy for which tighter bounds on the
size of the tracking neighborhood are derived. These proposed rate allocation
policies are computationally efficient in our setting since they implement a
single gradient projection iteration per channel measurement and each such
iteration relies on approximate projections which has polynomial-complexity in
the number of users.
