Space-frequency transmission achieving full diversity for frequency asynchronous cooperative relay networks with linear receivers

In cooperative communication systems, due to their distributed nature, multiple carrier frequency offsets (CFOs) may occur and make the channel time-varying, thus most existing space-time codes (STC) to collect diversity gain for the colocated multi-input multi-output (MIMO) systems may not be applied directly. In this paper, we propose a family of distributed space-frequency codes (SFCs) for cooperative transmissions with multiple CFOs and flat fading channels. These codes can achieve full cooperative (spatial) diversity with only linear receivers, such as zero-forcing (ZF) and minimum mean square error (MMSE) receivers, instead of the computationally exhausted maximum likelihood (ML) detector. The codes in this family have different symbol rates, orthogonality and performances for different number of relay nodes, which can be adjusted by choosing different design parameters. Actually, frequency-reversal SFC (FR-SFC), and frequency-shift SFC (FS-SFC) proposed in our previous paper are special cases of the new codes. Furthermore, new SFCs outperform both FD-SFC and FS-SFC can be obtained, from the systematic design.