Distributed collaborative space-time block codes for two-way relaying network

Utilizing the recently-developed unique factorization of signals and distributed Alamouti coding scheme, a distributed collaborative Alamouti space-time block code design is presented for a two-way amplify-and-forward (AF) relaying network, where both two sources and the relay are equipped with a single antenna. For such system, two asymptotic pairwise error probability (PEP) formulae are first derived for both fixed-gain AF and variable-gain AF over Rayleigh channels with the maximum likelihood detector. Then, subject to the constraints on a fixed transmission bit rate and unity average transmission energy, the optimal constellation combinations with the optimal energy-scales as the coefficients are attained by minimizing the dominant term of PEP. It is shown that the PEP and the average block error rate of the newly-designed code are superior to those of the conventional distributed Alamouti code.