Distributed Concatenated Recursive Alamouti-Circulant STBC for Two-Way Multi-Relay Networks

A general distributed multi-antenna two-way relaying network with multiple relays is considered in this paper. We first obtain a tight lower bound of pairwise error probability (PEP) of a maximum likelihood detector for the general distributed linear dispersion code for a half-duplex amplify-and-forward two-way relaying network (TWRN) consisting of two sources with each having single antenna and N relays with each having two antennas. Furthermore, by jointly considering signal precoding at the sources and signal processing at the relays, a general distributed concatenated recursive Alamouti-circulant space-time block code is proposed for the considered TWRNs. Our design ensures that the equivalent channel matrices at both source nodes are the so-called the recursive Alamouti-circulant matrices, with each block being a product of the two Alamouti channel matrices. Based on a lower-upper bound strategy and an induction method, asymptotic PEP formula is attained to show that given the optimal angle rotation matrix and the precoding matrix, the code can meet the lower bound of the diversity gain, as well as the maximum coding gain. In addition, the proposed rate one code turns to be effectively decodable.