The distribution of echo signal and required A/D precision

Adaptive echo cancellation is usually implemented with digital signal processing hardware. For a system with discrete signal levels the magnitude distribution of echo signals is dependent on both the number of signal levels and the duration of the echo path impulse response. When the duration of the echo path impulse response is relatively long compared with the signaling interval, the echo signal approaches the normal distribution. The required A/D (analog-to-digital) device precision, number of bits, is related to the required echo cancellation level, the distribution of the echo signal, and the required error rate. For a practical example of a high-bit-rate digital subscriber line, the required A/D precision is 14 bits. Computer simulations are also carried out to estimate the echo signal distribution and the error rate caused by A/D saturation