Distributed concatenated quasi-orthogonal space time block codes for two-way relay networks

In this paper, a half-duplex amplify-and-forward two-way relaying network consisting of two sources with each having a single antenna and N relays with each having two antennas is considered. For such a system, a tight lower bound of pairwise error probability (PEP) of a maximum likelihood (ML) detector for any distributed linear dispersion code with a fixed average amplifier is derived, revealing that diversity gain cannot decay faster than ln^N SNR/SNR^2N, where SNR is signal to noise ratio. Particularly for the network having two relays, a distributed concatenated quasi-orthogonal space-time block code is proposed with two significant advantages. One advantage is that the equivalent channel matrices at the both source nodes turn to be the block-circulant matrices, with each block being a product of the two Alamouti channel matrices. The other advantage is that the equivalent noises at the both source nodes are Gaussian and white. Therefore, like the quasi-orthogonal space-time block code for a multi-antennas system, the proposed code for the relaying system still maintains low-decoding complexity for the ML detector. Furthermore, two asymptotic PEP formulae are attained to show that the code presented in this paper achieves the maximum diversity gain, i.e., meeting the lower bound of diversity gain, as well as the maximum coding gain for the square quadrature amplitude modulation (QAM) constellation.