Multiple-frame precoding scheme for BICM over AF relay channels

This paper proposes a precoding scheme over multiple cooperative frames to increase the diversity order of a bandwidth efficient Bit Interleaved Coded Modulation (BICM) system over a Non-orthogonal Amplify-and-Forward (NAF) half-duplex single-relay channel. By deriving a union bound on the bit error probability, it is shown that the diversity gain function of the considered system is (N_f · d_H)-th power of that of uncoded cooperative systems, where N_f is the number of precoded cooperative frames and d_H is the minimum Hamming distance of the outer code. An optimal class of precoders is then derived to optimize the asymptotic coding gain. It is then shown that the source should transmit a superposition of all symbols in the broadcasting phases, while being silent in all cooperative phases for best asymptotic performance. By further analyzing the first iteration performance, a design criterion is then developed to find optimal superposition angles for good convergence behavior. A pragmatic approach is then proposed to find good rotation angles. Analytical and simulation results show that the proposed scheme provides a significantly higher order of time and cooperative diversities and better coding gains than previous precoding schemes.