Distributed beamforming algorithms for non-regenerative MIMO relay networks

In this paper, we investigate distributed beamforming design for non-regenerative MIMO relay networks, in which all nodes are equipped with multiple antennas. We first give an unified formulation for SNR maximizing beamforming algorithm, which is suitable for both MIMO relay and SISO relay networks, and for both instantaneous channel state information and stochastic channel state information. Based on the general formulation, we design two distributed SNR maximizing beamforming algorithms. First, we design a beamforming algorithm for MIMO relay based on instantaneous channel state information with individual power constraints, using positive semidefinite programming (SDP). In order to reduce network cost for channel estimation, second, we also deign a beamforming algorithm for MIMO relay networks based on stochastic channel state information. We prove that in a symmetric network for the beamforming algorithm based on stochastic channel state information with individual power constraints, there exists a closed-form solution that has almost the same performance as that of the numerical methods. This result can be easily extended to a general beamforming algorithm based on stochastic channel state information, but with total power constraint.