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Energy-efficient power allocation for amplify-and-forward MIMO relay channel

We consider a two-hop amplify-and-forward (AF) MIMO relay channel consisting one source, one AF relay and one destination, where each node is equipped with multi-antenna. For this scenario, most effort was made to maximize the rate or to minimize the sum power, while these schemes may not be energy-efficient when the ratio of rate to the sum power is used as the cost function. This motivates us to study a more meaningful and challenging problem: energy efficiency (EE) maximization under a rate requirement and individual node transmit power constraints. This work focuses on linear transceiver design: joint optimization of the source and the relay strategies when the minimum-mean-square-error (MMSE) receiver is employed. In order to tackle this non-convex optimization problem, the alternating optimization algorithm combined with fractional programming is applied to optimize each variable separately. In addition, we derive that under some conditions, the conventional schemes of rate maximization and sum-power minimization are also energy-efficient.