On Superposition Coding and Beamforming for the Multi-Antenna Gaussian Broadcast Channel

The capacity region of the Gaussian multiple-input, single-output (per user) Broadcast Channel (BC) using superposition coding is analyzed. Perfect channel state information is assumed both at the transmitter and the receivers. The achievable Signal-to-Interference-plus-Noise Ratio (SINR) region of BC and MAC using beamforming is considered, and it is shown that existing SINR-balancing results extend to the case of any crosstalk matrix between the different users. Optimal beamforming vectors are found, simplifying thus the analysis of the achievable rate-region. Finally, a modified form of beamforming is applied as an inner bound for the Van der Meulen Hajek Pursley (CMHP) rate-region in this model, and this is compared to the optimal capacity region and also to other sub-optimal strategies such as zero-forcing, for the BC.