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The outage behavior of non-orthogonal amplify-and-forward (NAF) and orthogonal amplify-and-forward (OAF) relaying protocols over a general one hop asynchronous cooperative network is examined when orthogonal frequency division multiplexing (OFDM) is used to combat synchronization error among the relays. The relays are only allowed to preform linear transformations over the received signals. It is shown that the asynchronous OFDM OAF protocol provides the same DMT as that of the corresponding synchronous counterpart; however, the asynchronous OFDM NAF protocol provides better DMT than the one of traditional NAF for large length code words and throughout the range of the multiplexing gain. In particular, in a single relay network, the asynchronous OFDM NAF provides DMT as great as the one of a 2 Ã 1 multiple input single output (MISO) channel.