Enhancement of Noise Performance in Digital Receivers by...

Available online at http://ijim.srbiau.ac.ir/

Int. J. Industrial Mathematics (ISSN 2008-5621)

Vol. 6, No. 4, 2014 Article ID IJIM-00472, 10 pages

Research Article

Enhancement of Noise Performance in Digital Receivers by Over

Sampling the Received Signal

A. Y. Hassan ∗†, S. M. Shaaban ‡

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Abstract

In wireless channel the noise has a zero mean. This channel property can be used in the enhancementof the noise performance in the digital receivers by oversampling the received signal and calculatingthe decision variable based on the time average of more than one sample of the received signal. Theaveraging process will reduce the effect of the noise in the decision variable that will approach to thedesired signal value. The averaging process works like a filter that reduces the noise power at itsoutput according to its averaging interval. Although the power spectrum of the noise does not changeaccording to the averaging process, the noise variance at the decision variable will be smaller thanthe channel noise variance. This paper studies this idea and show how the performance of digitalreceivers can be enhanced by oversampling the received signal. This paper shows another treatmentmethod to the noise problem in digital modulation systems.

Keywords : Wireless channel; Noise performance; Signal; Averaging interval.

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1 Introduction

Noise is the main corrupting element in anycommunication system. It is unavoidable in-

terference source in all communication channelsand the main source of errors and performancedegradations. A lot of researches have been doneto minimize the effect of the noise or to try to can-cel it. Some of these researches depend on mini-mizing the mean square error value between thechannel noise and another noise like signal whichgenerated from a noisy source and an adaptivefilter [1, 2, 6].Other approaches use the recursiveleast square (RLS) algorithm to minimize the er-ror square between the estimated signal with re-duced noise and the noisy measured signal [3].

∗Corresponding author. [email protected]†Faculty of Engineering, Benha university, Benha,

Egypt.‡Faculty of Engineering, Menofia University, Shebin

Elkom, Egypt.

The noise reduction receivers based on RLS algo-rithm are faster than those based on LMS algo-rithm however the LMS algorithm can reduce thenoise power more than the RLS algorithm. An-other research shows that the noise and signal fea-ture detection problem can be converted to statis-tical hypotheses tests based on the sample corre-lation in different orientations [4].This algorithmprovide ways of measuring the degree of noisewith respect to the degree of signal feature, andits adaptive noise reduction filtering frameworkprovides good performance with respect to theadaptive algorithms when the underlying noisesare from Gaussian or non-Gaussian distributions.In addition to adaptive algorithms, channel cod-ing may be used to enhance the noise reductionprocess as shown in [5]. The previous trials aredepending on a complex signal processing unitthat complicates the receiver structure howeverthe performance enhancement is not great espe-cially with the white noise case. On the other

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276 A. Y. Hassan, et al /IJIM Vol. 6, No. 4 (2014) 275-284

hand, we did not find any research based on thefact that the noise in wireless channel has a zeromean. This is an important statistical propertyof the noise that may be used to trim down theeffect of the noise on the transmitted data. Ourwork in this paper is based on the wireless chan-nel noise characteristics and the estimation the-ory that are shown in [8, 9, 10]. It is arranged asfollows. Section 2 shows the effect of the oversam-pling process of the received signal on the noisemean of the decision variable. Section 3 appliesthe proposed idea on the BPSK system which isan example of a wireless system however Section 4shows the oversampling gain effect on the BPSKprobability of error formula. Simulation resultsare shown in section 5. Finally the conclusionsare represented in Section 6.

2 The effect of oversampling onthe noise signal and the deci-sion variable

In wireless communication channel, the noise sig-nal that corrupts the desired transmitted signalis a sample function of a zero mean random pro-cess with a certain variance . The noise mean canbe estimated by calculating the time average ofthe discrete samples of the noise sample functionn(t) which will approach to the statistical averageof the noise process when the averaging period islarge as shown in the following equation.

limN→∞

1

N

N∑i=1

ni = E[n(t)] (2.1)

The last statement is true if the noise pro-cess is Ergodic which is the case for all physicalwireless communication channels [8],therefore thetime average will be used instead of the statisticalaverage to estimate the noise mean and varianceas shown in sections (2.1) and (2.2). The noise inall communication channels is additive. Thus, thedecision variable in any detector consists mainlyfrom two components. One is due to the desiredsignal and the other is the noise signal compo-nent.

d = s+ n (2.2)

d d is the decision variable or the sufficientstatistic, s is the desired signal component whichhas a constant value during the symbol interval,

and n is the noise signal component which is arandom variable. The statistical mean and vari-ance of the decision variable are represented byequations (??) and (??) respectively.

E[d] = E[s+ n] = E[s] + E[n] = s (2.3)

var[d] = var[s+ n] = var[n] (2.4)

If the decision variable in the last equationsis formed based on a single sample of the desiredsignal and the noise functions, the variance of thedecision variable will be the same as the varianceof the channel noise function . But if the deci-sion variable is formed based on the average ofmore than one observation sample, the varianceof the decision variable will be decreased by a fac-tor proportional to the number of samples in theaverage process. Sections (2.1) and (2.2) give themathematical proof of this observed result for thewhite and color noise cases respectively.

2.1 White noise case

In white noise case, the noise samples are inde-pendent. The estimation theory said that if Nstatistically independent samples are taken froma sample function of the noise process to estimatethe noise mean, the estimated mean will be

µ̂n =1

N

N∑i=1

ni (2.5)

ni is the ith sample of the white noise functionn(t) during one bit interval. This average is alsoa random variable. Its mean is equal to the actualnoise mean and its variance is depending on theused number of samples.

E[d] = E[µ̂n] =1

N

N∑i=1

E[ni] = 0 (2.6)

var[d] = var[µ̂n] = var[1

N

N∑i=1

ni]

=1

N

N∑i=1

var[ni] =σ2nN

(2.7)

The last two equations (2.6), (2.7) of the meanand variance of the estimated noise averages howthat if the number of noise samples is increased,

A. Y. Hassan, et al /IJIM Vol. 6, No. 4 (2014) 275-284 277

the estimated noise mean will approach to zerowith a variance that is inversely proportion to thenumber of samples used in the estimation process.This observation will be used in Section (3) to en-hance the performance of BPSK system which isan example of a wireless communication system.

2.2 Color noise case

The previous idea of reducing the variance of thedecision variable by averaging it over N samplesneeds the zero mean noise samples to be uncor-related (white). This case is achieved in all com-munication channels where the channel noise iswhite and Gaussian. But for the case of colorednoise samples, equations (2.6), (2.7) don’t holdbecause the noise samples are correlated. Thecorrelated noise samples are produced when thewhite noise samples pass through a system filter.The variance of the produced samples will be re-duced according to the system filter normalizedbandwidth Bn.

σ2nc =σ2nB

Fs= σ2nBn (2.8)

Fs is the sampling frequency and B is thebandwidth of the system filter. From equation(2.8), the color noise variance will be smallerthan the white noise variance. The variance ofthe estimated mean in the case of correlatednoise samples is

var(µ̂nc) =

1

N2

N∑i=1

N∑j=1

E[(nci − µnci)(ncj − µncj)] (2.9)

After some mathematical manipulations, thevariance will be

var(µ̂nc) =σ2ncN

+1

N2

N∑i=1

N∑j ̸=i

ρijσ2nc

∵ ρij = E[ninj ] = ρi−j

∵ var(µ̂nc) =σ2ncN

+σ2ncN

N−1∑i=1

ρi (2.10)

ρj is the correlation coefficient between two noisesamples vectors with j sample shift between them.From equation (2.10), it is clear that the averag-ing process of the color noise samples reduces thevariance of the color noise by a factor depends on

the number of samples in the averaging processand the correlation coefficient between the noisesamples. The variance of the estimated average ofcolor noise samples has an upper bound equals tothe color noise variance and a lower bound equalsto the white noise variance divided by N.

σ2nN

< var(µ̂n) < σ2nc (2.11)

As long as the variance of the correlated noisesamples depends on the sampling frequency, sooversampling the uncorrelated noise samples willreduce the variance of the correlated noise sam-ples produced at the output of the system fil-ter. A whitening filter may be used to convertthe noise samples to uncorrelated noise samples.But this will complicate the receiver structureand its enhancement on the performance - dueto the conversion of the color noise to white noise- can be achieved by the oversampling process.Simulation results agree with the proposed idea.The correlated noise samples variance will be de-creased by a factor greater than N and depend onthe noise bandwidth.

3 Theoretical analysis of theproposed idea on BPSK sys-tem

BPSK is a classical digital modulation systemthat uses two different phase angles to transmitbinary data. Equation (3.12) shows the discreteform of the transmitter BPSK signal sk for thekth symbol.

sk(N) = bk√2cos(2πfnn),

KN < n ≤ (k + 1)N, 0 < k < K (3.12)

K is the number of transmitted binary symbols,bk is the kth binary symbol, bk takes a value of1 or -1 according to the binary transmitted sym-bols 1 or 0 respectively. fn is the normalized fre-quency which equals to the ratio between the car-rier frequency and the sampling frequency. Inte-gral number of carrier cycles is assumed throughthe bit interval. N is the number of samples perbit

N =TbTs

(3.13)


The used discrete orthonormal basic function ψn

is a sinusoidal function.

ψn =√2cos(2πfnn) (3.14)

The transmitted symbol sk The transmitted sym-bol Et. Assuming that the transmitted symbolspass through a linear white Gaussian channel, thereceived discrete signal will be

r(n) = sk(n) + w(n) (3.15)

w(n) is a discrete sample function of a whiteGaussian noise process c(t) with a zero mean andσ2w variance. The receiver correlates the receivedsignal with the complex conjugate of the used or-thonormal basic function ψ(n) to form the deci-sion variable yk. Equation (3.16) represents theoutput of the discrete correlator in the receiver.

yk =

N∑n=1

bk2cos(2πfnn)cos(2πfnn)

+

N∑n=1

W (n)√2cos(2πfnn) (3.16)

In vector notation, the discrete correlator outputis:

yk = sTk φ+ wTφ = bkφTφ+ wTφ

= bk + zk (3.17)

bk has a constant value during the symbol timeinterval Tb but zk is a Gaussian random variable,so yk is a Gaussian random variable. Deep look-ing in equation (3.17) shows that yk is the scaledestimated average of the received samples duringthe symbol interval Tb and zk is the scaled es-timated average of the noise samples during thesame interval. zk represents also the time averageof the noise samples during the normalized sym-bol interval N. This time average or the estimatedaverage of the noise samples is a random variablein natural and its mean and its variance are re-lated to the mean and variance of the noise sam-ples that have been used in the calculation of thistime average. Equations (3.18) and (3.19) showthe statistics of the time average of the scalednoise samples.

E[zk] = E

[1

N

N∑n=1

w(n)√2cos(2πfnn)

]

=1

N

N∑n=1

E[w(n)]√2cos(2πfnn)=0 (3.18)

var[zk] = var

[ N∑n=1

w(n)√2cos(2πfnn)

]

=1

N2

N∑n=1

E[w2(n)]2cos2(2πfnn)=σ2wN

(3.19)

The expected value of yk equals to bkbecause theexpected value of zk equals zero.The variance ofthe decision variable yk equals to the variance ofthe time average zk.

E[yk]=E[bk + zk]=bk+E[zk]=bk (3.20)

var(yk)=var(bk+zk)=var(zk)=σ2wN

(3.21)

This result in the discrete domain differs fromthat in the continuous domain where the varianceof the decision variable in the continuous domainequals to the variance of the channel noise [9].The continuous domain case is a special case ofthe discrete domain result if the number of sam-ples per symbol is one, or a single value of noisesample is assumed to be constant in all the inter-val of the symbol. But this is not true becausethe noise varies during the symbol interval. Incontinuous signal detection, the decision variableyk is formed by the integration of the receivedsignal rk(t) multiplied by the orthonormal basicfunction ψ(t).

yk =1

Tb

∫ Tb

0rk(t)ψ

∗(t)dt (3.22)

The integration is done over the bit period, so thedecision variable takes the average of the desiredand the noise signals over that period. If morethan one sample of the received signal is used inthe average calculation, the signal to noise ratioat the output of the correlator will be smallerthan the signal to noise ratio at the input of thecorrelator. To use more than one sample of the re-ceived signal, it should be oversampled by a sam-ple frequency equals to

Fs = NRb (3.23)

N is the number of samples per bit and Rb isthe data bit rate. By over sampling the receivedsignal and taking the average of these samples,the decision variable will get closer to the desiredsignal value and the noise samples average willget closer to the statistical noise mean which iszero.


Figure (1) shows the power spectrum densityof the base band channel noise signal and thepower spectrum density of the average noise sam-ples that affects on the decision variable. Thechannel noise samples have a constant power atthe input of the correlator detector.

In Figure (1(a)), the channel noise bandwidthequals fs. For the case of single sample detection,the sampling frequency equals to the bit rate Rb.The channel noise power is equal to the decisionvariable noise power.

Pdn = Pcn =

∫ Rb/2

−Rb/2Ncn(f)df

= NoRb, fs = Rb (3.24)

No Nois the channel noise power spectrum den-sity value. On the other hand, if N samples areused in the detection process, the sampling fre-quency will equal to NRb as shown in equation(3.23). Although the channel noise power is con-stant, the noise power spectrum density will bedecreased when the noise bandwidth is increaseddue to the averaging process of N noise sam-ples in the correlator to form the decision vari-able, therefore the decision variable noise powerin the signal bandwidth Rb will be smaller thanthe channel noise power.

Pdn =

∫ Rb/2

−Rb/2Ncn(f)df = NoRb (3.25)

N′o =

No

N(3.26)

The performance of binary signaling systems inwhite noise channel is controlled by the signal tonoise ratio of the decision variable. This ratiodiffers from the channel signal to noise ratio atthe input of the detector. The channel signal tonoise ratio is defined as

SNRC=Signal power

Channel noise power=Ps

Pcn(3.27)

The signal power is related to the bit energy as

Ps = EbRb, Eb =

∫ Tb

0|p(t)|2dt (3.28)

p(t) is the bit pulse shape. The channel signalto noise ratio is related to the decision variablesignal to noise ratio by the following equation.

SNRc=EbRb

NoRb/N=N

Eb

No=N SNRc (3.29)

In all classical communication literatures, thechannel signal to noise ratio is used as the de-cision variable signal to noise ratio assuming thatthe receiver front end before the detector is noisefree. This is true if the detector forms the decisionvariable by observing only one sample during thebit interval. But this is not the case of the corre-lator detector which forms the decision variableby integrating the multiplication between the re-ceived signal with a suitable basics orthonormalfunction over the symbol interval.

4 Adding the oversampling gaineffect on the expression of theBPSK system probability oferror

We areready nowto add a correction factor in theequation of the probability of error in BPSK sys-tem when the channel SNR is used. This cor-rection factor represents the oversampling gainthat is achieved by oversampling the received sig-nal and averaging the noise samples during thesymbol period. The classical probability of errorequation of BPSK system is:

Pe =1

2erfc

(√Eb

No

)(4.30)

This equation relates the system probability of er-ror with the channel SNR where No is the powerspectrum density of the channel noise and Eb isthe transmitted signal energy per bit. Howeveraccording to the previous discussion this is onlytrue if single sample of the received signal is usedin the calculation of the decision variable. On theother hand, if N samples of the received signal areused, the decision variable SNR will be increasedby a factor of N. This factor is the oversamplinggain which represents the number of the samplesof the received signal per symbol period. Con-sequently, the proposed probability of error forBPSK will depend on the decision variable SNRinstead of the channel SNR as shown in the fol-lowing equation:

Pe =1

2erfc

(√Eb

Nd

)(4.31)

Eb/Nd is the decision variable SNR. This equa-tion relates the probability of error to the deci-sion variable signal instead of the channel signal.


Equation (4.31 can be written as a function of thechannel SNR but after adding the oversamplinggain which is the number of samples per symbolperiod.

Pe =1

2erfc

(√NEb

No

)(4.32)

Before the equation (4.32), there were two meth-ods to decrease the probability of error in the re-ceived bit stream. The first method is increasingthe energy per bit which means more power mustbe transmitted or lower bit rate should be used.The second method is decreasing the noise powerspectrum density which depends on the physicalnature of the channel and in many cases it is verydifficult to do this.

Now and according to the equation (4.32),there is a third method to increase the signal tonoise ratio and decreasing the probability of er-ror. This method is by over sampling the receivedvector and using more than one sample in thecalculation of the decision variable. This methodwill complicate the calculations in the detectionprocess but it will save the transmitted power andthe used bit rate.

The gain in the SNR that is achieved by over-sampling the received signal is similar to the pro-cess gain that is achieved in DSSS-BPSK system.In DSSS receiver, the decision variable is formedby integrating the received data multiplied by thespreading code. Here the received signal is sam-pled by the code rate which equals to the spread-ing rate. The channel noise will be sampled bythe same rate, so more than one sample of thenoise will be taken during the bit interval if a sin-gle noise sample is taken during the chip period.The correlator in the detector will average N sam-ples of the received signals and this will lead to anenhancement of the system performance. The en-hancement in performance is due to the averagingof the channel noise samples where the varianceof the average is smaller than the variance of thechannel noise samples by the process gain.

5 Simulations

The simulation results of the previous researches[1, 2, 3, 4, 5, 6, 7] are not shown here because oftwo reasons. The first is that most of these re-searches apply their ideas on the voice and videosignals and when we apply them on a noisy BPSK

system they gave a little and in some cases noenhancement. The second reason is that thesealgorithms fall to work if the noise power is highand the SNR is below a certain threshold. Onthe other hand, our algorithm works for any SNRvalue and it has a linear SNR gain as show in Sec-tion (5.3).

The simulation results of the proposed ideasthat are discussed in this paper are representedin three subsections. The first subsection dis-cusses the relation between the variance of thewhite noise and the color noise and how the noisebandwidth affects the value of the noise powerand power spectrum density. The second subsec-tion shows the difference between the probabil-ity density functions of the channel noise and thedecision variable noise. The last section presentsthe application of the proposed ideas on the wellknown system which is the binary shift keyingsystem.

Figure 1: (a) The PSD of the channel noisesamples (b) The PSD of the decision variablesamples

5.1 Variance of the white noise and thecolor noise

AAny white noise has a fixed power spectrumdensity but the power of the white noise is in-finity because its bandwidth is infinity. On theother hand, if the channel noise is sampled witha sampling frequency of Fs, the noise bandwidthBcw will be bounded by Fi/2 as shown in equa-tion (5.33).

0 ≤ Bcw ≤ Fs

2(5.33)


0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Frequency

Figure 2: The power spectrum density ofthe samples of white noise signal

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Frequency

Figure 3: The power spectrum density ofthe samples of white noise signal

The noise samples of the white noise signal willin this case have a fixed power. The varianceof these samples which represents the power ofthe white noise samples will equal to the powerspectrum density of the noise multiplied by thesampling frequency.

σ2w = 2BcwNo

2= NoFs

(5.34)

∵ No =σ2wFs

(5.35)

This is the relation between the white noise powerand the power spectrum density which is depend-ing on the sampling frequency. Figure (2) showsthe power spectrum density of a vector of 106

white noise samples with 10dB variance whichis generated using MATLAB.

−5 0 5 10 15w

N=1N=10N=50N=100

Figure 4: The PDF of the decision variablenoise for the case of white Gaussian noisechannel

0 0.5 1w

0 0.2 0.4 0.6 0.8 1−100

−80

−60

−40

−20

0

20

40

Frequency

Po

we

r S

pe

ctr

um

Ma

gn

itu

de

(d

B)

N=1N=10N=50N=100

Figure 5: (a) The PDF of the decision vari-able noise for the case of color Gaussian noisechannel (b) The PSD of the used color noise

The noise power spectrum density is a fixedparameter of any communication channel. It isalways a constant value according to the noiseactivities in the channel. On the other hand, thenoise samples that are processed by the receiverwill have a fixed power which equals to the noisepower spectrum density multiplied by the sam-pling frequency at the input of the receiver asshown by be equation (5.34).

If a color noise with the same power is gener-ated by passing the previous white noise vectorthrough any linear filter, the resultant color noisepower spectrum density should be increased asshown in Figure (3) because the noise power isfixed. Here the normalized color noise bandwidthis 0.2.

From the previous figures, due to the fact that


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Figure 6: (a) The BER of BPSK detectorin WGN channel (b) The BER of BPSK de-tector in CGN channel

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Figure 7: (a) The BER of BPSK detectorversus the number of samples in WGN chan-nel (b) The BER of BPSK detector versusthe number of samples in CGN channel

the received noise signal has a fixed power spec-trum density, the power of the noise will bechanged by changing the sampling frequency ofthe white noise signal or the noise bandwidth ofthe color noise.

5.2 Probability density functions ofthe channel noise and the decisionvariable noise

In this subsection the differences among the PDFsof the noise samples in the decision variable whichis formed by averaging of N noise samples areshown for different sampling frequencies. Figure(4) shows the PDFs of the decision variable forthe white Gaussian noise channel case with N=1,10,50, and 100 samples per symbol period. The

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Figure 8: (a) The DVSNR versus the CSNRin WGN channel (b) The DVSNR versus theCSNR in CGN channel

variance of the noise in the decision variable willbe decreased when the number of samples in thesymbol period is increased. This result is alsoachieved with color Gaussian noise channel al-though the noise samples are correlated. Figure(5(a)) shows the PDFs of the decision variablefor color noise channel with N= 1, 10, 50 and 100samples per symbol period. Figure (5(b)) showsthe PSD of this channel noise.

5.3 Probability of error in the BPSKusing the new idea

Here the simulation results of the detection of aBPSK signal which is corrupted by a white andcolor Gaussian noise are represented. In whitenoise case, the channel signal to noise power ra-tio (CSNR) is varied from -20 dB to 10 dB butin color noise, the CSNR is varied from -13dB to9dB. The bit error rate in a vector of 107receivedbinary symbols is calculated each time. Figures(6(a)) and (6(b)) show the bit error rate in the re-ceived data vector versus the CSNR for the whiteand the color noise channel cases respectively.The decision variable of the correlator detector isformed based on the averaging of different num-bers of samples per symbol period. The cases ofa single received sample, 10 received samples, 50received samples, and 100 received samples persymbol period are shown in these figures. It isclear that the noise performance is enhanced asthe number of samples per symbol period is in-creased. The rate of performance enhancement inthe white noise channel is better than the rate of


enhancement in the color noise channel becausethe color noise samples are correlated.

Figures (7(a)) and (7(b)) show the plot of thebit error rate in the received data versus the num-ber of samples per symbol period at certain chan-nel signal to noise ratio values. These figuresshow that the performance enhancement is notlinear with the number of samples per symbolperiod. The bit error rate will asymptoticallyapproach to zero as the number of samples persymbol period approaches to infinity which agreeswith the theoretical study. Figures (8(a)) and(8(b)) show also the relation between the chan-nel signal to noise ratio (CSNR) and the deci-sion variable signal to noise ratio (DVSNR). In-creasing the number of samples in the averagingprocess to form the decision variable each symbolperiod will increase the decision variable SNR be-cause the average process will decrease the vari-ance of the noise samples and hence it will de-crease the noise power spectrum density.

The increasing in the decision variable SNR inwhite noise case is greater than the increasing inthe decision variable SNR in color noise case forthe same reason of the correlation between thenoise samples in the color noise case. Also thefigure shows that the enhancement in the DVSNRis nonlinear with the increasing of the number ofsamples in per symbol interval.

6 Conclusion

The noise performance in digital receivers can beenhanced by oversampling the received signal andcalculating the time average of the correlator out-put based on more than one sample in the deci-sion variable. This enhancement can be consid-ered as the oversampling gain effect in the de-cision variable. The time average will approachto the desired signal value where the noise aver-age will approach to zero. The noise power inthe signal bandwidth will be decreased by a fac-tor equals to the number of the samples on thesymbol period that will be used in the averagingprocess. The decrement of the noise power in thedecision variable will increase the decision vari-able signal to noise ratio and this will enhance thesystem probability of error. This enhancement inthe probability of error needs neither more trans-mitted power nor increasing in the signal band-width but only it needs an increase in the pro-

cessing operations on the receiver. The noise per-formance enhancement that was discussed in thispaper is valid for both white noise and color noisecases where the performance enhancement in thewhite noise case is greater than the performanceenhancement in the color noise case.

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Ashraf Y. Hassan: received theB.Sc. degree (with honors) andthe M.S. degree in electrical en-gineering from, Benha university,Benha, Egypt, in 2000 and 2004,respectively, and the Ph.D. degreein Electronics and Electrical Com-

munications engineering from Cairo University,Cairo, in 2010. From 2000 to 2010, he served asa research and teaching assistant at the electricaltechnology department in Benha Faculty of En-gineering. At 2010, he employed as an assistantprofessor in electronics and communication engi-neering in the electrical engineering department.He works nine years as a researcher in the re-search and development center in Egyptian Tele-phone Company from 2000 to 2009. From 2012till now he works as a visitor assistant professor inNorthern Border University Faculty of Engineer-ing, Saudi Arabia. His current research interestsinclude detection and estimation theory, digitalcommunication systems, modeling of time vary-ing channels, interference cancellation techniques,signal processing, coding for high-data-rate wire-less and digital communications and modem de-sign for broadband systems.

Shaaban M. Shaaban: received theB.Sc. degree (with honors) in elec-trical engineering, M.SC. degree inengineering mathematics, and thePh.D. degree in engineering math-ematics from Menofia University,Shebin Elkom, Egypt in 2002, 2008

and 2010, respectively From 2004 to 2010, heserved as a research and teaching assistant atthe Basic Science Engineering department in She-bin Elkom Faculty of Engineering. At 2010, heemployed as an assistant professor in engineer-ing mathematics in Basic Science Engineering de-partment. His current research interests includerough set theory, fuzzy mathematics, data min-ing, fault diagnosis and operations research.

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