Transmit Beamforming with Power Adaptation in Downlink Multi-User Systems

This paper addresses power adaptation in the context of beamforming in the downlink of a cellular system. Specifically, we consider a system consisting of a base station (BS) with multiple antennas and multiple users each with a single antenna, in which the BS selects the user with the best channel for transmission. Compared to the scheme minimizing the bit error rate (BER) using a fixed instantaneous power, the BER performance can be further improved by adapting the instantaneous power according to the channel of the selected user. The optimal power adaptation (OPA) policy is derived, and its BER is compared with the case of a sub-optimal policy called channel inversion (CI). With a novel analytical approach, the BER performances of OPA and CI are quantified and CI is shown to be near-optimal for a multi-user multi-antenna system at moderate to large SNR, unlike the single-user single-antenna case. Finite peak power constraint is also considered for both OPA and CI.