Full diversity space-frequency codes for frequency asynchronous cooperative relay networks with linear receivers

In this paper, we propose a family of distributed space-frequency codes (SFCs) for frequency asynchronous cooperative relay networks with multiple carrier frequency offsets (CFOs) and flat fading channels. The codes have the special structures that the columns of each code matrix can be divided into several orthogonal groups and each group is stacked by several sub-blocks with Toeplitz structure. These codes possess two interesting properties: a) Even under the frequency-asynchronous scenario, the codes can, namely, if R relay nodes participate the cooperation adopting the proposed SFCs, then at the destination node, the achievable diversity order is R; b) Only, such as zero-forcing (ZF) and minimum mean square error (MMSE) receivers, are required to collect the full cooperative diversity, instead of the maximum likelihood (ML) detector as utilized in most existing STC (SFC) schemes. The codes in this family have different symbol rates, orthogonality and performances for different numbers of relay nodes, which can be adjusted by choosing different design parameters. It is shown that frequency-reversal SFC (FR-SFC), and frequency-shift SFC (FS-SFC) proposed in previous papers are only two special members of the code family, and new SFCs outperforming both of them are proposed.