Rate balancing for the multi-antenna Gaussian broadcast channel

In this work we study the optimal transmission strategy for a multi-antenna Gaussian broadcast channel in which each user requires a specific rate. These rate requirements correspond to the respective service which the mobile is using. Both the transmitter and the receivers are equipped with multiple antennas. We assume that the base station has perfect channel state information. The mobiles have perfect channel state information regarding their own channel but can not cooperate. This leads to the nondegraded multi-antenna Gaussian broadcast channel. We propose an algorithm which tries to fulfill the rate requirements of all mobiles and maximizes the minimum rate factor which is defined as the quotient of available rate and rate requirement for each mobile. The algorithm, balances out the rate factors for all mobiles until an equilibrium is reached. We present a necessary condition for the optimal solution. Finally, all theoretical results are illustrated by numerical simulations.