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The problem of power allocation is studied for a multiple-input multiple-output (MIMO) decode-and-forward (DF) two-way relaying (TWR) system consisting of two source nodes and one relay. It is shown that achieving maximum sum-rate in such a system does not necessarily demand the consumption of all available power at the relay. Instead, the maximum sum-rate can be achieved through efficient power allocation with minimum power consumption. Deriving such power allocation, however, is nontrivial due to the fact that it generally leads to a nonconvex problem. In Part I of this two-part paper, a sum-rate maximizing power allocation with minimum power consumption is found for MIMO DF TWR in which the relay optimizes its own power allocation strategy given the power allocation strategies of the source nodes. An algorithm is proposed for efficiently finding the optimal power allocation of the relay based on the proposed idea of relative water-levels. The considered scenario features low complexity due to the fact that the relay optimizes its power allocation without coordinating the source nodes. As a tradeoff for the low complexity, it is shown that there can be waste of power at the source nodes due to the lack of coordination between the relay and the source nodes. Simulation results demonstrate the performance of the proposed algorithm and the effect of asymmetry on the considered system.

Sum-Rate Maximization With Minimum Power Consumption for MIMO DF Two-Way Relaying— Part I: Relay Optimization