Nonlinear effects of adaptive predictors for stationary and chirped input signals

This dissertation investigates the nonlinear effects of adaptive predictors in stationary and nonstationary environments. The least-mean-square (LMS) and recursive-least-squares (RLS) algorithms with tapped-delay line structures are studied. The nonstationary input signals are modeled as linearly chirped narrowband signals.; The error transfer function approach is applied to the adaptive predictor application, and the total mean squared error (MSE) of the LMS adaptive predictor is approximated. It shows that for 1-step LMS adaptive predictor, the nonlinear effect is negligible. For multiple-step LMS predictors, the nonlinear effect can be significant and the range of parameters where the nonlinear effect is observable is much wider compared with the 1-step case. This can be interpreted by looking at the information content used by the adaptive predictor, the finite Wiener predictor, and the optimal estimator. A general bound is also derived, which is the 1-step infinite-length Wiener predictor. The error feedback coefficients of the LMS and RLS algorithms are compared to show that LMS algorithms use information from past errors more efficiently than the RLS algorithms, thus the nonlinear effect in LMS prediction can be significant, but negligible in the RLS prediction.; The class of nonstationary input signals which will be considered for adaptive prediction is the linearly-chirped narrowband input signals for varying chirp rates and bandwidth. This class of signals has been used to represent signals whose spectrum is frequency offset and shifted with time in a nonstationary mobile communications environment. Since they do not have a fixed power spectral density, the error transfer function approach is not directly applicable. However, since the linearly chirped signal has a constant spectral shifting rate, this special class of nonstationary inputs can be analyzed as stationary inputs by an unchirped transform. An error transfer function approach is derived for the rotated LMS and RLS algorithms with stationary input signals to approximate the MSE of chirped signal prediction. An analytical expression of the LMS/NLMS predictor MSE is derived and compared with the Wiener predictor performance. It shows that while LMS adaptive predictor with chirped input signal gives a more degraded performance compared to the LMS adaptive predictor with stationary input signal, the nonlinear effect still exists and can be significant. When the adaptation step-size is selected wisely, the optimal steady-state performance of predictors will have a very small difference in the performance for chirped and stationary inputs.