Theoretical analysis of symbol error rates of (4,12) circular-signal-set constellation for some detection schemes

The (4,12) circular-signal-set constellation [or (4,12) QAM] has been propo sed for 16APSK in view of both the minimum Euclidean distance between mappe d signal points and the realization of differential phase detection. Usuall y, the optimum value of the ring ratio, which is the ratio of the inner and outer ring level of signal constellation, is decided as one of the paramet ers of 16APSK by using the geometrical approach when the channel SNR is ass umed to be quite large. However, the optimum value should be calculated by its symbol error rate to realize the best performance over all channel SNRs . From this point of view, symbol error rates of (4,12) QAM for three detec tion schemes are analyzed theoretically, and the optimum ring ratios for th ese detections are indicated in this paper. The performance of the envelope amplitude detection is expressed as the sum of PSK's performance and the e ffect of amplitude detection, which causes degradation of its performance. The optimum ring ratio for envelope detection is smaller when the channel S NR is lower, although the optimum value for ideal coherent detection become s larger. The procedure used to analyze (4,12) QAM can also be adapted for star QAM, which is a conventional signal constellation of 16APSK. (C) 2000 Scripta Technica, Electron Comm Jpn.