Optimal design of distributed concatenated Alamouti codes for relay networks using uniquely-factorable QAM constellations

In this paper, a novel distributed concatenated Alamouti code is devised for a one-way relaying network consisting of two end nodes with each having a single antenna and one relay node equipped with two antennas. With the aid of the newly developed uniquely-factorable constellation pair (UFCP) generated from square quadrature amplitude modulation (QAM) constellation and by jointly processing the noisy signals received at the relay node, such a design allows the terminal nodes and the relay node to transmit their own information concurrently at the symbol level, and turns the equivalent channel between the two end nodes into a product of two Alam-outi channels, thus, called UFCP concatenated Alamouti space-time block code (STBC) while maintaining the equivalent noise is still white Gaussian, thereby, leading to a symbol-by-symbol decodable optimal maximum-likelihood (ML) receiver. In addition, an asymptotic symbol error probability (SEP) formula is derived with the ML detector, showing that the maximum diversity gain function is achieved, which is proportional to ln SNR/SNR
²
. Furthermore, an optimal power loading scheme minimizing the asymptotic SEP is proposed.