Adaptive recursive algorithm with logarithmic transformation for nonlinear system identification in α -stable noise

Zhao, Haiquan; Lu, Lu; He, Zhengyou; Chen, Badong

doi:10.1016/j.dsp.2015.08.004

Cited by 18 publications

(16 citation statements)

References 36 publications

(51 reference statements)

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“…The RLogLMP algorithm overcomes these limitations by applying a logarithmic transformation and minimizing the new cost function. In addition, RLogLMP improves the convergence rate, as demonstrated by Zhao et al…”

Section: Performance Resultsmentioning

confidence: 80%

“…Recently, Wu et al developed an algorithm based on filtered‐x LMS with a logarithmic transformation (FxLogLMS), which was demonstrated to be stronger than existing algorithms for active noise control in the presence of α ‐stable noise. Motivated by the FxlogLMS algorithm, Zhao et al developed a cost function for the RlogLMP algorithm, which can be constructed as

\begin{matrix} right J_{p} (n) & left = \sum_{i = 1}^{n} λ^{n - i} \log^{p} (1 + | e (i) |) & right \\ right & left = \sum_{i = 1}^{n} λ^{n - i} \log^{p} (1 + | z (i) - h^{T} (n) x (i) |), \end{matrix}

where the forgetting factor, λ ∈[0,1], controls the convergence performance of the algorithm, h (0)=0.…”

Section: Adaptive Channel Identification Methodsmentioning

confidence: 99%

“…According to Zhao the goal of RlogLMP algorithm is to minimize the cost function J p ( n ). Indeed, the gradient of J p ( n ) with respect to h ( n ) is given by the following equation:

\nabla J_{p} false[h false(n false) false] = p true \sum_{i = 1}^{n} λ^{n - i} \frac{\log^{p - 1} false(1 + false| e false(i false) false| false)}{1 + false| e false(i false) false|} sign false{e false(i false) false} x false(i false) .

…”

Section: Adaptive Channel Identification Methodsmentioning

confidence: 99%

“…Substituting e ( i )= z ( i )− h T ( n ) x ( i ) into , we have

true \sum_{i = 1}^{n} λ^{n - i} ν false(i false) x false(i false) x^{T} false(i false) h false(n false) = true \sum_{i = 1}^{n} λ^{n - i} ν false(i false) x false(i false) z false(i false),

where

ν (n) = \frac{\log^{p - 1} (1 + | e (n) |)}{(1 + | e (n) |) | e (n) |} .

The expression of h ( n ) is obtained from as follows:

h false(n false) = P false(n false) q false(n false),

where

P false(n false) = Q^{- 1} false(n false), Q false(n false) = true \sum_{i = 1}^{n} λ^{n - i} ν false(i false) x false(i false) x^{T} false(i false),

and

q false(n false) = true \sum_{i = 1}^{n} λ^{n - i} ν false(i false) x false(i false) z false(i false) .

…”

Section: Adaptive Channel Identification Methodsunclassified

“…P ( n ) can be updated by using Woodbury's matrix inversion lemma:

P false(n false) = λ^{- 1} P false(n - 1 false) - λ^{- 1} k false(n false) x^{T} false(n false) P false(n - 1 false),

where the gain vector k ( n ) is defined by

k false(n false) = \frac{ν false(n false) P false(n - 1 false) x false(n false)}{λ + ν false(n false) x^{T} false(n false) P false(n - 1 false) x false(n false)} .

…”

Section: Adaptive Channel Identification Methodsunclassified

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A new combination of adaptive channel estimation methods and TORC equalizer in MC‐CDMA systems

Zidane

Dinis

2020

Int J Communication

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Summary Adaptive systems identification has been widely studied, but most studies have focused on the convergence of these methods. Applications of equalization systems have also received much attention. This paper presents a new combination of adaptive Broadband Radio Access Networks (BRAN) channel identification algorithms for multicarrier code division multiple access (MC‐CDMA) systems downlink equalization. In fifth‐generation (5G) wireless communications, MC‐CDMA is expected to support the associated networks. The BRAN E channel parameters, representing an outdoor scenario normalized for MC‐CDMA systems, are identified using a recursive least mean pth power algorithm with logarithmic transformation (RlogLMP). For validity and test aim, this algorithm is compared with the existing recursive least square (RLS) and least mean square (LMS) algorithms. Moreover, we use the estimated coefficients in the adaptive equalization problem. We give a review of the threshold orthogonality restoring combining (TORC) equalizer, which is coupled with the presented algorithms to counteract channel fading, as evaluated by the bit error rate (BER). Our performance results show that the RlogLMP algorithm can estimate the measured BRAN E channel with good efficiency for various values of the signal‐to‐noise ratio (SNR), as compared with the classical algorithms RLS and LMS. In adaptive equalization problems, the achieved results demonstrate that two thresholds ρTH in the TORC equalizer minimize the performance degradation, in terms of the BER, of the MC‐CDMA system under multipath channel fading with very good accuracy, especially if the coefficients are estimated with the specific case of the power p in the RlogLMP algorithm.

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Section: Performance Resultsmentioning

confidence: 80%

\begin{matrix} right J_{p} (n) & left = \sum_{i = 1}^{n} λ^{n - i} \log^{p} (1 + | e (i) |) & right \\ right & left = \sum_{i = 1}^{n} λ^{n - i} \log^{p} (1 + | z (i) - h^{T} (n) x (i) |), \end{matrix}

where the forgetting factor, λ ∈[0,1], controls the convergence performance of the algorithm, h (0)=0.…”

Section: Adaptive Channel Identification Methodsmentioning

confidence: 99%

“…According to Zhao the goal of RlogLMP algorithm is to minimize the cost function J p ( n ). Indeed, the gradient of J p ( n ) with respect to h ( n ) is given by the following equation: