Fair resource allocation in multiple access channels

Abstract

We consider the problem of resource allocation in a multiple access channel. Our objective is to obtain rate and power allocation policies that maximize a general concave utility function of average transmission rates over the information theoretic capacity region of the multiple-access channel. We consider several different scenarios. First, we address the utility maximization problem in a non-fading channel and present an iterative gradient projection algorithm that uses approximate projection. By exploiting the polymatroid structure of the capacity region, we show that the approximate projection can be implemented in time polynomial in the number of users. Second, we consider resource allocation in a fading channel. Optimal rate and power allocation policies are presented for the case that power control is possible and channel statistics are available. For the case where transmission power is fixed and channel statistics are unknown, we propose a greedy rate allocation policy and provide bounds on the performance difference of this policy and the optimal policy in terms of channel variations and structure of the utility function. This policy does not require queue-length information. Moreover, we present numerical results that demonstrate superior convergence rate performance for the greedy policy compared to queue-length based policies. In order to reduce the computational complexity of the greedy policy, we present approximate rate allocation policies which track the greedy policy within a certain neighborhood that is characterized in terms of the speed of fading.