Adaptive Algorithms for Symbol Period

A least-mean-square (LMS) and a recursive-least-square (RLS) algorithm are derived for estimation of the symbol period in communication signals. The algorithms are based on measurements of the time elapsed between two consecutive transitions detected in noisy signals. Number of symbol periods between the transitions is estimated too. In order to have the number equal to the true one, the initial symbol period estimate must be between derived bounds and gain scheduling must be applied to the algorithms. The bounds and scheduling depend on the jitter probability distribution width and on maximum and instantaneous number of the symbol periods between two consecutive transitions. It is shown that suuciently accurate initial signal period estimates can be obtained by K-means clustering algorithms. Simulations connrm convergence of the algorithms, as well as their possibility to track time-varying symbol periods.