Design of fractional-order variants of complex LMS and NLMS algorithms for adaptive channel equalization

Shah, Syed Muslim; Samar, Raza; Khan, Noor M.; Raja, Muhammad Asif Zahoor

doi:10.1007/s11071-016-3279-y

Cited by 35 publications

(24 citation statements)

References 44 publications

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“…The BB method, also known as the two-step gradient method, was initially proposed by Barzilai and Borwein (1988). It was applied to solve various unconstrained optimization problems (Dai et al, 2006;Nesterov, 2013;Tan et al, 2016) later. The method has an improved convergence rate compared with the gradient method.…”

Section: The Proposed Concurrent Mcma and Dd With Bb Methods The Bb Methodsmentioning

confidence: 99%

“…The MCMA changes the cost function of CMA (Shah et al, 2017 ) from real field to complex field, and its cost function is:…”

Section: Blind Equalizationmentioning

confidence: 99%

“…As is known, inter-symbol interference (ISI) is a major impairment for improvement in capacity or data transmission rate in wireless communication systems (WCS), especially in the field of robot wireless control (Lewis et al, 2020;Ye et al, 2020). Over the past decades, a variety of equalization methods, as well as channel estimation algorithms (Macchi and Eweda, 1984;Johnson et al, 1998;Yang et al, 2002;Chen and Chng, 2004;Ashmawy et al, 2009;Liyi et al, 2009;Yuan and Lin, 2010;Kim et al, 2012;Bhotto and Bajić, 2015;Haykin, 2015;Shah et al, 2017), have been proposed to relieve the ISI effects, thus compensating for channel distortion. The essence of equalization is to filter the signal, and the adaptive filter can automatically adjust its tap system, so as to achieve the best channel compensation effect.…”

Section: Introductionmentioning

confidence: 99%

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Concurrent Modified Constant Modulus Algorithm and Decision Directed Scheme With Barzilai-Borwein Method

Xiang

Yang³

et al. 2021

Front. Neurorobot.

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At present, in robot technology, remote control of robot is realized by wireless communication technology, and data anti-interference in wireless channel becomes a very important part. Any wireless communication system has an inherent multi-path propagation problem, which leads to the expansion of generated symbols on a time scale, resulting in symbol overlap and Inter-symbol Interference (ISI). ISI in the signal must be removed and the signal restores to its original state at the time of transmission or becomes as close to it as possible. Blind equalization is a popular equalization method for recovering transmitted symbols of superimposed noise without any pilot signal. In this work, we propose a concurrent modified constant modulus algorithm (MCMA) and the decision-directed scheme (DDS) with the Barzilai-Borwein (BB) method for the purpose of blind equalization of wireless communications systems (WCS). The BB method, which is two-step gradient method, has been widely employed to solve multidimensional unconstrained optimization problems. Considering the similarity of equalization process and optimization process, the proposed algorithm combines existing blind equalization algorithm and Barzilai-Borwein method, and concurrently operates a MCMA equalizer and a DD equalizer. After that, it modifies the DD equalizer's step size (SS) by the BB method. Theoretical investigation was involved and it demonstrated rapid convergence and improved equalization performance of the proposed algorithm compared with the original one. Additionally, the simulation results were consistent with the proposed technique.

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Section: The Proposed Concurrent Mcma and Dd With Bb Methods The Bb Methodsmentioning

confidence: 99%

“…The MCMA changes the cost function of CMA (Shah et al, 2017 ) from real field to complex field, and its cost function is:…”

Section: Blind Equalizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Concurrent Modified Constant Modulus Algorithm and Decision Directed Scheme With Barzilai-Borwein Method

Xiang

Yang³

et al. 2021

Front. Neurorobot.

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“…In the basic LMS algorithm, the value of μ usually remains constant, which is obviously not suitable for the iterative process. This gives rise to the normalized least mean square (NLMS) algorithm [26,27], an LMS algorithm with variable step size.…”

Section: Lms Algorithmmentioning

confidence: 99%

An Adaptive Filtering Algorithm for Non-Gaussian Signals in Alpha-Stable Distribution

Yang¹

2020

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Currently, many adaptive filtering algorithms are available for the non-Gaussian environment, namely, least mean square (LMS) algorithm, recursive least square (RLS) algorithm, least mean fourth (LMF) algorithm, and subspace minimum norm (SMN) algorithm. Most of them can converge to the steady-state, but face various constraints in the presence of alpha (α)-stable noises. To solve the problem, this paper aims to develop an adaptive filtering algorithm for non-Gaussian signals in α-stable distribution, drawing on the merits of existing adaptive filtering algorithms. Firstly, the authors introduced the theory of α-stable distribution, the central limit theorem and fractional lower-order statistics (FLOS). Next, two classic adaptive filtering algorithms, RLS and LMS, were summarized, and compared through tests. On this basis, the FLOS-SMN algorithm was designed in the light of the features of the LMS and the SMN, which applies to the filtering of non-Gaussian signals in αstable distribution. Finally, the proposed algorithm was proved as faster, more stable and more adaptable than the traditional method.

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“…The least-mean-square (LMS) algorithm is widely used in many fields, such as system identification [1,2], echo cancellation [3], adaptive channel equalization [4], adaptive antenna array [5], and adaptive spectral line enhancement [6], due to its good robustness, low computational complexity, and simple structure. However, it is well known that the convergence rate and steady-state error of the algorithm are directly related to the adaptation step size of a conventional LMS algorithm.…”

Section: Introductionmentioning

confidence: 99%

A Variable Step‐Size Leaky LMS Algorithm

Zhao

Zhang

2021

Wireless Communications and Mobile Computing

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The leaky LMS algorithm has been extensively studied because of its control of parameter drift. This unexpected parameter drift is linked to the inadequacy of excitation in the input sequence. And generally leaky LMS algorithms use fixed step size to force the performance of compromise between the fast convergence rate and small steady-state misalignment. In this paper, variable step-size (VSS) leaky LMS algorithm is proposed. And the variable step-size method combines the time average estimation of the error and the time average estimation of the normalized quantity. Variable step-size method proposed incorporating with leaky LMS algorithm can effectively eliminate noise interference and make the early convergence, and final small misalignments are obtained together. Simulation results demonstrate that the proposed algorithm has better performance than the existing variable step-size algorithms in the unexcited environment. Furthermore, the proposed algorithm is comparable in performance to other variable step-size algorithms under the adequacy of excitation.

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Design of fractional-order variants of complex LMS and NLMS algorithms for adaptive channel equalization

Cited by 35 publications

References 44 publications

Concurrent Modified Constant Modulus Algorithm and Decision Directed Scheme With Barzilai-Borwein Method

Concurrent Modified Constant Modulus Algorithm and Decision Directed Scheme With Barzilai-Borwein Method

An Adaptive Filtering Algorithm for Non-Gaussian Signals in Alpha-Stable Distribution

A Variable Step‐Size Leaky LMS Algorithm

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