Comparison of l∞-norm and l1-norm optimization for multi-antenna downlink transmission

The authors consider a typical downlink scenario, where independent data streams are submitted via an M-element antenna array to K non-cooperating single antenna receivers. Assuming that meaningful channel information is available at the transmitting base station, recent results indicate that the optimal transmission strategy is to use a spatial linear pre-filter per user (also known as beamformer). The spatial diversity and processing gain that is obtained by spreading the signals in the spatial domain, may significantly improve the signal-to-interference-ratio (SIR). Assuming that a fair sharing of resources is required, the design goal should be to balance the SIR levels so as to meet certain target values γ₁...γ_K.