On Extended RLS Lattice Adaptive Variants: Error-Feedback, Normalized, and Array-Based Recursions

Abstract

Error-feedback, normalized, and array-based recursions represent equivalent RLS lattice adaptive filters which are known to offer better numerical properties under finite-precision implementations. This is the case when the underlying data structure arises from a tapped-delay-line model for the input signal. On the other hand, in the context of a more general orthonormality-based input model, these variants have not yet been derived and their behavior under finite precision is unknown. This paper develops several lattice structures for the exponentially weighted RLS problem under orthonormality-based data structures, including error-feedback, normalized, and array-based forms. As a result, besides nonminimality of the new recursions, they present unstable modes as well as hyperbolic rotations, so that the well-known good numerical properties observed in the case of FIR models no longer exist. We verify via simulations that, compared to the standard extended lattice equations, these variants do not improve the robustness to quantization, unlike what is normally expected for FIR models.