Statistical CSI based zero-forcing beamforming for cooperative two-cell downlink transmission

In this paper we present a local channel correlation based zero-forcing (ZF) beamforming framework for the cell edge users. Without the instantaneous CSI (ICSI) assisting, we derive the exact expression of the averaged pairwise error probability (PEP) upper bounds at both of the receivers. According to the derived PEP bounds, an multi-objective optimization problem is formulated to get the elaborate power allocation and ZF beamforming design with the knowledge of local statistical channel state information (SCSI) at the transmitter side. By factorizing each beamforming matrix as the multiplication of two matrices, we can avoid inter-user interference through column orthogonal matrix design. Moreover, the original complicated optimization problem can be further decoupled into four simple sub-optimization problems. Then utilizing the Lagrange multiplying method, we finally achieve the feasible distributed statistical ZF beamforming design, which only involves the distributed computations based on the local channel correlations. Both theoretical analysis and simulation results confirm that the multi-cell spatial diversity gain can be fully exploited with only local SCSI. For comparison, the traditional perfect ICSI based ZF beamforming is analyzed and discussed. It is shown that in the high regime of signal-to-noise ratio (SNR), the diversity gain of the proposed statistical ZF beamforming is even better than that achieved by the conventional ICSI-aided ZF beamforming.