Computationally efficient MMSE and MMSE-DFE equalizations for asynchronous cooperative communications with multiple frequency offsets

In cooperative communications, due to distributed nature, cooperative transmission may not be either time or frequency synchronized. In this paper, we propose computationally efficient minimum mean square error (MMSE) and MMSE decision feedback equalizer (MMSE-DFE) equalizers for cooperative communication systems when multiple time offsets and frequency offsets 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 the 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.