Effect of logarithmic quantization on QAM data communication

It has been shown that, when a quadrature-amplitude-modulation (QAM) data signal is transmitted over a channel that includes pulse-code-modulation (PCM) codecs, the resulting noise around the final received constellation points grows with the distance of the point from the origin. The analysis of this effect is extended to show that when a QAM data signal is transmitted over a channel that includes logarithmic quantization, the resulting noise distribution about the final received constellation points is elliptical. Typically, the radial component of noise variance around an outer point is approximately three times the tangential component. The variation of noise among constellation points decreases with the intersymbol interference at the codec input. Formulas are derived giving the signal-dependent noise components as a function of the channel characteristics of the analog transmit and receive access legs. Experimental results confirm the analysis