Computationally efficient equalization for asynchronous cooperative communications with multiple frequency offsets

In cooperative communications, time and frequency synchronization is an important issue needed to be addressed in practice. Due to the nature of cooperative communications, multiple frequency offsets may occur and the traditional frequency offset compensations may not apply. For this problem, equalization for the time-varying channel has been used in the literature, where the equalization matrix inverse needs to be retaken every symbol. In this paper, we propose computationally efficient minimum mean square error (MMSE) and MMSE decision feedback equalizers (MMSE-DFE) when multiple frequency offsets are present, where the equalization matrix inverses do not need to be retaken every symbol. Our proposed equalization methods apply to linear convolutively coded cooperative systems, where linear convolutive space-time coding is used to achieve the full cooperative diversity when there are timing errors from the cooperative users or relay nodes, i.e., asynchronous cooperative communication systems.