A Distributed Space-Frequency Coding for Cooperative Communication Systems with Multiple Carrier Frequency Offsets

In cooperative communications, due to the distributed nature, multiple different carrier frequency offsets (CFOs) may be present 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 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 a distributed space- frequency code (SFC), called frequency-reversal SFC, for such ISI channels in the frequency domain to achieve the cooperative spatial diversity, where the space-frequency coding concept is different from the one in the literature and also has a different role. Furthermore, we show that, with only linear receivers, such as zero-forcing (ZF) and minimum mean square error (MMSE) receivers, our code achieves the full cooperative diversity.