Contents I. Introduction
The sum capacity and the entire capacity region of a multiple-input–multiple-output (MIMO) downlink (DL) channel with per-antenna or per-antenna-group power constraints were recently discovered in [1], [2]. The minimum-power beamformer design for multiple-input–single-output (MISO) DL under per-antenna constraints was also proposed in [1]. The sum capacity can sometimes result in very nonuniform rate allocation between users. In order to guarantee instantaneous quality of service (QoS) for all users, the symmetric capacity becomes an important performance metric for delay constrained applications. The weighted symmetric capacity is defined so that the weighted user rates are equal, while their rates belong to the boundary of the capacity region [3]. This enables the system to control the rates assigned to users that belong to distinct service priority classes. An iterative algorithm to find the weighted symmetric capacity with a sum power constraint was recently proposed in [3].
