Tracking analysis of augmented complex least mean square algorithm

Abstract

The augmented complex least mean-square (ACLMS) algorithm is a suitable algorithm for the processing of both second-order circular (proper) and noncircular (improper) signals. In this paper, we provide tracking analysis of the ACLMS algorithm in the non-stationary environments. Using the established energy conservation argument, we derive a variance relation that contains moments that represent the effects of non-stationary environment. We evaluate these moments and derive closed-form expressions for the excess mean-square error (EMSE) and mean-square error (MSE). The derived expressions, supported by simulations, reveal that unlike the stationary case, the steady-state EMSE, and MSE curves are not monotonically increasing functions of the step-size parameter. We also use this observation to optimize the step-size learning parameter. Simulation results illustrate the theoretical findings and match well with theory.

Kompleks düzlemde büyük-ölçekli regresyon: Bilgilendirici olmayan verileri çevrimiçi olarak sansürleyen CRLS algoritmalarının başarım analizi

“…Bu sayede hem dairesel hem de dairesel olmayan kompleks-değerli verilerin ikinci-dereceden istatistiksel özelliklerin tamamı tek bir matris içerisinde değerlendirilmiştir [31][32][33][34][35][36][37][38]. Literatürde artırılmış istatistiklerin; biyomedikal, haberleşme, CASP, güç sistemleri gibi birçok farklı alanda sıklıkla kullanıldığı ve başarımı ciddi anlamda artırdığı gözlemlenmiştir [31][32][33][34][35][36][37][38][42][43][44][45][46][47][48][49][50][51][52][53]. Artırılmış istatistiğin ortaya çıkmasıyla, literatürde yer alan CASP algoritmaları; son zamanlarda kavramsal olarak kesin lineer (strictly linear, SL) ve geniş lineer (widely lineer, WL) model tabanlı algoritmalar olarak ikiye ayrılmıştır.…”

Tracking performance of incremental augmented complex least mean square adaptive network in the presence of model non‐stationarity

“…It is shown that the widely linear based adaptive filters provide a smaller mean-square error in the steady-state than that of the strictly linear algorithms [24,25]. So far different stand-alone adaptive filters have been introduced in the literature, such as the widely linear least mean square (WL-LMS) [26], augmented complex least mean square (ACLMS) [27,28], augmented affine projection [29], and widely linear recursive least squares algorithms [30]. In order to deal with three and four dimensional signals, quaternion domain adaptive filters have been developed [31][32][33].…”