We propose double-differential (DD) modulation for the amplify-and-forward protocol over Nakagami- m fading channels with carrier offsets. We propose an emulated maximum ratio combining (EMRC) decoder, which could be used by the double-differential receiver in the absence of exact channel knowledge. Approximate bit error rate (BER) analysis is performed for the proposed double-differential modulation-based cooperative communication system. The proposed double-differential system is immune to random carrier offsets, whereas the conventional single-differential modulation-based cooperative system breaks down. In addition, the proposed scheme is able to perform better than the same rate training-based cooperative system which utilizes training data for finding estimates of carrier offsets and channel gains.