Space-Time Trellis Codes with Asynchronous Full Diversity up to Fractional Symbol Delays

To achieve full cooperative diversity in a relay network, most of the existing space-time coding schemes require the synchronization between terminals. A family of space-time trellis codes that achieve full cooperative diversity order without the assumption of synchronization has been recently proposed, where it is assumed that the delays occurring at the relays must be integer multiples of the symbol duration. In this paper, we consider a cooperative system in which the delays can be fractional symbol duration and, correspondingly, multiple sampling per symbol interval is used at the destination. We show that the previously proposed space-time trellis codes for the system with integer symbol delays can still achieve asynchronous full diversity in the new scenario. Furthermore, compared with the applications in the system with integer symbol delays, the decoding complexity of the optimal Viterbi algorithm for the codes does not increase in the system with fractional symbol delays.