Optimal amplify-and-forward scheme based on superposition modulation over relay channels

This paper presents an optimal transmission scheme based on superposition modulation for a bandwidth efficient bit interleaved coded modulation (BICM) system over a nonorthogonal amplify-and-forward (NAF) half-duplex single-relay channel. Based on the asymptotic analysis, it is first demonstrated that in the first time slot, the source only needs to send the superposition of the first symbol and the rotated version of the second symbol, while being silent in the remaining slot to achieve the best asymptotic performance. It is then shown that a rotation angle that maximizes the minimum Euclidean distance of the superposition constellation should be used for good convergence behavior. An optimal rotation angle is then analytically determined for various modulation schemes. Both analytical and simulation results show that the proposed transmission scheme not only exploits full cooperative diversity but also offers a significant coding gain over previously proposed systems for NAF channels with good convergence property.