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This paper proposes a simple variable step size Least Mean Square (LMS) algorithm for adaptive identification of Infinite-Impulse-Response (IIR) filtering system. The proposed algorithm is called Fast Variable Step Size LMS (FVSSLMS) which incorporates a recursively variable adaptation step size based on error square multiplying by a constant. The...
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Citations
... The main operation of these filters is minimizing the error square between the desired signal and the input signal. Various adaptive algorithms are used to minimize this error, such as Least Mean Square [5], Recursive Least Square [6], and Affine Projection [7], which have been proven robust approaches for noise removal applications. Moreover, these algorithms have many advantages and limitations, making them suitable for many applications. ...
... It is used in conjunction with diagnosis systems to achieve accurate results [2]. Several adaptive algorithms have been used in adaptive filters for noise cancellers, including the Least Mean Square (LMS) [3], Recursive Least Square (RLS) [4], and Affine Projection (AP) algorithms [5]. The LMS-based adaptive filter has a simple construction but suffers from a low convergence speed. ...
... Adaptive system identification had a long history of many types of research ranged from the implementation of neural networks [5]- [9] to swarm optimization algorithms [10]- [14], reaching to the application of LMS adaptation algorithm on IIR and FIR adaptive filters on different applications [3], [15]- [18]. Application of genetic algorithm and its variant in system identification are studied in [4], [19] respectively. ...
... In adaptive filtering, GA operates on a set of filter parameters (the population of chromosomes), in which a fitness values are specified to each individual chromosome. The cost function in adaptive filtering is taken as the Mean Square Error (MSE) which is given by [4] ( 15) where is the window size over which the errors will be accumulated; ...
Our aim in this paper is to show how simple adaptive IIR filter can be used in system identification. The main objective of our research is to study the LMS algorithm and its improvement by the genetic search approach, namely, LMS-GA, to search the multi-modal error surface of the adaptive IIR filter to avoid local minima and finding the optimal weight vector when only measured or estimated data are available. Convergence analysis of the LMS algorithm in the case of colored input signal, i.e., correlated input signal is demonstrated via the input's power spectral density and the Fourier transform of the autocorrelation matrix of the input signal. Simulations have been carried out on adaptive filtering of IIR filter and tested on white and colored input signals to validate the powerfulness of the genetic-based LMS algorithm.
... Since they are stochastic gradient based algorithms, they usually have a trade-off between the convergence rate and the misadjustment because of the constant stepsize [3]. To enhance the performance of the LMS algorithm, several variable step-size algorithms have been developed [4], [5], [6]. In [7], authors proposed a function controlled variable step-size LMS algorithm. ...
The convergence rate of the least-mean-square (LMS) algorithm deteriorates if the input signal to the filter is correlated. In a system identification problem, this convergence rate can be improved if the signal is white and/or if the system is sparse. We recently proposed a sparse transform domain LMS-type algorithm that uses a variable step-size for a sparse system identification. The proposed algorithm provided high performance even if the input signal is highly correlated. In this work, we investigate the performance of the proposed TD-LMS algorithm for a large number of filter tap which is also a critical issue for standard LMS algorithm. Additionally, the optimum value of the most important parameter is calculated for all experiments. Moreover, the convergence analysis of the proposed algorithm is provided. The performance of the proposed algorithm has been compared to different algorithms in a sparse system identification setting of different sparsity levels and different number of filter taps. Simulations have shown that the proposed algorithm has prominent performance compared to the other algorithms.
... This trade-off is more prominent in a high-level measurement noise or if the input signal is highly correlated [4]. To overcome these problems, several adaptive algorithms have been developed [2][3][4][5][6][7][8][9][10][11] in the recent years. ...
The recently proposed function controlled variable step-size least-mean-square (FCVSSLMS) algorithm has shown high performance in different noise environments. The performance of the algorithm can be improved further if the system is sparse. In this paper, we propose a new algorithm based on the FCVSSLMS algorithm. The proposed algorithm imposes an approximate penalty in the cost function of the FCVSSLMS algorithm. We also present the convergence analysis of the proposed algorithm and derive the stability criterion. The performance of the proposed algorithm is compared to those of the variable step-size least-mean-square, more robust variable step-size least-mean-square, FCVSSLMS algorithm and reweighted zero-attracting least-mean-square algorithm in a system identification setting with an additive white Gaussian noise and additive correlated Gaussian noise. The proposed algorithm has shown high performance compared to the others in terms of the convergence rate and mean square deviation.
In this paper, an improved high-speed adaptive filter is proposed and implemented using a field-programmable gate array platform. Specifically, a new filter structure combining systolic and convex architectures has been analyzed and compared with conventional filter architectures. The new filter structure efficiently removes power line interference noise from electrocardiogram signals at high convergence speeds. The systolic architecture is used to improve the convergence speed of the filter, and the convex architecture is used in combination to improve the signal-to-noise ratio of the filter. One fast filter was designed using the retimed delay recursive least square algorithm (recursive least square filter design with systolic architecture), and it was combined with one slow filter designed using the least mean square algorithm based on convex combination architecture. The proposed filter architectures are assessed for electrocardiogram noise cancellation, obtained from the MIT-BIH database, and the performance is compared with various filter structures in terms of the signal-to-noise ratio, convergence speed, learning behaviors, and complexity. The results show an improvement in signal-to-noise ratio of 24.2% and an increase in convergence speed of 50% when compared with conventional filter structures.
