LMS adaptation with correlated data--A scalar example

In this note, the statistical behavior of the complex scalar LMS adaptation algorithm is investigated when the input data stream consists of statistically dependent inputs. The asymptotic time constant of the mean behavior of the algorithm is evaluated, taking into account the time correlation properties of the input data sequence. It is shown that the behavior of the correlated data case does not degrade significantly from the uncorrelated case until the input sequence is very highly correlated (ρ > 0.99).