# Adaptive Equalization of binary encoded signals Using LMS Algorithm

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2 SSRG International Journal of Electronics and Communication Engineering (SSRG-IJECE) volume issue7 Sep Adaptive equalization is the technique used to reliably transmit data through a communication channel. Ideally, if the channel is ideal, we can demodulate the signal perfectly at the output without causing any error. However, in practice, all the channels are non-ideal and noisy in nature. So, to recover the original signal after demodulation, our aim is to find an equalization filter which will minimize the error between original transmitted signal and demodulated signal passed through equalization filter. Least Mean Square (LMS), has been proposed to perform this operation of equalization. Here our intention is to adjust the tap weights and calculate the error performance for the different binary encoded signals like Unipolar and polar and bipolar encoded sequences with and without return to zero. The rest of this paper is organized as follows. In section,explains the modeling of the communication channel. The rd section narrates the basic concept Channel equalization. Section explains the detailed analysis of LMS Algorithm. The 5 th section gives the results and discussion. Section concludes the papers along with future research directions are discussed.. Modeling the communication channel We assume the impulse response of the channel in the form h( [ cos( ( n ))] for n,, w otherwise The filter input signal will be u ( h * a v h( k) a( n k) v( where the noise variance. v Here both the MA Process and AR Processes are used to perform the equalization process The number of transverse equalization filter coefficients are being considered are, the weights (parameter) of the filter are symmetric with respect to the middle tap (n=5) and the channel input is delayed by 7 units to provide the desired response to the equalizer.. CHANNEL EQUALIZATION An equalization filter typically allows the user to adjust one or more parameters that determine the overall shape of the filter's transfer function as explained in the earlier section. Equalizers are used to overcome the negative effects of the channel. Different kinds of Equalizer are available in the literature like Adaptive Equalizer, Fractionally Spaced Equalizer, Blind Equalization, Decision-Feedback Equalization, Linear Phase Equalizer, T- Shaped Equalizer [], Dual Mode Equalizer[] and Symbol Spaced Equalizer. Our concentration is only the adaptive equalizer consists of a tapped delay line [5] and adaptive algorithm (LMS Algorithm). The equalizer outputs a weighted sum of the values in the delay line and updates the weights to prepare for the next symbol period. The general channel and equalizer pair and the structure of adaptive equalizers are depicted in Figs.& respectively. ISSN: Page

3 SSRG International Journal of Electronics and Communication Engineering (SSRG-IJECE) volume issue7 Sep Input x(t) Channel (H(f)) Equalizer(/H(f)) y equ (t) Fig.: The general channel and equalizer pair Fig.: The block diagram of adaptive equalization equipment To transmit a digital message, which can be a sequence of bits corresponding to voltage levels in modulation technique, through a noisy communication channel with impulse response given by h(. We can simplify the channel complexity by assuming that the channel noise is AWGN (Additive White Gaussian Noise) in nature and is independent of transmitted signal. So, the received signal u( at the demodulator can be given equation, L u( d( k) h( n k) v( k where d( is the transmitted digital message, L is the length of FIR approximation of channel distortion filter[]. Our aim is now to determine d ( such that Mean square error J, the difference between d( and ( minimized. e ( d( d( J E( e( ) We determine d (. LMS Algorithm using the adaptive equalizer based on LMS algorithm shown in Fig.. To make exact measurements of the gradient J ( vector at each iteration n, and if the step-size parameter is suitably chosen, then the tap-weight vector computed by using the steepest descent algorithm would converge to the optimum wiener solution [7]. The exact measurements of the gradient vector are not possible and since that would require prior knowledge of both the autocorrelation matrix R of the tap inputs and the cross correlation vector between the tap inputs w( and the desired response d(, the optimum wiener solution could not be reached [8]. d is ISSN: Page

5 SSRG International Journal of Electronics and Communication Engineering (SSRG-IJECE) volume issue7 Sep requires that step size should be less than the inverse of energy of the correlation matrix of received signal. One of the most important observations from these learning curves is that the algorithm converges faster for channel corresponding Channel parameters Channel input response h( Learning curve for Unipolar WRZ Ee ( for LMS algorithm a m p l itu d e... a m p l itu d e Original Unipolar WRZ to be transmitted Received Unipolar WRZ signal (noise + distortio..8. a m p l itu d e... a m p litu d e (a) (b) Fig.. (a) Adaptive equalization of LMS Algorithm using AR Process of Unipolar WRZ Channel input response h( Learning curve for Unipolar WRZ Ee ( for LMS algorithm a m p lit u d e... a m p lit u d e Original Unipolar WRZ to be transmitted Received Unipolar WRZ signal (noise + distortio a m p litu d e... 5 am plitud e Fig.5. (a) Adaptive equalization of LMS Algorithm using MA Process of Unipolar WRZ Channel input response h(.. Learning curve for PWRZ E e ( for LMS algorithm Original Unipolar PWRZ to be transmitted Received Unipolar PWRZ signal (noise + distortio Fig.. (a) Adaptive equalization of LMS Algorithm using AR Process of Polar WRZ ISSN: Page 5

6 SSRG International Journal of Electronics and Communication Engineering (SSRG-IJECE) volume issue7 Sep.8 Channel input response h(.5 Learning curve for PWRZ Ee ( for LMS algorithm Original Unipolar PWRZ to be transmitted Received Unipolar PWRZ signal (noise + distortio Fig.7. (a) Adaptive equalization of LMS Algorithm using MA Process of Polar WRZ Channel input response h(.5 Learning curve for Bipolar WRZ Ee ( for LMS algorithm Original Bipolar WRZ to be transmitted Received Bipolar WRZ signal (noise + distortio Fig.8. (a) Adaptive equalization of LMS Algorithm using AR Process of Bipolar WRZ Channel input response h(.5 Learning curve for Bipolar WRZ Ee ( for LMS algorithm Original Bipolar WRZ to be transmitted Received Bipolar WRZ signal (noise + distortio Fig.9. (a) Adaptive equalization of LMS Algorithm using MA Process of Bipolar WRZ Channel input response h( Learning curve for Unipolar RZ Ee ( for LMS algorithm Original Unipolar RZ to be transmitted Received Unipolar RZ signal (noise + distortio Fig.. (a) Adaptive equalization of LMS Algorithm using AR Process of Unipolar RZ ISSN: Page

7 SSRG International Journal of Electronics and Communication Engineering (SSRG-IJECE) volume issue7 Sep Channel input response h( Learning curve for Unipolar RZ Ee ( for LMS algorithm Original Unipolar RZ to be transmitted Received Unipolar RZ signal (noise + distortio Fig.. (a) Adaptive equalization of LMS Algorithm using MA Process of Unipolar RZ Channel input response h( Learning curve for polar WRZ Ee ( for LMS algorithm Original polar WRZ to be transmitted - 5 Received polar WRZ signal (noise + distortio Fig.. (a) Adaptive equalization of LMS Algorithm using AR Process of polar RZ Channel input response h( Learning curve for polar RZ Ee ( for LMS algorithm Original polar RZ to be transmitted - 5 Received polar RZ signal (noise + distortio Fig.. (a) Adaptive equalization of LMS Algorithm using MA Process of polar RZ Channel input response h( Learning curve for Bipolar RZ Ee ( for LMS algorithm Original Bipolar RZ to be transmitted Received Bipolar RZ signal (noise + distortio Fig.. (a) Adaptive equalization of LMS Algorithm using AR Process of Bipolar RZ ISSN: Page 7

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