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Cooperative communication through relaying can improve the performance of communication systems under multipath fading conditions. Increasing the number of relays will also boost the performance of the system, but since relays transmit through orthogonal channels, this improvement is at the cost of bandwidth or rate of the system. A two-hop multi-relay decode-and-forward cooperative system is proposed in which selected relays transmit simultaneously in the same band, and therefore, there is no rate or bandwidth loss. To mitigate the error propagation due to incorrect decoding of symbols at the relays, we use a selection relaying method in which a relay transmits in the second hop if the channel quality between the relay and the source exceeds a minimum threshold regardless of the relay-destination link. In our proposed beamforming scheme, the phase of selected relays for transmission in the second hop …