Performance of Nonuniform Constellations on the Gaussian Channel

Testing of high speed voiceband modems has revealed a significant increase in distortion for points near the perimeter of a QAM signal constellation. This distortion increases with distance from the center of the constellation and limits performance at data rates above 19.2 kb/s. The perimeter distortion can be reduced by transforming the signal constellation so that points near the center are closer together, and points near the perimeter are further apart. When the channel SNR is high, such a transformation reduces immunity to Gaussian noise because points near the center of the transformed constellation are closer together than in a uniformly spaced constellation with the same average power.