  We consider the problem of rate and power allocation in a fading
multiple-access channel. Our objective is to obtain rate and power allocation
policies that maximize a utility function defined over average transmission
rates. In contrast with the literature, which focuses on the linear case, we
present results for general concave utility functions. We consider two cases.
In the first case, we assume that power control is possible and channel
statistics are known. In this case, we show that the optimal policies can be
obtained greedily by maximizing a linear utility function at each channel
state. In the second case, we assume that power control is not possible and
channel statistics are not available. In this case, we define a greedy rate
allocation policy and provide upper bounds on the performance difference
between the optimal and the greedy policy. Our bounds highlight the dependence
of the performance difference on the channel variations and the structure of
the utility function.
