A unifying theory for uplink and downlink multiuser beamforming

The problem of multiuser beamforming and power control for spatially dispersive, frequency flat channels is addressed, assuming that the base station is equipped with an antenna array and knows the second-order statistics of the channel. There is an interesting duality between the uplink and the downlink problem. In particular, it is shown that both cases can be solved efficiently by an iterative optimization scheme, wherein the conventional uplink beamformer plays a central role. The antenna weights that solve the uplink problem also solve the more complicated downlink problem. The reason for this can be found in the special structure of the crosstalk matrix coupling all users. This leads to an elegant theory, which may also prove useful for solving related problems.