| Summary: | This study deals with the error probability optimisation problem in three-phase bidirectional amplify and forward relaying systems. Different from the common two-phase strategy, in the three-phase counterpart, the relay power is split into two different terminals in terms of data error probability. With such a three-phase division, the authors present a unified optimisation algorithm based on the exact symbol error probability (SEP) and its upper bound expression. In addition, by virtue of the dual decomposition algorithm, the authors derive the optimal power allocation and demonstrate its uniqueness at both terminals and the relay node. Moreover, the unified optimisation algorithm can be reduced to some special cases, such as the maximum minimisation problem and unbalanced link problem. The proposed results reveal that the proposed algorithm has a significant impact on SEP reduction.
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