This work proposes diffusion normalized least mean M-estimate algorithm based on the modified Huber function, which can equip distributed networks with robust learning capability in the presence of impulsive interference. In order to exploit the system's underlying sparsity to further improve the learning performance, a sparse-aware variant is also developed by incorporating the $l_0$ -norm of the estimates into the update process. We then analyze the transient, steady-state and stability behaviors of the algorithms in a unified framework. In particular, we present an analytical method that is simpler than conventional approaches to deal with the score function since it removes the requirements of integrals and Price's theorem. Simulations in various impulsive noise scenarios show that the proposed algorithms are superior to some existing diffusion algorithms and the theoretical results are verifiable.

Diffusion Normalized Least Mean M-estimate Algorithms: Design and Performance Analysis

This paper presents a family of robust set-membership normalized subband adaptive filtering (RSM-NSAF) algorithms for acoustic echo cancellation (AEC). By using a new robust set-membership error bound, the RSM-NSAF algorithm obtains improved robustness against impulsive noises and decreased steady-state misalignment relative to the conventional set-membership NSAF (SM-NSAF) algorithm. To exploit the sparsity of the impulse response, the $L_{0}$ norm constraint robust set-membership NSAF ( $L_{0}$ -RSM-NSAF), robust set-membership improved proportionate NSAF (RSM-IPNSAF), and $L_{0}$ norm constraint robust set-membership improved proportionate NSAF ( $L_{0}$ -RSM-IPNSAF) algorithms are derived by minimizing a differentiable cost function that utilizes the Riemannian distance between the updated and previous weight vectors as well as the $L_{0}$ norm of the weighted updated weight vector. Simulations in AEC application confirm the improvements of the proposed algorithms in performance.

Robust Set-Membership Normalized Subband Adaptive Filtering Algorithms and Their Application to Acoustic Echo Cancellation

Bias compensated zero attracting normalized least mean square adaptive filter and its performance analysis

Sparsity-aware subband adaptive algorithms with adjustable penalties

This paper proposes a diffusion proportionate affine projection sign algorithm for distributed estimation of sparse vector over network. The algorithm is derived by minimizing l 1 -norm intermediate error vector subject to a weighted constraint on the filter coefficients, where the positive definite weighting matrix is designed to accelerate the convergence of the nonzero coefficients for sparse vector estimation. Due to 1 1 -norm error minimization, the algorithm achieves robust performance against the impulsive interferences. Simulation results show that the proposed algorithm outperforms the existing distributed estimation strategies in terms of the convergence rate in various impulsive-interference environment.

Diffusion proportionate affine projection sign algorithm for distributed estimation over network

Transient analysis of l0-LMS and l0-NLMS algorithms

In general, theoretical analyses of adaptive filtering algorithms employ statistical approximations in order to render the derivations tractable. Among such hypotheses, the statistical independence between the current adaptive coefficients and past input vectors is a very popular one. Unfortunately, this simplification gives rise to discrepancies with respect to empirical results, especially for large values of the step-size parameter. In this Letter, this issue is overcome by the usage of an exact expectation analysis (i.e. a stochastic model that does not employ the above-mentioned independence assumption) of the least-mean-squares adaptive algorithm. The authors analysis is also generalised in order to address the common case of coloured additive noise, an issue that is so far missing from the literature. The accuracy of the advanced model is verified through simulations.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/el.2018.6675

Karen da S. Olinto

Papers

Transient analysis of l0-LMS and l0-NLMS algorithms

Exact analysis of the least-mean-square algorithm with coloured measurement noise