BER Analysis ofImpulse Noise inOFDM System Using LMS,NLMS&RLS
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This paper analyzes the impact of impulse noise on Orthogonal Frequency Division Multiplexing (OFDM) systems and evaluates the performance of different adaptive algorithms such as LMS, NLMS, and RLS in mitigating this noise. The study highlights the importance of coding and interleaving techniques in enhancing robustness against burst errors in OFDM systems. Simulation results indicate that the RLS algorithm performs best under high signal-to-noise ratios, while NLMS offers a better balance between simplicity and performance compared to LMS.
![BER Analysis of Impulse Noise in OFDM System Using LMS, NLMS & RLS
DOI: 10.9790/0661-17325055 www.iosrjournals.org 51 | Page
After OFDM signal transmitted from the transmitter antenna, the signals go through all the anomaly
and hostility of wireless channels. After receiving the signal, the receiver downconverts the signal and converts
to digital domain using ADC convertor, symbol timing and synchronization are performed. After ADC
conversion, symbol timing and synchronization is achieved. Then OFDM signal is demodulated using an FFT
block. After that, channel estimation is performed using the demodulated pilots. Using the estimation, the
complex received data are obtained which are demapped according to the transmission constellation diagram. At
this moment the originally transmitted bit stream are recovered using FEC decoding and de-interleaving.
III. Impulse Noise
Impulse noise is generated by spurious sources such as switching of electrical AC sources.
Impulse noise can be broadly classified as
Fig2 Types of Impulse Noise
Periodic impulses consists of impulses of longer duration &occurring periodically in time.Aperiodic
impulse noise is characterized by impulses occurring at random time. In this paper we concentrate on aperiodic
impulse noise.
There are different statistical model available for modelling aperiodic impulse noise .The most
commonly used models are Gaussian mixture model, Middleton’s Class A model and symmetric alpha stable
mode [1].
IV. Algorithms
1) Least Mean Square (LMS)
In the Lest Mean Square(LMS) algorithme(n) is minimized in the mean square sense with changes in
the filter tap weights. The algorithm converges to a set of tap-weightswhen the processes X(𝑛)&d(𝑛) are jointly
stationary, which on average, are equal to the Wiener-Hopf solution. The LMS algorithm is a practical scheme
for realizing Wiener filters, without explicitly solving the Wiener-Hopf equation
𝑒(𝑛) = 𝑑(𝑛) − 𝑦(𝑛)
The cost function J(𝑡) chosen for the steepest descent algorithm determines the coefficient solution obtained by
using adaptive filter. If the MSE cost function is chosen, the resulting algorithm depends on statistics of s(𝑡)
&d(𝑡) because of the expectation operation that defines this cost function is the least square cost function given
by
𝐽(𝑡) = ά(i)(d i − w′(t)s(i))2t
i=0
The weight update equation for LMS can be represented as
W(𝑡 + 1) = 𝑊(𝑡) + µ𝑒(𝑡)𝑆(𝑡)
Where µ is learning factor, requires only multiplications and additions to implement. In effect, the iterative
nature of the LMS coefficient updates is a form of time-averaging that smoothers the errors in the instantaneous
gradient calculation to obtain a more reasonable estimate of the true gradient.](https://image.slidesharecdn.com/i017325055-151215043134/85/BER-Analysis-ofImpulse-Noise-inOFDM-System-Using-LMS-NLMS-RLS-2-320.jpg)
![BER Analysis of Impulse Noise in OFDM System Using LMS, NLMS & RLS
DOI: 10.9790/0661-17325055 www.iosrjournals.org 52 | Page
2) Normalized Least Mean Square (NLMS)
The NLMS algorithm is the extension of the standard LMS algorithm, the NLMS algorithms
implementation is very similar to that of the LMS algorithm. Each iteration of the NLMS algorithm requires
these steps to be followed
The adaptive filter output is calculated by the equation
An error signal is calculated as the difference between the desired signal and the filter output
The input vector step size value is calculated as
The filter tap weights are updated in preparation for the next iteration
Each iteration of the NLMS algorithm requires 3N+1 multiplications, this is only N more than the standard LMS
algorithm. This is an acceptable increase considering the gains in stability and echo attenuation achieve [3].
3) Recursive Least Square (RLS)
Recursive least squares algorithms have a faster convergences speed and do not exhibit the Eigen value spread
problem. RLS algorithms calculate J(n) by using the following equation
Where N is the filter length and λ is the forgetting factor. This algorithm calculates not only the instantaneous
value e2
(n) but also the past values, such as e2
(n–1), e2
(n– 2), ..., e2
(n–N+1). The value range of the forgetting
factor is (0, 1]. When the forgetting factor is less than 1, this factor specifies that this algorithm places a larger
weight on the current value and a smaller weight on the past values. The resulting E[e2
(n)] of the RLS
algorithms is more accurate than that of the LMS algorithms.
Fig3 RLS Block Diagram
Calculate the adaptive filter output signal y(n).
The error signal e(n) is calculated by using the following equation
e(n) = d(n)–y(n).
The filter coefficients are updated by using the following equation
Where the filter coefficient is vector and is the gain vector is defined by the following
equation
Where λ is the forgetting factor and P(n) is the inverse correlation matrix of the input signal.](https://image.slidesharecdn.com/i017325055-151215043134/85/BER-Analysis-ofImpulse-Noise-inOFDM-System-Using-LMS-NLMS-RLS-3-320.jpg)
![BER Analysis of Impulse Noise in OFDM System Using LMS, NLMS & RLS
DOI: 10.9790/0661-17325055 www.iosrjournals.org 55 | Page
Fig11BER Analysis Using RLS Algorithm
VI. Simulation Description
The graphs shown above contains BER plots for the LMS,NLMS and RLS algorithms. The graphs are
plotted for the various SNR values. By varying the SNR values we can observe the variation in BER values as
shown in above plots. As we take the SNR between 0 and 4, the BER of individual algorithms increased over a
period of internal and then decreased. Of those algorithms we executed RLS showing minimum BER when
compared with the LMS and NLMS algorithms, and after RLS algorithm, NLMS algorithm showing better
performance than LMS algorithm.
VII. Conclusion
In this research the above algorithms, LMS algorithm is the most popular adaptive algorithm, because
of the low computational complexity. Even though, the LMS algorithm suffers from slow and data dependent
convergence behaviour. Where NLMS algorithm, an equally simple, but more robust variant of the LMS
algorithm, exhibits a better balance between simplicity and performance than the LMS algorithm. Due to its
good characteristics the NLMS has been largely used in real-time applications but RLS has more sustainability
to higher SNR compared to LMS & NLMS, RLS is better among the algorithms used.
References
[1]. T.Y. Al-Naffouri, A.A Quadeer and G.Caire, “Impulse Noise Estimation and Removal for OFDM
Systems”.
[2]. Sumi Mathew, PrasanthMurukan, “Periodic Impulse Noise Reduction in OFDM based Power Line
Communication”
[3]. AlokPandey, L.D Malviya “Comparitive Study of LMS & NLMS Algorithms in Adaptive Equalize”.
[4]. T.Y. Al-Naffouri, A.A Quadeer and G.Caire, “Impulse Noise Estimation and cancellation in DSL using
orthogonal clustering”.
[5]. Vidya S. Bhosale, V.N. Ghodke “Comparitive Study of RLS&LMS Algorithms for OFDM System”.
[6]. M. Zimmermann and K. Dostert, “An analysis of the broadband noise scenario in power line networks,”
2000 International Symposium on Power line Communications and its Applications.
[7]. D. Fertonani and G. Colavolpe, “On reliable communications over channels impaired by bursty impulse
noise,” IEEE Trans. Commun., vol. 57, no. 7, pp. 2024–2030, July 2009.
[8]. J. Lin, M. Nassar, and B. L. Evans, “Impulsive noise mitigation in powerline communications using
sparse Bayesian learning,” IEEE J. Sel.AreasCommun., vol. 31, no. 7, pp. 1172–1183, Jul. 2013.
[9]. A. Al-Dweik, A. Hazmi, B. Sharif, and C. Tsimenidis,“Efficient interleaving technique OFDM system
over impulsive noise channels,” in Proc. 2010 IEEE Int. Symp. Pers. Indoor and Mobile Radio Comm
[10]. T. Starr, M. Sorbara, J. M. Cioffi, and P.J.Silverman, DSL Adcances. Prentice Hall Professional, 2003.](https://image.slidesharecdn.com/i017325055-151215043134/85/BER-Analysis-ofImpulse-Noise-inOFDM-System-Using-LMS-NLMS-RLS-6-320.jpg)
BER Analysis ofImpulse Noise inOFDM System Using LMS,NLMS&RLS
- 1. IOSR Journal of Computer Engineering (IOSR-JCE) e-ISSN: 2278-0661,p-ISSN: 2278-8727, Volume 17, Issue 3, Ver. II (May – Jun. 2015), PP 50-55 www.iosrjournals.org DOI: 10.9790/0661-17325055 www.iosrjournals.org 50 | Page BER Analysis ofImpulse Noise inOFDM System Using LMS,NLMS&RLS Dr.E.V.Krishna Rao1 ,K.Srikanth2 ,Sk.Nadeem Farooq3 ,B.Sriram4 Y.Chandana5 1,2,3,4,5 Department ofElectronics and Communication Engineering 1, 2, 3,4,5, K L University, Vaddeswaram, Guntur, Andhra Pradesh Abstract:Orthogonal Frequency Division Multiplexing (OFDM) scheme is also used as a digital multi carrier modulation method .Alarge number of closely spaced orthogonal sub-carrier signals are used to carry data on several parallel data streams or channels. While OFDM is ideally suited to deal with frequency selective channels and AWGN, its performance may be dramatically impacted by the presence of impulse noise. In fact, very strong noise impulses in the time domain might result in the erasure of whole OFDM blocks of symbols at the receiver. BER analysisis done by using various adaptive algorithms and Impulse noise impact can be observed. I. Introduction Orthogonal Frequency Division Multiplexing (OFDM) is a modulation scheme widely used in wired systems (DSL, PLC) and wireless systems (WiMAX, 3GPP LTE). Various issues are linear distortion due to inter symbol interference(ISI),Inter-carrier Interference(ICI) additive white Gaussian noise (AWGN) and impulse noise. OFDM is ideally suited to handle ISI by frequency domain transmission and equalization using the Inverse Discrete Fourier Transform (IDFT)/ Discrete Fourier Transform (DFT) cyclic prefix and the effect of AWGN is eliminated using an appropriate level of coded modulation, impulse remains a limiting factor. II. OFDM System In the OFDM system coding techniquessuch as forward error control/coding (FEC) coding and interleaving is added to the OFDM system needed to protect against burst errors(robustness). An OFDM system is called codded OFDM(COFDM) system when both channel coding and interleaving are done. In a digital domain binary input data are collected and FEC coded with schemes such as convolution codes. To obtain diversity gain bit stream are interleaved. Afterwards, 16-QAM a group of channel codded bits are mapped to corresponding constellation points. Then at this point the data are represented as complex numbers and they are serial. Known pilot symbol are mapped with known mapping scheme can be inserted at this moment. A serial to parallel converter is applied and the IFFT operation is performed on the parallel complex data. The transformed data are grouped together again, as per the number of required transmission subcarriers. Cyclic prefix is inserted in every block of OFDM data according to the system specification and the data are multiplexed in a serial fashion. At this point of time the data are OFDM modulated and ready to be transmitted. A time-domain digital data is transform to time-domain analog data using DAC. RF modulation is performed and the signal is up-converted to transmission frequency. Fig1 Basic OFDM System with AWGN & Impulse Noises
- 2. BER Analysis of Impulse Noise in OFDM System Using LMS, NLMS & RLS DOI: 10.9790/0661-17325055 www.iosrjournals.org 51 | Page After OFDM signal transmitted from the transmitter antenna, the signals go through all the anomaly and hostility of wireless channels. After receiving the signal, the receiver downconverts the signal and converts to digital domain using ADC convertor, symbol timing and synchronization are performed. After ADC conversion, symbol timing and synchronization is achieved. Then OFDM signal is demodulated using an FFT block. After that, channel estimation is performed using the demodulated pilots. Using the estimation, the complex received data are obtained which are demapped according to the transmission constellation diagram. At this moment the originally transmitted bit stream are recovered using FEC decoding and de-interleaving. III. Impulse Noise Impulse noise is generated by spurious sources such as switching of electrical AC sources. Impulse noise can be broadly classified as Fig2 Types of Impulse Noise Periodic impulses consists of impulses of longer duration &occurring periodically in time.Aperiodic impulse noise is characterized by impulses occurring at random time. In this paper we concentrate on aperiodic impulse noise. There are different statistical model available for modelling aperiodic impulse noise .The most commonly used models are Gaussian mixture model, Middleton’s Class A model and symmetric alpha stable mode [1]. IV. Algorithms 1) Least Mean Square (LMS) In the Lest Mean Square(LMS) algorithme(n) is minimized in the mean square sense with changes in the filter tap weights. The algorithm converges to a set of tap-weightswhen the processes X(𝑛)&d(𝑛) are jointly stationary, which on average, are equal to the Wiener-Hopf solution. The LMS algorithm is a practical scheme for realizing Wiener filters, without explicitly solving the Wiener-Hopf equation 𝑒(𝑛) = 𝑑(𝑛) − 𝑦(𝑛) The cost function J(𝑡) chosen for the steepest descent algorithm determines the coefficient solution obtained by using adaptive filter. If the MSE cost function is chosen, the resulting algorithm depends on statistics of s(𝑡) &d(𝑡) because of the expectation operation that defines this cost function is the least square cost function given by 𝐽(𝑡) = ά(i)(d i − w′(t)s(i))2t i=0 The weight update equation for LMS can be represented as W(𝑡 + 1) = 𝑊(𝑡) + µ𝑒(𝑡)𝑆(𝑡) Where µ is learning factor, requires only multiplications and additions to implement. In effect, the iterative nature of the LMS coefficient updates is a form of time-averaging that smoothers the errors in the instantaneous gradient calculation to obtain a more reasonable estimate of the true gradient.
- 3. BER Analysis of Impulse Noise in OFDM System Using LMS, NLMS & RLS DOI: 10.9790/0661-17325055 www.iosrjournals.org 52 | Page 2) Normalized Least Mean Square (NLMS) The NLMS algorithm is the extension of the standard LMS algorithm, the NLMS algorithms implementation is very similar to that of the LMS algorithm. Each iteration of the NLMS algorithm requires these steps to be followed The adaptive filter output is calculated by the equation An error signal is calculated as the difference between the desired signal and the filter output The input vector step size value is calculated as The filter tap weights are updated in preparation for the next iteration Each iteration of the NLMS algorithm requires 3N+1 multiplications, this is only N more than the standard LMS algorithm. This is an acceptable increase considering the gains in stability and echo attenuation achieve [3]. 3) Recursive Least Square (RLS) Recursive least squares algorithms have a faster convergences speed and do not exhibit the Eigen value spread problem. RLS algorithms calculate J(n) by using the following equation Where N is the filter length and λ is the forgetting factor. This algorithm calculates not only the instantaneous value e2 (n) but also the past values, such as e2 (n–1), e2 (n– 2), ..., e2 (n–N+1). The value range of the forgetting factor is (0, 1]. When the forgetting factor is less than 1, this factor specifies that this algorithm places a larger weight on the current value and a smaller weight on the past values. The resulting E[e2 (n)] of the RLS algorithms is more accurate than that of the LMS algorithms. Fig3 RLS Block Diagram Calculate the adaptive filter output signal y(n). The error signal e(n) is calculated by using the following equation e(n) = d(n)–y(n). The filter coefficients are updated by using the following equation Where the filter coefficient is vector and is the gain vector is defined by the following equation Where λ is the forgetting factor and P(n) is the inverse correlation matrix of the input signal.
- 4. BER Analysis of Impulse Noise in OFDM System Using LMS, NLMS & RLS DOI: 10.9790/0661-17325055 www.iosrjournals.org 53 | Page V. Simulation Results Fig4Transmitted OFDM Signal Fig5OFDM Transmitted Spectrum Fig6Channel Output with Impulse Noise
- 5. BER Analysis of Impulse Noise in OFDM System Using LMS, NLMS & RLS DOI: 10.9790/0661-17325055 www.iosrjournals.org 54 | Page Fig7Original Message Signal Fig8Recovered Noisy Signal Using RLS Fig9BER Analysis using LMS Algorithm Fig10BER Analysis Using NLMS Algorithm
- 6. BER Analysis of Impulse Noise in OFDM System Using LMS, NLMS & RLS DOI: 10.9790/0661-17325055 www.iosrjournals.org 55 | Page Fig11BER Analysis Using RLS Algorithm VI. Simulation Description The graphs shown above contains BER plots for the LMS,NLMS and RLS algorithms. The graphs are plotted for the various SNR values. By varying the SNR values we can observe the variation in BER values as shown in above plots. As we take the SNR between 0 and 4, the BER of individual algorithms increased over a period of internal and then decreased. Of those algorithms we executed RLS showing minimum BER when compared with the LMS and NLMS algorithms, and after RLS algorithm, NLMS algorithm showing better performance than LMS algorithm. VII. Conclusion In this research the above algorithms, LMS algorithm is the most popular adaptive algorithm, because of the low computational complexity. Even though, the LMS algorithm suffers from slow and data dependent convergence behaviour. Where NLMS algorithm, an equally simple, but more robust variant of the LMS algorithm, exhibits a better balance between simplicity and performance than the LMS algorithm. Due to its good characteristics the NLMS has been largely used in real-time applications but RLS has more sustainability to higher SNR compared to LMS & NLMS, RLS is better among the algorithms used. References [1]. T.Y. Al-Naffouri, A.A Quadeer and G.Caire, “Impulse Noise Estimation and Removal for OFDM Systems”. [2]. Sumi Mathew, PrasanthMurukan, “Periodic Impulse Noise Reduction in OFDM based Power Line Communication” [3]. AlokPandey, L.D Malviya “Comparitive Study of LMS & NLMS Algorithms in Adaptive Equalize”. [4]. T.Y. Al-Naffouri, A.A Quadeer and G.Caire, “Impulse Noise Estimation and cancellation in DSL using orthogonal clustering”. [5]. Vidya S. Bhosale, V.N. Ghodke “Comparitive Study of RLS&LMS Algorithms for OFDM System”. [6]. M. Zimmermann and K. Dostert, “An analysis of the broadband noise scenario in power line networks,” 2000 International Symposium on Power line Communications and its Applications. [7]. D. Fertonani and G. Colavolpe, “On reliable communications over channels impaired by bursty impulse noise,” IEEE Trans. Commun., vol. 57, no. 7, pp. 2024–2030, July 2009. [8]. J. Lin, M. Nassar, and B. L. Evans, “Impulsive noise mitigation in powerline communications using sparse Bayesian learning,” IEEE J. Sel.AreasCommun., vol. 31, no. 7, pp. 1172–1183, Jul. 2013. [9]. A. Al-Dweik, A. Hazmi, B. Sharif, and C. Tsimenidis,“Efficient interleaving technique OFDM system over impulsive noise channels,” in Proc. 2010 IEEE Int. Symp. Pers. Indoor and Mobile Radio Comm [10]. T. Starr, M. Sorbara, J. M. Cioffi, and P.J.Silverman, DSL Adcances. Prentice Hall Professional, 2003.