Optimal Precoding in the Relay and the Optimality of Largest Eigenmode Relaying with Statistical Channel State Information

An optimal precoding method for a multiple antenna relay node is investigated in order to maximize the achievable rate of the cooperative communication system. It is assumed that only the channel covariance matrices of the relay´s receive and transmit channels are available to the relay and that the antennas of the relay are correlated. It is shown that the optimal transmission from the relay should be conducted in the direction of the eigenvectors of the channel covariance matrix. Moreover, necessary and sufficient conditions are derived under which the relay transmission achieves capacity by transmitting from the strongest eigenvector only; this method is called Largest Eigenmode Relaying (LER). The exact result contains an expectation operation that needs to be solved numerically; to reduce the computational complexity, novel methods are proposed that lead to closed-form solutions. A lower bound for the optimal region of LER is derived. Moreover, the effect of the number of source antennas on the optimality of LER is investigated asymptotically. The simulation results show very little difference between the regions in which LER is optimal when the source is equipped with a finite or an infinite number of antennas.