In current cooperative communication schemes, to achieve cooperative diversity, synchronization between terminals is usually assumed, which may not be practical since each terminal has its own local oscillator. In this paper, based on the stack construction proposed by Hammons and El Gamal, we first construct a family of space-time trellis codes for BPSK modulation scheme that is characterized to possess the full cooperative diversity order without the synchronization assumption. We then

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... ize this family of the space-time trellis codes from BPSK to higher order QAM and PSK modulation schemes based on the unified construction proposed by Lu and Kumar. Some diversity product properties of space-time trellis codes are studied and simplified decoding methods are discussed. Simulation results are given to illustrate the performance of the newly proposed codes. Index Terms-Asynchronous cooperative diversity, multiple-input multiple-output (MIMO), sensor networks, space-time trellis codes.