Constellation design for decode-and-forward relay networks with adaptive modulation

In this paper, we consider constellation design for decode-and-forward relay networks with adaptive modulation, which improves the diversity combining gain by averaging over all transmission branches the bit reliability variations brought by multilevel modulation formats. A novel bit-error-rate expression for maximal ratio combining of M-ary Quadrature Amplitude Modulation (M-QAM) signals with different modulation levels is derived based on log-likelihood ratios and employed as the metric to optimize the respective constellation schemes for source and relay nodes. A heuristic algorithm with very low computational complexity is proposed as a suboptimal solution to this problem and its concept is demonstrated by analyzing the combining process of 8QAM and 64QAM signals. Computer simulations under AWGN and Rayleigh fading channels show that our proposed constellation scheme improves the diversity combining gain effectively at the expense of only a marginal implementation complexity increase.