ISSN: ISO 9001:2008 Certified International Journal of Engineering Science and Innovative Technology (IJESIT) Volume 3, Issue 3, May 2014

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1 Nonlinear Adaptive Equalization Based on Least Mean Square (LMS) in Digital Communication 1 Manoj, 2 Mohit Kumar, 3 Kirti Rohilla 1 M-Tech Scholar, SGT Institute of Engineering and Technology, Gurgaon, Haryana 2,3 Assistant Professor, SGT Institute of Engineering and Technology, Gurgaon, Haryana Abstract:- In this paper, the least mean square based adaptive equalization in digital communication system is presented. We analyze a digital channel and perform channel equalization using an adaptive equalization based on least mean square criteria. The parameters that are uses to analysis the performance of adaptive equalizer are Channel adaptation, asymptotic performance and Convergence rate. The Results shows that the channel adaptation is possible accurately and systematically with the proposed equalization techniques. The simulation result shows the superiority of this equalization approach that it can accurately adaptation of the channel compared to the existing equalization techniques. Finally, convergence rate indicate that this technique perform the equalization task with great accuracy and with less time consumption. Keywords: - Least mean square, Adaptive equalization, Decision feedback equalizer, nonlinear equalization. I. INTRODUCTION Over the last three decades, the use of equalizer has been reported in digital communication applications to mitigate inter symbol interference (ISI) [1][2]. Decision feedback Equalization provides a good compromise between performances and complexity, delivering a much better performance than a linear equalizer at a much lower complexity than that of the optimum detector the maximum likelihood sequence estimation (MLSE). As the communication speed is increasing rapidly over the years. Long haul transmission in digital communications usually consists of several keys area to ensure the data transfer is error-free. Equalization is considered to be a powerful technique to cope with channel distortions in high speed data transmissions [3]-[5]. Digital communication channel is mainly characterized selective channel both time and frequency. While multipath propagation gives rise to frequency selectivity, mobility and/or carrier frequency offset give rise to time selectivity. Frequency selectivity implies intersymbol interference (ISI) [6]. On the other hand, time selectivity results in a spreading of the transmitted signal in the frequency domain or the so-called Doppler spread. Therefore, to provide reliable communication, advanced and efficient channel equalization and estimation techniques are necessary. Equalizers, in general, can be classified according to their structure, i.e., as linear or nonlinear (e.g., decision feedback) equalizers. Equalizers can also be classified according to the optimization criterion used for the design. In particular, equalizers can be classified as zero forcing (ZF) when a solution that forces ISI to zero is sought, MMSE [11] when the equalizer optimizes the mean-square error of the symbol estimate, or maximum likelihood when the maximum-likelihood sequence estimation (MLSE) criterion is utilized. In this paper, the least mean square based adaptive equalization in digital communication system is presented. We analyze a digital channel and perform channel equalization using an adaptive equalization based on least mean square criteria. The parameters that are uses to analysis the performance of adaptive equalizer are Channel adaptation, asymptotic performance and Convergence rate. The rest of the paper is organized as follows: Section II defines the system model for error free date transmission in communication system. In Section III, equalization theory for channel equalization in digital communication is presented. Section IV explain the adaptive equalization used for the intersymbol interference removal in digital communication and selection of the nonlinear equalizer over linear equalizer.. In Section V, 420

2 shows simulation results based on the following performance evaluation parameters such as Channel adaptation, asymptotic performance and Convergence rate. Finally, a conclusion is made. II. SYSTEM MODEL High speed communications channels are often impaired by channel intersymbol interference and additive noise. Adaptive equalizers are required in these communications systems to obtain reliable data transmission. A discrete time model of a digital communications system is depicted in Fig. 1, where a digital sequence s ( t ) is transmitted through a dispersive channel with transfer function H(z). The transmitted symbol sequence s(t) is assumed to be an equiprobable and independent binary sequence taking values from {+l,-1}. The channel output is corrupted by an additive white Gaussian noise e(t). The task of the equalizer is to recover the transmitted symbols based on the channel observation y(t). Fig. 1 System Model III. EQUALIZATION THEORY In digital communication, the received pulse shape, h r (t) is usually determined by the fiber impulse response, h f (t), and the transmitted pulse shape, h t (t). h r (t) = h t (t) * h f (t) where * denotes convolution. Normally, the transmitted pulse shape is known, leaving the engineer to estimate the impulse response of the fiber, which is often difficult to characterize. However, studies have shown that for a fiber that exhibits mode coupling, its impulse response is close to a cosine-squared shape in both the time and frequency domain [10]. h f (t) = exp[-(t 2 /(2(αT) 2 ))] / [sqrt(2π)]( αt) As such, it is highly probable that when a series of pulses is transmitted, overlapping will occur due to pulse broadening caused by dispersion as discussed in the previous section. Therefore, to reduce the pulse broadening that causes the resulting ISI, a suitable equalizer with a frequency response of H eq (w) may be implemented. H eq (ω) = H out (ω ) / H A (ω ) where H out (ω) = F[h out (t)], is the desired output pulse shape, and H A (ω) = F[h A (t)], is the total dispersive response of the system and F denotes Fourier transform. As equalization makes up one of the main parts of an receiver together with the detector and amplifier, the equalizer is often designed to include the effects of the channel as well as the degradations caused by the amplifier. IV. NONLINEAR EQUALIZER Decision-feedback equalization was first introduced by Austin. Such equalizers are usually used in conjunction with a linear forward equalizer to remove ISI. One drawback of the linear equalization used in both partialresponse maximum-likelihood (PRML) and DFE detectors is that it typically introduces high frequency boost, which causes noise enhancement [10]. In a Decision Feedback Equalizer [3], both the feed forward and feedback filters are essentially linear filters. It is a non-linear structure because of the non-linear operation in the feedback loop (decision threshold); its current output is based on the output of previous symbols. 421

3 The reason for choosing DFE over linear equalizer is that the latter s performance in channel that exhibit nulls is not effective. Noise enhancement in these regions and long impulse response are a problem. The basic reason for this problem is that in linear filtering, the desired signal and noise are processed together, causing noise enhancement problem. This is particularly detrimental to an optical channel, which suffers from amplitude distortion and attenuation. Fig. 2 Nonlinear Equalizer In contrast, the decision feedback equalizer has zero noise enhancements in the feedback loop. As such, its performance is superior to the linear equalizer. The principle operation of the DFE is that a weighted sum of past decisions is subtracted from the incoming signal, with the feedback taps weights being exactly equal to the amplitude of corresponding pulse post cursors at each sampling instant. Therefore, if the decisions (output of the decision threshold) are correct, the ISI from the already-detected pulses is completely removed with no enhancement of the noise. The input to the feedback filter comes from the output of the decision threshold device, and the coefficients are adjusted. To cancel the ISI on the current symbol as discussed earlier. The above DFE structure has N1+N2+1 feed forward taps and N3 feedback taps. The output of the equalizer is given by: k= + where C * n is the tap gain and y n is the input for the forward filter, F i * is the tap gain for the feedback filter and d i (i<k) is the previous decision made on the detected signal [7][8]. The DFE decodes channel inputs on a symbol-by-symbol basis and uses past decisions to remove trailing ISI [11]. The minimum mean square error decision feedback equalizer optimizes the feed forward and feedback filter to minimize the mean-square error. Given its many advantages, there are two main problems surrounding the application of the DFE, namely, error propagation and slow convergence rate. V. EXPERIMENTAL RESULTS This section present the results of the simulations performed of adaptive equalizers using Matlab 7.11(2011a. The results were analyzed and presented using the parameters set to evaluate the performance of an adaptive equalizer. Following parameter are uses to analysis the performance of adaptive equalizer 1. Channel adaptation 2. Asymptotic performance 3. Convergence rate 422

4 Fig. 3: Impulse Response of simulated Channel with taps Fig. 4: Impulse Response of estimated Channel with taps The channel is assumed to be unknown at the receiver side. Fig. 3 shows the Impulse Response of simulated Channel with 7 taps using nonlinear equalization. Fig. 4 shows the Impulse Response of estimated Channel with 7 taps using nonlinear equalization. Fig. 5 shows the Nonlinear Equalizer of the channel. Fig. 6 shows the asymptotic performance for nonlinear equalization. Fig. 7 shows the active tap detection in nonlinear equalization. Simulation results show that joint schemes that utilize hard equalizer outputs for channel estimation outperform those that utilize soft equalizer outputs. The Results shows that the channel adaptation is possible accurately and systematically with the proposed equalization techniques. The simulation result shows the superiority of this equalization approach that it can accurately adaptation of the channel compared to the existing equalization techniques. 423

5 Fig. 5 Nonlinear Equalizer of the channel Fig. 6 Asymptotic performance for nonlinear equalization Fig. 7 active tap detection in nonlinear equalization 424

6 VI. CONCLUSIONS This paper presents the adaptive equalization technique to mitigate the effects of ISI digital communication channel. The adaptive equalizer was implemented using the Least Mean Square (LMS) technique nonlinear equalization of the unknown channel. The channel is assumed to be unknown at the receiver side. The simulation result shows the superiority of this equalization approach that it can accurately adaptation of the channel compared to the existing equalization techniques. Finally, convergence rate indicate that this technique perform the equalization task with great accuracy and with less time consumption. REFERENCES [1]. P. Monsen, "Feedback Equalization for Fading Dispersive Channels," IEEE Trans. Information Theory, vol. 17, 56-64, Jan [2]. J. G. Proakis, Digital Communications, fourth Ed. New York: McGraw-Hill, [3]. N. AI-Dhahir, and J.M. Ciaffi, "MMSE decision-ceedback equalizers: Finite-length results," IEEE Trans. Inform. Theory, vol. 41, no. 4, July 1995, pp [4]. G. D. Forney, Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference, IEEE Trans. Inform. Theory, vol. IT-18, pp , [5]. F. R. Magee and J. G. Proakis, Adaptive maximum-likelihood sequence estimation for digital signals in the presence of intersymbol interference, IEEE Trans. Inform. Theory, vol. IT-19, pp , [6]. B. Mulgrew and C.F.N. Cowan, Adaptive Filter and Equalisers. Boston, MA Kluwer Academic, [7]. C. Belfiore and J. Park, Decision feedback equalization, Proc. IEEE, vol. 67, no. 8, pp , Aug [8]. N. Al-Dhahir and J. M. Cioffi, MMSE decision-feedback equalizers: Finite length results, IEEE Trans. Inf. Theory, vol. 41, no. 4, pp , Jul [9]. Theodore S. Rappaport, Wireless Communications Principles and Practice 2nd edition, Prentice Hall Communications Engineering and Emerging Technologies Series, Upper Saddle River, New Jersey, [10]. Benjamin Seng Boon Tan, Equalization in Communications, University of Queensland, October [11]. Simon Hakin and Thomas Kailath, Adaptive Filter Theory,Pearson Publication, Fourth Edition,

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