Space-time trellis codes with asynchronous full diversity up to fractional symbol delays

A family of space-time trellis codes that are associated with shift-full-rank (SFR) generator matrices and thus achieve asynchronous full cooperative diversity order 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 letter, we consider a cooperative communication system in which the delays can be fractional (rational) symbol durations and, correspondingly, multiple sampling per symbol interval is used at the destination. We show that the previously proposed space-time trellis codes can still achieve asynchronous full diversity in fractional symbol delay scenarios if their generator matrices satisfy a relaxed definition of SFR matrices, namely, q-shift-full-rank (q-SFR) matrices, and therefore, more designs for their generator matrices than the SFR ones become available. 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 and some performance gains can be observed in the system with fractional symbol delays.