Scutari “On the maximum common rate in multiple access channels using multiple antenna transceivers”, submitted to

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 multi-user water-filling solution. However, maximizing the sum-rate may yield very low (even null) rates for users experi-encing 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 com-mon rate, under the constraint of a fixed total transmitted power. In this paper, we will show how to solve this prob-lem, providing this maximum common rate and the power allocation and code selection necessary to achieve it. In par-ticular, we will show that in case of transmission over linear time-invariant channels, the solution for the finite block case