Performance Analysis of Zero-Forcing Equalizer for ISI Reduction in Wireless Channels

Performance Analysis of Zero-Forcing Equalizer for ISI Reduction in Wireless Channels

Pragya Sharma

Maharana Pratap College Of Technology and Management, Gwalior (M.P)

Abstract

The technique of equalization to compensate for the effect of the channel which causes distortion in transmitted signal. Different kinds of equalizers are used depending upon the application of the system and upon the kind of communication channel. These application range from acoustic echo cancellers to video de-ghosting system. The purpose of equalization system is to compensate for transmission-channel distortion such as signal affected as frequency depended phase or as amplitude attenuation. Besides correcting for channel frequency response anomalies, The equalizer can cancel the effects of multipath signal component. They may require significantly longer filter spans than simple spectral equalizers, but the principle of operations are essentially the same. This project aims at studying and simulation of ZF equalization technique. Simulation results shows that ZF equalization can greatly improve the bit error rate of the system as compared to system without using the same equalizer. The effect has been observed at different effects of ISI.

Keywords-Zero Forcing equalizers ,ISI, BER, Linear Equalizer.

1. Introduction

   In the design of large and complex digital systems, it is often necessary to have one device communicate digital information to and from other device. One advantage of digital information is that it tends to be far more resistant to transmitted and interrupted errors than information symbolized in an analog medium, this accounts for the clarity of digitally encoded telephone, compact audio disks and for much of the enthusiasm in the engineering community for digital communication technology. However digital communication has its own unique pitfalls and there of different and incompatible ways in which it can be sent. There main paths of the telecommunication system are transmitter Receiver, Channel. our main focus will be imparted to the receiver in this section called equalizer. The

   equalizer is used to estimate the transmitted bits/symbols in such a way that it eliminates the effect of channel. The Zero forcing equalizer is used in this context.Main objective of ZF equalizer is to compensate the effect of ISI.ZF unlike MMSE is useful in mitigating the ISI effect rather than induced noise in the signal. comparison of using ZF algorithm as equalizer will be done against using a simple algorithm for equalization.

2. Equalization

   There are number of procedures presented to counter the outcome of Multipart promulgation. Space diversity, frequency diversity channel equalization and amplitude equalization are the most commonly used. Among these ,space diversity and frequency diversity need a all common classification .In analogue broadcasting systems bandwidth overhead ,which is not eagerly obtainable in nearly,these signal diversity procedures were used and have been modified to digital systems without any difficulty that go through extremely discerning interference

   2.1 Linear Equalization

   A renowned receiver system for mitigating Inter- Symbol Interference (ISI) is the linear equalization. Least squares error cost function or mean square error cost functions are usually minimized for the computation of linear equalizers.

   Fig: The presence of additive noise in Linear equalization of an FIR channel.

   We can calculate the zero forcing equalizer. if we identify the noise first order and second order statistics

   and channel impulse response and the input. A supposition that will be used all over this effort is that the input is self sufficient and identically disseminated, among unit variance and zero mean and noise is white Gaussian therefore the recipient can utilize this information.

   Fig: A feedforward filter, a feedback filter and a decision device in a decision feedback equalizer.

3. Zero Forcing Algorithm

   In first insight let us consider different parameters used

   in Zero forcing equalization .Let H E (z) be the

   1. Principle of ISI

      If the channel response (or the channel transfer function) for a specific channel is H(s) then the input signal is multiplied by the reciprocal of this. This is intended to remove the effect of channel from the received signal, in particular the ISI. The zero forcing equalizer removes all ISI, and is ideal when greatly at frequencies f where the channel response H(j2f) has a

      equalizing circuit filter. The LTI filter with transfer function H E ( z) is considered to be the ZF equalizer. The only way to the ISI is to choose H E (z) such that the output of equalizer gives back the estimated output., i.e., Ik for all k. The filter transfer function needs to be specified such that it becomes the multiplicative inverse of the channel response G(z) i.e.,

      I

      k

      small magnitude (i.e. near zeroes of the channel) in the

      H E ( z)

      1

      G( z) . This method is what we call the

      attempt to invert the channel completely. A more balanced linear equalizer in this case is the minimum

      mean-square error equalizer, which does not usually

      Zero-Forcing equalization as the ISI component is forced to Zero. It must be noted that the impulse

      eliminate ISI completely but instead minimizes the

      response

      hE , k

      need to be an infinite length sequence.

      total power of the noise and ISI components in the output.

      To see this, let us evaluate the signal-to-noise ratio at the output of the zero forcing equalizer when the

      transmission filter HT ( f ) is fixed and the matched

   2. Functions of Linear Equalizer

      Linear Equalizers are normally useful on channels with a comparatively plane frequency response, Where the

      filter is used as the receiving filter, i.e.,

      R C

      H ( f ) H * ( f )H * ( f )

      T

      (1)

      ISI is not harsh. Though, when there are null in the frequency range of the acknowledged signal, a linear

      In this case , it is easy to see that the digital filter

      H (z) is given by

      equalizer execute badly, in its efforts to reverse the

      channel frequency response. a linear filter extensively increases the noise at the locality of the void (Null).The

      H e j 2 fT

      N0

      2T n

      HT f

      n n

      2

      T HC f T

      ( 2)

      deprived presentation of linear equalizers in channels with harsh ISI limits their utilization in wireless channels, which frequently have spectral nulls.

      and the PSD of the colored Gaussian noise samples

      nk is given by

      2

   3. Decision feedback Equalization

   j fT

   e

   nk

   N0

   2T n

   HT f

   n n

   T HC f T

   (3)

   W

   Decision feedback Equalization feed forward path,like an linear equalization, a DFE utilizes a reaction filter

   Hence, the noise-whitening filter

   HW (z)can be chosen as

   with the intention of feedback preceding conclusion and utilize them to minimize ISI .It is observed from the figure that input to the feedback filter approaches

   H (e j 2 fT )

   1

   H (e j 2 fT )

   from the production of the decision device, symbolized

   And the PSD of the Whitened-noise samples n~ is

   k

   by s(i ) N 0

   The objectives of this device is to plot the estimator

   2 .As a result, the overall digital filter G(z) is

   s(i

   ) which is achieavable by joining the

   G(e j 2 fT )

   H (e j 2 fT )H

   (e j 2 fT )

   H (e j 2 fT )

   productivity of the feed-forward filter and feedback W ( 5)

   filter, to the continuous position in the symbol

   Now, we choose the zero forcing filter HE (z) as

   collection .Now in linear equalization ,the feed-forward filter decreases ISI by endeavouring to strength the

   E

   collective scheme C(z)F(z) to be nearby to

   H (e j 2 fT )

   1

   G(e j 2 fT )

   1

   H (e j 2 fT )

   (6)

   Since the zero forcing filter simply inverts the effect of

   C(z)F (z) z

   the channel on the original information symbols

   I k ,

   the signal component at its output should be exactly

   www.ijert.org 2

   I k .If we model the I k as iid random variables with zero mean and unit variance ,then the PSD of the signal component is 1and hence the signal energy at the

   equalizer at receiver. The graph obtained in this case is shown below:

   1

   1

   2T df

   output of equalizer is just

   12T T .on the other

   hand ,the PSD of the noise component at the output of

   N0 H (e j 2 fT ) 2

   the equalizer is 2 E .hence the noise energy

   at the equalizer output is

   12T N0

   12T 2

   H (e j 2 fT

   2

   ) df

   .defining the SNR as the

   E

   ratio of the signal energy to the noise energy ,we have

   SNR

   1

   N

   0 2T

   1

   2 2T n

   HT f

   n

   T HC f

   1 1

   2

   n df

   T

   Notice that the SNR depends on the folded spectrum of the signal component at the input of the receiver. if there is a certain region in the folded spectrum with very small magnitude, then the SNR can be very poor

4. Simulation Results

   The simulation of the project is comprised of a number of comparisons. We have compared the effect of received signal by applying the zero forcing equalizer with and without the effect of ISI .The analytical result of the Rayleigh-faded channel and AWGN (Additive White Gaussian Noise) are also compared with the simulation results.

   In first scene, we will look towards the effect of ISI on the received signal with some noise without applying the ZF equalizer at receiver. The graph obtained in this case is shown below

   Fig:BER comparison without applying the ZF equalizer under the effect of ISI

   In second scene, we will look towards the effect of ISI on the received Signal with some noise with using ZF

   Fig: BER comparison using ZF equalizer under the effect of ISI.

   If we combine both of the above mentioned graphs, we see that by applying the ZF equalizer the BER v/s SNR result is better than without applying the same equalizer For creating the effect of ISI in received signal while using MATLAB tool, we apply a filter which is freq (frequency) cut. The frequency cut is designed in such a way that if increases its value, the ISI effect decreases. Let us first consider case in which the value of freq cut is 50. The graph shows the effect of BER v/s SNR for freq cut=50

   Fig: BER comparison by setting the ISI co-efficient freq cut=50

   Now let us consider the second case in which the value of co-efficient freq cut=100. The ISI effect decreased. The graph shows the effect of ISI on the received signal at freq cut=100

   Fig: BER comparison by setting the ISI co-efficient freqcut=100

   If the value of ISI coefficient is further increased to freq cut=200, we can see that the effect of ISI is further decreased.

   The graph shows the effect of ISI on the received signal for freq cut=200

   Fig: BER comparison by setting the ISI co-efficient freqcut=200

   Similarly for freq cut=600, the figure shown below shows that both the graphs (with and without applying ZF effect) are approximately coincides with each other

   Fig: BER comparison by setting the ISI co-efficient freqcut=600

   The above results of all the figures shows us that graph of BER v/s SNR for both the cases (with and without applying ZF effect) shows the same result at the zero ISI effect. From this theory, it has been concluded that the ISI affects the bit-error-rate just like the noise and the zero-forcing equalizer is much useful for mitigating the effect of the bit error rate introduced by ISI. The other equalizers like MMSE and RLS etc do not usually eliminate the ISI effect completely but instead minimizes the total power of noise

5. Conclusion

   From the above mentioned simulations, we can conclude that the effect of ISI can be decreased (mitigated) using a specialized equalizing technique called Zero-forcing. The above Figures shows that the effect of ISI causes an increase of Bit Error Rate. By applying the Zero-Forcing equalizer, the bit error rate is decreased.

6. Acknowledgement

The author express her sincere thanks to, The management, The Director, The Principal Maharana Pratap college of Technology college, for their constant support and encouragement.

References

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International Journal of Engineering Research & Technology (IJERT)

ISSN: 2278-0181

Vol. 1 Issue 8, October – 2012