This paper analyzes the effects of nonlinear quantizers, used in T1 carrier systems, on the performance of QAM and trellis code modulated (TCM) voice-band data communication modems, and introduces a method to counteract the effects of these nonlinearities. The effects of nonlinear quantizers used in the T1 carrier systems is modeled as a source of multiplicative noise whose variance is proportional to the amplitude of the quantized signal. The relation between variance of the multiplicative noise, characteristics of the nonlinear quantizer, and impulse response of the pulse shaping filters used in the modems are derived. Effects of multiplicative noise on the performance of QAM and TCM modems are analyzed. A method for the design of QAM and TCM signal constellations is introduced which counteracts the harmful effects of nonlinear quantizers. It is shown that the new constellations provide 2-3 dB performance improvements in multiplicative noise channels at the expense of losing less than 0.5 dB in additive noise channels.
