Performance analysis of adaptive filters equipped with the dual sign algorithm

On the Performance Analysis of the Least Mean M-Estimate and Normalized Least Mean M-Estimate Algorithms with Gaussian Inputs and Additive Gaussian and Contaminated Gaussian Noises

“…For the DS nonlinearity, (19) agrees with the results in [34], and moreover, Mathews et al showed that the resulting equation is convergent using the Doob's theorem [43,44]. (19) also agrees with the result in [35] for LMS algorithm with EF nonlinearity, in which the difference equation was approximated with a differential equation and it was showed that there are two possible adapting phases, the nonlinear and linear ones.…”

“…All the above results can also be readily generalized to the simpler LMS case. Moreover, the new results also agree with the conventional LMS algorithm [1], the LMS algorithms with dual sign (DS) nonlinearity [34] and the error function (EF) nonlinearity [35]. Monte Carlo simulation results confirm that the NLMM algorithm offers improved robustness to impulsive noise over the NLMS algorithm, and are in good agreement with the theoretical analysis.…”

“…Using the conventional Price's theorem [31][32][33], new decoupled difference equations describing the mean and mean square convergence behaviors are derived. The final results closely resemble the classical results for LMS in [1] and can be easily reduced to related works such as [34,35]. Moreover, it is found that the nonlinearity will in general slow down the adaptation rate and the normalization process will always speed up the maximum convergence rate of the NLMS algorithms over their LMS counterparts if the eigenvalues of the input autocorrelation matrices are unequal.…”

“…Another interpretation of (6) is that the error term is passed through a nonlinear device = (e). This type of adaptive filtering algorithms has been studied previously for the error-function nonlinearity [35] and the sign nonlinearity [34]. The former concludes that the nonlinearity will slow down the convergence rate, while the latter is mainly introduced to reduce the implementation complexity.…”

On the Performance Analysis of a Class of Transform-domain NLMS Algorithms with Gaussian Inputs and Mixture Gaussian Additive Noise Environment

“…The LMS algorithm with error function nonlinearity was studied in [23]. A related algorithm is the dual-sign LMS [24] algorithm. The former concluded that the nonlinearity will slow down the convergence rate, while the latter is mainly introduced to reduce the implementation complexity.…”