Distributed space-frequency codes for cooperative communication systems with multiple carrier frequency offsets

In cooperative communications, due to the distributed nature, multiple different carrier frequency offsets (CFOs) may occur and make the channel time-varying. It is hard for the receiver to compensate multiple CFOs from multiple relay nodes simultaneously. Thus, the conventional space-time codes to collect cooperative diversity for co-located multi-input multi-output (MIMO) systems may not be applied directly. In this paper, we consider the cooperative transmission with multiple CFOs when the channels from relay nodes to destination node are flat (frequency-non-selective) fading. We approximate a flat fading channel with CFO as a block time-invariant intersymbol-interference (ISI) channel in the frequency domain. We then propose two distributed space-frequency codes (SFC) for such ISI channels in the frequency domain to achieve the cooperative full spatial diversity, where the space-frequency coding concept is different from the one in the literature and also has a different role. One is called frequency-reversal SFC and the other is called frequency-domain linear convolutive SFC. Furthermore, we show that, with only linear receivers, such as zero-forcing (ZF) and minimum mean square error (MMSE) receivers, our codes achieve the full cooperative diversity.