Distributed Space-Frequency Coding over Amplify-and-Forward Relay Channels

In this paper, the design of distributed space- frequency codes (DSFCs) for wireless relay networks employing the amplify-and-forward (AAF) protocol is considered. The term distributed comes from the fact that the space-frequency code is distributed among randomly located relay nodes. DSFCs are designed to achieve the multi-path (frequency) and cooperative diversities of the wireless relay channels. We derive sufficient conditions for the proposed code design to achieve full diversity based on minimizing the pairwise error probability (PEP). We prove that the proposed DSFC can achieve full diversity of order LN, where L is the number of paths of the channel and N is the number of relay nodes, for any N and for the cases of L = 1 (flat, frequency-nonselective fading channel) and L = 2 (two-ray fading channel).