A simple soft decision method for the 2-circular 16QAM constellation

In this paper, the 2-circular 16QAM constellation and its soft decision method are studied. By maximizing the decision region of the constellation, the optimal design rule is presented. For the optimal 2-circular 16QAM constellation with maximal minimum decision region Π/2, a simple method is also proposed to compute the soft information for the received signal. When the turbo code is used in the LAS/CDMA system, the BER performance is evaluated over AWGN channel to prove the optimality of the proposed 2-circular 16QAM constellation and to compare the proposed method with the other approximate method, which is used to compute log-likelihood ratio (LLR) information. The simulation results indicate that the proposed method is 0.75 dB and 0.1 dB better at BER 1e-3 and 1e-5 respectively for the optimal constellation. When the computational complexity is estimated by the number of the multiplication and addition operations, the proposed soft decision method is much simpler.