Approximate Error Rate Performance of 8-Point AM-PM Signal Constellations on Voiceband Telephone Channels

The purpose of this paper is a detailed comparison of the error rate performance of six 8-point signal constellations under the conditions of Gaussian noise alone, or combined with either phase jitter, second order harmonic, or third order harmonic distortion for application to the voiceband telephone channel. An approximate evaluation technique is developed for inclusion of the effects of second and third order harmonic distortion which was found to be in agreement with laboratory performance measurements of several of the signal constellations reported here. A signal constellation, which consists of points in a circle surrounding a single point in the center (denoted the 1-7 constellation), was found to be superior to the other 5 constellations considered under the conditions of Gaussian noise combined with second or third order harmonic distortion. Under the condition of phase jitter not exceeding 1.5 degrees RMS, it is also superior to the other constellations. Thus, it appears that the 1-7 constellation in conjunction with a good phase locked loop would offer superior performance.