Transform domain Variable Step-size Griffiths Least Mean Square adaptive algorithm and its applications

Abstract

This paper proposes discrete cosine Transform domain Variable Step-size Griffiths Least Mean Square (TVGLMS) algorithms with and without desired signal decomposition, which are robust to noise. For the TVGLMS algorithms, the robust gradient and robust Variable Step-size (VSS) are achieved by using the Griffiths gradient. The transform domain due to its input orthogonalization, improves the convergence rate without any requirement of explicit noise variance estimate. The TVGLMS algorithms are applied to system identification and linear/Decision Feedback Equalizers (DFE). For system identification with white observation noise, the Smoothed Ensemble Average Square Error (SEASE) index reduces by 20dB and 12dB for with and without the desired signal decomposition respectively, over the existing transform domain VSS. For colored observation noise the SEASE reduction is by 14dB and 7dB for the two cases in order. An improvement in the bit error for linear equalizer, 50% and for DFE, 70% is achieved by TVGLMS.