Symmetric Capacity of MIMO Downlink Channels

This paper studies the symmetric capacity of the MIMO downlink channel, which is defined to be the maximum rate that can be allocated to every receiver in the system. The symmetric capacity represents absolute fairness and is an important metric for slowly fading channels in which users have symmetric rate demands. An efficient and provably convergent algorithm for computing the symmetric capacity is proposed, and it is shown that a simple modification of the algorithm can be used to compute the minimum power required to meet given downlink rate demands. In addition, the difference between the symmetric and sum capacity, termed the fairness penalty, is studied. Exact analytical results for the fairness penalty at high SNR are provided for the 2 user downlink channel, and numerical results are given for channels with more users