In this paper, the transient behavior of the complex-LMS adaptive filter is studied when the adaptive filter is operating on a fixed or sweeping complex frequency sine-wave signal. A first-order difference equation is derived for the mean weights and its closed form solution is obtained. The transient response is represented as a function of eigenvectors and eigenvalues of the input correlation matrix. The mean-square error of the algorithm is evaluated as well. The relation between the mean-square error and a sweeping rate is obtained. An optimal convergence parameter and filter length can be determined for cancellation of sweeping sine-wave signals.
Because the structure of constrained complex filtered-x LMS algorithm is similar to the conventional LMS algorithm, the transient behavior of the constrained complex filtered-x LMS is investigated as well. For the constrained complex filtered-x LMS, effect of secondary path delay is considered as well as that of the frequency sweeping rate on the tracking capability.
