The outage behavior of various 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. We consider non-orthogonal selection decode-and-forward (NSDF), orthogonal selection decode-and-forward (OSDF), non-orthogonal amplify-and-forward (NAF), and orthogonal amplify-and-forward (OAF) relaying protocols and analyze the diversity multiplexing gain tradeoff (DMT) in all scenarios. The transmitting nodes cooperatively construct an asynchronous OFDM space-time code by re-sending the source messages over a common time interval and a common frequency bandwidth. It is shown that in decode-and-forward (DF) type protocols, the asynchronous network provides a diversity gain greater than or equal to the one of the corresponding synchronous network in the limit of code word length and throughout the range of multiplexing gain. In amplify-and-forward (AF) type protocols, in which the relays are only allowed to preform linear transformations over the received signals, 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 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 2x1 multiple input single output (MISO) channel.
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