Network beamforming based on second order statistics of the channel state information - Havary-Nassab, V.; Shahbazpanahi, S.; Grami, A.; Zhi-Quan Luo (2008 IEEE International Conference on Acoustics, Speech and Signal Processing, 2008)
The problem of distributed beamforming is considered for a network which consists of a transmitter, a receiver, and r relay nodes. Assuming that the second order statistics of the channel coefficients are available, we design a distributed beamforming technique via maximization of the receiver signal-to-noise ratio (SNR) subject to individual relay power constraints. We show that using semi-definite relaxation, this SNR maximization can be turned into a convex feasibility semi-definite programming problem, and therefore, it can be efficiently solved using interior point methods. We also obtain a performance bound for the semi-definite relaxation and show that the semi-definite relaxation approach provides a c-approximation to the (nonconvex) SNR maximization problem, where c = O((log r) -1 ) and r is the number of relays.