Exact and approximate log-likelihood ratio of M-ary QAM with two-time dimensions

A ()-ary QAM scheme maps a binary symbol into two-consecutive signal points (signal vector). It provides very lower PAPR than the conventional QAM because it removes corner signal points. For the scheme, this paper discusses an exact analysis of log-likelihood ratio calculation of the signal vector and signal point, and an approximated method to reduce hardware complexity for the channel coding. Numerical results show that the approximated method provides lower hardware complexity and small performance gap compared to exact one. Also, the PAPR and error performances of ()-ary QAM are compared with the one of conventional QAM.