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A key issue in the full-rate alternate-relaying cooperative communication systems is the interference which is caused by the simultaneous transmission of the source and one of the relays. In this study, the authors propose maximum-likelihood (ML) detectors to mitigate the interference in such systems. Unlike previous work in which interference cancellation is required at the destination, the authors exploit the interference signal as a beneficial resource to develop an optimal detector. It is shown that the optimal detector can be implemented by parallel Viterbi algorithms. The major drawback of the proposed optimal detector is the delay because the destination has to receive and store the entire frame before performing data detection. Owing to the inevitable delay restriction, a sub-optimal detector is developed. In contrast with the optimal detector, the sub-optimal detector exploits two consecutive received packets to decode one packet. It turns out that the sub-optimal detector significantly reduces the required delay, memory size and bandwidth loss, with a slight increase of the bit-error-rate and the computational complexity. Extensive simulation results have been presented to demonstrate the effectiveness of the proposed detectors.