Analysis of adaptive LMS estimator with cyclic sequences in complex frequency domain

Cyclic sequences are usually employed as the reference sequences in the adaptive filtering systems for signal or channel estimation. In this situation, the stability of an adaptive filter can be analyzed by an equivalent transfer function in complex frequency domain. For several special classes of cyclic reference sequences, the stability bounds of the adaptive filter with least mean-square (LMS) algorithm and its variants, leaky-LMS (L-LMS) and minimum output variance LMS (MOV-LMS), are obtained. Effects of these algorithms on the resultant transfer functions and the stability bounds are also investigated.