Performance analysis of the LMS algorithm with a tapped delay line (two-dimensional case)

This paper presents exact analytical results of the LMS performances on correlated data vectors. The case addressed here is of data vectors constructed from a tapped delay line. While the results are for the two-dimensional case, they do provide indications of the effect this structure of data vectors, so common to LMS applications, has on LMS performance. They show conclusively the possibility of bias in weight vector mean value and its source. There is also a clear increase in MSE values over the case with uncorrelated data and a decrease of the convergence region of adaptation coefficient. The results presented here strongly suggest that the correlation inherent to the above-mentioned data vectors could be a factor in some applications.