Diversity–Multiplexing Tradeoff of Asynchronous Decode-and-Forward Cooperative Networks

The diversity-multiplexing tradeoff (DMT) of a general two-hop asynchronous cooperative network is examined for orthogonal and nonorthogonal selection decode-and-forward relaying protocols. The transmitter nodes send pulse amplitude modulation signals, in which information symbols are linearly modulated by a shaping waveform to be sent to the destination. We consider two different cases of band-limited and time-limited shaping waveforms. In each case, the DMT performance of the asynchronous and synchronous networks is compared. It is proved that in the band-limited system scenario, the asynchronism does not incur any performance loss, and the same DMT as that of the corresponding synchronous network is obtained for both protocols. In the time-limited-system scenario, the bandwidth is expanded for high values of signal-to-noise ratio. In this scenario, it is observed that only asynchronous signaling is able to exploit the extra degrees of freedom of the channel. The asynchronous network in this scenario provides better DMT performances for both protocols throughout the range of the multiplexing gain.