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In this study, the authors propose two high spectral efficient relaying protocols with low communication overhead including: the priority-based relay selection (PRS), and the priority-based relay selection with incremental transmission (PRSIT). Relay selection and scheduling are integrated in the proposed protocols to achieve full diversity order as well as high spectral efficiency. The authors then define the communication overhead per allocated time slot to a user as the number of required signalling bits for channel estimation and implementing corresponding communication procedures. In this study, the authors show that their proposed protocols have much lower communication overhead comparing with other high spectral efficient cooperative protocols such as opportunistic relaying (OR) and OR with incremental transmission while their achieved diversity-multiplexing trade off performances are the same as those protocols. The authors further show that the average communication overhead for the PRS and PRSIT is a logarithmic function of the number of users while it is a linear function in OR and OR with incremental transmission. Simulation results also show that however, the authors proposed protocols impose much lower communication overhead, they either outperform or act closely to the existing cooperative protocols in the outage probability.