Energy Efficient Transmission in Multi-User MIMO Relay Channels with Perfect and Imperfect Channel State Information

We design novel transmission strategies to maximize the energy efficiency (EE) of the uplink multi-user multiple-input and multiple-output relay channel. In this channel, K multi-antenna users communicate with a multi-antenna base station (BS) through a multi-antenna relay. To achieve the goal of EE maximization, we propose new iterative algorithms to jointly optimize the multi-user precoder and the relay precoder under transmit power constraints for two cases. In the first case, the perfect global channel state information (CSI) is available, while in the second case, the CSI between the relay and the BS is imperfect. To surmount the non-convexity of our formulated EE optimization problems in both cases, we introduce the parameter subtractive function into the proposed algorithms. Then, the EE parameter in the parameter subtractive function is updated by Dinkelbach's algorithm in the perfect CSI case, and by the bisection method in the imperfect CSI case. Moreover, in the perfect CSI case, the relay precoder is optimized by the diagonalization operation and the multi-user precoder is optimized based on the weighted minimum mean square error method. Differently, in the imperfect CSI case, we apply the sign-definiteness lemma to promote the semidefinite programming formulation of the EE optimization problem. Furthermore, we present the numerical results to demonstrate that our proposed iterative algorithms have a good convergence rate in both cases. In addition, we show that our proposed iterative algorithms achieve a higher EE performance than the existing algorithms in both CSI cases.