Effects of Biases on Digitally Implemented Data‐Driven Echo Cancelers

Abstract

In this paper the effects of biases, of a hardware origin, on the performance of a digitally implemented data‐driven echo canceler are studied both analytically and experimentally. It is shown that, as a consequence of any such bias, the canceler tap weights can randomly drift; however, in contrast to voice‐type cancelers and fractionally spaced equalizers, the data‐driven canceler will not drift into instability. Nevertheless, the canceler's performance can be severely degraded, even for very small amounts of bias. The main result of this paper is a quantitative study of the canceler's performance as a function of the biases and the canceler's various design parameters, such as the number of tap coefficients and the step size used in the tap adjustment algorithm. Although the study concentrates on the biases introduced by two's‐complement arithmetic, the results are general enough to be used with any type of arithmetic, provided that the biases introduced by these different types of arithmetic are known. Some of the analytical results have been verified experimentally, in real time, on a digital signal processor constructed at AT&T Bell Laboratories and AT&T Information Systems. Specifically, it is shown how the bias introduced by rounding the product of commercially available two's‐complement multipliers can be eliminated by a proper choice of the values of the canceler's input symbols. © 1985 AT&T Technical Journal