In this paper, we propose double-differential (DD) modulation for amplify-and-forward (AAF) cooperative communications system. The proposed system works very well in the presence of carrier offsets without any channel knowledge, where the previously proposed differential AAF cooperative system breaks down. We have derived the approximate symbol error rate (SER) of the proposed system. In addition, numerical power allocation is proposed to further improve the performance of the system. The proposed cooperative system outperforms the same rate trained cooperative system and conventional direct transmission based DD system.
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