Coupled adaptive prediction and system identification: a statistical model and transient analysis

A significant drawback of the least mean square (LMS) algorithm is slow convergence speed when the input covariance matrix is ill-conditioned. Two structures are presented and studied for increasing the convergence speed for this case. The structures incorporate a prewhitening filter prior to the usual LMS adaptation. When the prewhitening filter is also adaptive the input to the LMS algorithm is nonstationary. An analysis of the coupling effect between the two adaptive algorithms show that the adaptive prewhitener has the capability of significantly speeding up to LMS adaptation as compared to a system without prewhitening. When the prewhitening filter is fixed (nonadaptive), the structure is shown to be equivalent to the filtered-X LMS algorithm. Stability conditions and transient means behavior are given in the time domain, in terms of the parameters of the pre-whitening filter