The effect of the forgetting factor on the RI adaptive algorithm in system identification

Abstract

The recently proposed Recursive Inverse (RI) algorithm was shown to have a similar mean-square-error (mse) performance as the Recursive-Least-Squares (RLS) algorithm with reduced complexity. The selection of the forgetting factor has a significant influence on the performance of the RLS algorithm. The value of the forgetting factor leads to a tradeoff between the stability and the tracking ability. In a system identification setting, both the filter length and a leakage phenomenon affect the selection of the forgetting factor. In this paper, we first analytically show that this leakage phenomenon and the filter length have much less influence on the performance of the RI algorithm. Simulation results, in a system identification setting, validate the theoretical results.

Leakage Analysis of the Rsor Algorithm

“…A similar analysis gives the following iteration for the RI algorithm (Ahmad et al, 2011b, Salman et al, 2017.…”

“…For example, the leakage signal causes a residual error and inefficient cancellation of noise signal in adaptive noise cancellation applications, or imperfect rejection of echo signal in echo cancellation applications (Haykin, 2002, Paleologu et al, 2008, Ciochină et al, 2009. The effects of forgetting factor and filter length on the leakage phenomenon of RLS and RI algorithms have been studied in detail (Ciochină et al, 2009, Ahmad et al, 2011b. In this article, it is aimed to perform a similar leakage analysis for the RSOR algorithm.…”

Recursive inverse algorithm: Mean-square-error analysis

“…It was shown that the RI algorithm performs considerably better than the LMS algorithm and its variants. It was also shown that its performance regarding convergence rate and excess MSE approaches to that of the RLS in various settings [17][18][19][20], with less computational complexity (2.5N 2 + 3.5N mult./div. and 2N 2 + N add./sub.)…”

“…[1]. In previous publications on the RI algorithm [1,[17][18][19][20], there has been no detailed study of its learning behavior performance. The main contribution of this paper is the derivation of analytical results for the learning behavior of the RI algorithm.…”

Discrete wavelet transform-based RI adaptive algorithm for system identification

“…Adaptive filtering plays an essential role in many signal processing applications. The least-meansquare (LMS) algorithm's simplicity made it very commonly used in adaptive signal processing applications such as system identification [1], echo cancelation [2], channel equalization [3,4], and interference cancelation [3,5]. The main drawback of the LMS algorithm is that it suffers from low convergence rate when the input signal is highly correlated.…”