Convergence properties of optimal adaptive carrier phase jitter predictors for sinusoidal jitter

Carrier recovery systems in high performance digital modem receivers must remove carrier phase jitter as well as track carrier phase and frequency offsets. A popular approach to removing periodic phase jitter is to use an adaptive LMS FIR linear predictor with baud spaced taps to predict the jitter angle one baud in the future. Experimentally, the convergence rates for such predictors were found to depend heavily on the jitter frequency. It is well known in adaptive filter theory that the predictor convergence rate depends on the eigenvalues of the correlation matrix of the input signal. By allowing jitter predictors with a given number of taps to have tap spacings greater than one baud and by deriving a general formula for the eigenvalues of the appropriate correlation matrix, it is shown how to design predictors exhibiting optimal convergence rates over a range of commonly observed jitter frequencies.<>