Distributed multi-cell zero-forcing beamforming in cellular downlink channels

For a multiple-input single-output (MISO) downlink channel with M transmit antennas, it has been recently proved that zero-forcing beamforming (ZFBF) to a subset of (at most) M "semi-orthogonal" users is optimal in terms of the sum-rate, asymptotically with the number of users. However, determining the subset of users for transmission is a complex optimization problem. Adopting the ZFBF scheme in a cooper-ative multi-cell scenario renders the selection process even more difficult since more users are involved. In this paper, we consider a multi-cell cooperative ZFBF scheme combined with a simple sub-optimal users selection procedure for the Wyner downlink channel setup. According to this sub-optimal procedure, the user with the "best" local channel is selected for transmission in each cell. It is shown that under an overall power constraint, a distributed multi-cell ZFBF to this sub-optimal subset of users achieves the same sum-rate growth rate as an optimal scheme deploying joint multi-cell dirty-paper coding (DPC) techniques, asymptotically with the number of users per cell. Moreover, the overall power constraint is shown to ensure in probability, equal per-cell power constraints when the number of users per-cell increases.