Achieving the Sum Rate Capacity of MIMO Downlink Communications With Better Fairness

Transmission schemes taking both sum rate and fairness into account for dirty paper coding (DPC) based MIMO downlink communications are investigated in this paper. In contrast to existing works which have mostly focused on maximizing the sum rate, we first investigate the problem of finding the maximal sum rate achieved by DPC when the qualitative notions of fairness such as max-min fairness and proportional fairness are employed. This corresponds to a nonconvex problem and cannot be solved by usual weighted sum rate techniques. Several efficient methods for finding the optimal solutions are presented in this paper when the order of users is adjustable during DPC encoding. Simulation results show surprisingly and impact greatly on the design of practical systems that it is often possible to achieve the sum rate capacity with absolute fairness, i.e., an equal rate for each user, when multiple encoding orders of users are used during transmission. When sum rate capacity and absolute fairness cannot be achieved at the same time, the optimal tradeoff between sum rate and fairness is also provided for a general class of quantitative fairness measures.