On the maximum common rate in multiple access channels

Given a multiple access channel, it is well known that the criterion of maximum sum-rate, under the constraint of a given transmitted power for each user, leads to the multiuser water-filling solution. However, maximizing the sum-rate may yield very low (even null) rates for users experiencing the deepest fades. Our goal is to introduce a fairness principle so that all users can transmit at the same rate. The question is then what is the maximum value of such a common rate, under the constraint of a fixed total transmitted power. In this paper, we will show how to solve this problem, providing this maximum common rate and the power allocation and code selection necessary to achieve it. In particular, we will show that in case of transmission over linear time-invariant channels, the solution for the finite block case, using cyclic prefixes, is given by an OFDMA strategy, with a proper power and frequency distribution among the users.