Average Mean Square Deviation Research Articles

A Low Complexity Proportionate Generlized Correntropy-Based Diffusion LMS Algorithm With Closed-Form Gain Coefficients

This brief proposes a correntropy-based proportionate diffusion algorithm with low computational complexity. The proportionate diffusion algorithms in the literature suffer from a high computational complexity due to the complicated calculation process of the coefficients of the gain matrix, i.e., by solving an optimization problem or solving a linear system of equations via a matrix inversion. In this brief, by defining a proper correntropy kernel function and suitably assuming a wise constraint, the gain matrix coefficients are derived in a closed-form formula. In fact, the correntropy kernel function is used to determine the gain coefficients. This closed-form formula significantly reduces the computational complexity of the proposed algorithm. Moreover, a condition of uniform convergence for the distributed estimation algorithm at each time instant is obtained analytically. Simulation results show the lower steady-state Normalized Mean Square Deviation (NMSD) and lower computational complexity of the proposed algorithm compared to some other competing algorithms.

Robust Variable Step-Size Reweighted Zero-Attracting Least Mean M-Estimate Algorithm for Sparse System Identification

The reweighted zero-attracting least mean square (RZA-LMS) algorithm has good performance in sparse system identification. However, the convergence performance of the RZA-LMS algorithm degrades in the impulsive noise environment. In this brief, a reweighted zero-attracting least mean M-estimate (RZA-LMM) algorithm is proposed to address the issue. The RZA-LMM algorithm employs the M-estimate cost function with a sparsity-aware penalty term and is derived by using the unconstrained minimization method. In order to further enhance the convergence speed and reduce the steady-state error of the RZA-LMM algorithm, a variable step-size reweighted zero-attracting least mean M-estimate (VSSRZA-LMM) algorithm is proposed. The variable step-size scheme, which adopts the M-estimate cost function with a sparsity-aware penalty term and a constrained term of the step-size, is obtained by using the constrained minimization method. Besides, the mean-square stability is analyzed to obtain the range of the step-size, which guarantees the stabilization of the proposed algorithms. The computer simulation results show that the proposed RZA-LMM algorithm achieves better convergence performance than the RZA-LMS algorithm, and the proposed VSSRZA-LMM algorithm exhibits better convergence performance in terms of convergence speed and steady-state normalized mean square deviation (NMSD) than the RZA-LMM algorithm for sparse system identification in the impulsive noise environment.

A Frequency Domain LMS Algorithm with Dynamic Selection of Frequency Bins

Frequency-domain (FD) adaptive filter algorithms are able to achieve a low computational complexity by using the overlap-and-save implementation means compared to time-domain (TD) ones. In this article, we propose a new FD least-mean-square (FD-LMS) algorithm which dynamically selects frequency bins in order to reduce the computational complexity and maintain the convergence performance of the conventional FD-LMS. The optimal selection of frequency bins is derived by the largest decrease between the successive FD mean square deviations (MSDs) at every data block. Simulation results show that the proposed algorithm provides a low steady-state normalized MSD (NMSD) and similar convergence rate compared to the conventional FD-LMS algorithm. In addition, it gains a low computational complexity.