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

Multiple frequency offsets (CFO) in cooperative communications are difficult, if not impossible, to compensate completely at the destination node. The multiple CFO make the channel time-varying, and thus the conventional space-time codes to collect diversity gain for co-located multi-input multi-output (MIMO) systems may not be applied directly. In a previous paper, we proposed a distributed space-frequency code (SFC), called frequency-reversal SFC (FR-SFC), for cooperative transmissions with multiple CFOs and flat fading channels. We have shown that this code can achieve the full cooperative diversity with only linear receivers, such as zero-forcing (ZF) and minimum mean square error (MMSE) receivers. However, the code is not bandwidth efficient when the relay nodes are more than 3. To have a higher bandwidth efficiency, in this paper we propose a new distributed SFC called frequency-domain linear convolutive SFC(FLC-SFC). The symbol rates of the new codes approach 1 when code block length is sufficiently larger than the number of relay nodes. Furthermore. It achieves the full cooperative diversity with linear receivers.