Effect of colored noise on the performance of LMS adaptive equalizers and predictors

The effect of colored noise on the performance of the least-mean-square algorithm is investigated in two different applications: adaptive equalization and adaptive prediction. In both cases, the input signal usually consists of a signal component and a noise component that may be white or colored. In adaptive equalization, the desired signal is usually noise-free while in adaptive prediction the desired signal is a delayed version of the input signal. For both cases, expressions are obtained to show the effect of colored noise on the average weight coefficients, the minimum mean-square error, and the average steady state mean-square error. A comparison is made between the effect of colored noise on the performance of the algorithm and the effect of white noise.<>