A new exact method for computing the average symbol error probability of tw
o-dimensional M-ary signaling in slow fading is presented. The method is ge
nerally applicable to polygonal decision regions, The exact average symbol
error rate of coherent 16-star-QAM is obtained and compared to that of 16-r
ectangular-QAM. New results for optimum ring ratios of 16-star QAM in addit
ive white Gaussian noise (AWGN) and in slow fading are also given in this l
etter.