D-MG Tradeoff of DF and AF Relaying Protocols over Asynchronous PAM Cooperative Networks

The diversity multiplexing tradeoff of a general two-hop asynchronous cooperative network is examined for various relaying protocols such as non-orthogonal selection decode-and-forward (NSDF), orthogonal selection decodeand-forward (OSDF), non-orthogonal amplify-and-forward (NAF), and orthogonal amplify-and-forward (OAF). The transmitter nodes are assumed to send pulse amplitude modulation (PAM) signals asynchronously, in which information symbols are linearly modulated by a shaping waveform to be sent to the destination. We consider two different cases with respect to the length of the shaping waveforms in the time domain. In the theoretical case where the shaping waveforms with infinite time support are used, it is shown that asynchronism does not affect the DMT performance of the system and the same DMT as that of the corresponding synchronous network is obtained for all the aforementioned protocols. In the practical case where finite length shaping waveforms are used, it is shown that better diversity gains can be achieved at the expense of bandwidth expansion. In the decode-andforward (DF) type protocols, the asynchronous network provides better diversity gains than those of the corresponding synchronous network throughout the range of the multiplexing gain. In the amplify-and-forward (AF) type protocols, the asynchronous network provides the same DMT as that of the corresponding synchronous counterpart under the OAF protocol; however, a better diversity gain is achieved under the NAF protocol throughout the range of the multiplexing gain. In particular, in the single relay asynchronous network, the NAF protocol provides the same DMT as that of the 2× 1 multiple-input single-output (MISO) channel. Index Terms Asynchronous relay networks, relaying protocols, cooperative diversity, diversity multiplexing gain tradeoff.