BER PERFORMANCE OF BPSK AND QPSK OVER RAYLEIGH …

12

Int. J. Elec&Electr.Eng&Telecoms. 2014 Rajani Katiyar et al., 2014

BER PERFORMANCE OF BPSK AND QPSK OVERRAYLEIGH CHANNEL AND AWGN

CHANNEL

Abdul Haq N1, Rajani Katiyar1* and Padmaja K V2

*Corresponding Author: Rajani Katiyar, [email protected]

Fading problem is a major impairment of the wireless communication channel. To mitigate thefading and to have reliable communications in wireless channel, coding technique is oftenemployed. In this paper it is the comparisons of BPSK and QPSK over Rayleigh Channel andAWGN channel in terms of bit error rate.

Keywords: Fading problem, Wireless communication, Coding technique, BER performance

INTRODUCTIONBPSK is the simplest form of Phase ShiftKeying (PSK). It uses two phases which areseparated by 180° and so can also be termed2-PSK. It does not particularly matter exactlywhere the constellation points are positioned.This modulation technique is the most robustof all PSKs since it takes the highest level ofnoise or distortion to make the demodulatorreach an incorrect decision. QPSK is knownas quaternary PSK, quadriphase PSK, 4-PSK,or 4-QAM. QPSK uses four points on theconstellation diagram, equispaced around acircle. With four phases, QPSK can encodetwo bits per symbol. The mathematicalanalysis shows that QPSK can be used either

ISSN 2319 – 2518 www.ijeetc.comVol. 3, No. 2, April 2014

© 2014 IJEETC. All Rights Reserved

Int. J. Elec&Electr.Eng&Telecoms. 2014

1 Electronics and Communication, R.V.C.E., Bangalore, India.2 Instrumentation Department, R.V.C.E., Bangalore, India.

to double the data rate compared with a BPSKsystem while maintaining the same bandwidthof the signal, or to maintain the data-rate ofBPSK but halving the bandwidth needed.

In telecommunication transmission, the BitError Rate (BER) is the percentage of bits thathave errors relative to the total number of bitsreceived in a transmission, usually expressedas ten to a negative power. For example, atransmission might have a BER of 10 -6

meaning that, out of 1,000,000 bitstransmitted, one bit was in error. The BER isan indication of how often a packet or otherdata unit has to be retransmitted because ofan error. Too high a BER may indicate that aslower data rate would actually improve overall

Research Paper

13


transmission time for a given amount oftransmitted data since the BER might bereduced, lowering the number of packets thathad to be resent.

Rayleigh Fading ModelThe phase of each path can change by 2

radian when the delay Tn(t) changes bycf1

. If fcis large, relative small motions in the mediumcan cause change of 2radians. Since thedistance between the devices are much largerthan the wavelength of the carrier frequency, itis reasonable to assume that the phase isuniformly distributed between 0 and 2radians and the phases of each path areindependent. When there are large numbersof paths, applying Central Limit Theorem, eachpath can be modeled as circularly symmetriccomplex Gaussian random variable with timeas the variable. This model is called Rayleighfading channel model.

Additive White Gaussian NoiseThe transmitted waveform gets corrupted bynoise ‘n’, typically referred to as AdditiveWhite Gaussian Noise (AWGN). Incommunications, the AWGN channel model isone in which the only impairment is the linearaddition of wideband or white noise with aconstant spectral density (expressed as wattsper hertz of bandwidth) and a Gaussiandistribution of amplitude. The model does notaccount for the phenomena of fading,frequency selectivity, interference, nonlinearityor dispersion. However, it produces simple,tractable mathematical models which areuseful for gaining insight into the underlyingbehavior of a system before these otherphenomena are considered. AWGN is

commonly used to simulate background noiseof the channel under study, in addition tomultipath, terrain blocking, interference, groundclutter and self-interference that modern radiosystems encounter in terrestrial operation.

BER for BPSK in Rayleigh FadingChannelThe previous chapter the discussion aboutBER (bit error rate) for BPSK modulation in asimple AWGN channel has been presented.The present chapter deals with the BER forBPSK in a Rayleigh multipath channel. In abrief discussion on Rayleigh channel, wherewe stated that a circularly symmetric complexGaussian random variable is of the form

imre jhhh

where real and imaginary parts are zero meanindependent and identically distributedGaussian random variables with mean 0 andvariance 2. The magnitude |h|, which has aprobability density,

0,2

2

22

hehhPh

Figure 1: BER for BPSK Modulationin Rayleigh Channel

14


‘h’ is called a Rayleigh random variable. Thismodel, called Rayleigh fading channel model,is reasonable for an environment where therepresent a large number of reflectors.

Keying (BPSK), the binary digits 1 and 0maybe represented by the analog levels bE

and bE respectively. The system model isas shown in the Figure below.

The performance (Eb/N0 vs BER) of BPSKmodulation (with coherent detection) overRayleigh Fading channel and its comparisonover AWGN channel is discussed.

We first investigate the non-coherentdetection of BPSK over Rayleigh Fadingchannel and then we move on to the coherentdetection. For both the cases, we consider asimple flat fading Rayleigh channel (modelledas a single tap filter with complex impulseresponse h). The channel also adds AWGN

Figure 2: BER Probability Curvfor BPSK Modulation

BER for QPSK Over AWGNConsider that the alphabets used for a QPSK(4-QAM) is

jQPSK 11

BER for BPSK in AWGN Channel: Here,we will derive the theoretical equation for BitError Rate (BER) with Binary Phase ShiftKeying (BPSK) modulation scheme in AdditiveWhite Gaussian Noise (AWGN) channel. TheBER results obtained using Matlab simulationscripts show, good agreement with the derivedtheoretical results. With Binary Phase Shift Eb/N0 vs BER for BPSK over Rayleigh Channeland AWGN Channel.

Figure 3: Constellation Plot for QPSK(4-QAM) Constellation

Figure 4: QPSK Symbol Error ProbabiltyCurv for Eb/N0 vs BER for BPSK OverRayleigh Channel and AWGN Channel

15


noise to the signal samples after it suffers fromRayleigh Fading.

Figure 5: Eb/N0 BER Over Rayleighand AWGN Channel

Bit Error Rate (BER) versus Signal-to-Noise Ratio (SNR) over Rayleigh fadingchannel and the AWGN for QPSK modulationscheme.

simulated and evaluated for BPSK systems.Based on data generated by computersimulation of BPSK modulation techniques forBER calculation the following results areobtained. Bit Error Rate (BER) versus Signal-to-Noise ratio (SNR) over Rayleigh fadingchannel and the AWGN for BPSK modulationscheme.

CONCLUSIONIn case of BPSK as compared to the AWGNcase, around 25 dB degradation thus the studyof BPSK over Rayleigh Channel and AWGNchannel says that the amount of energyrequired for transmission over AWGN channelis lesser than the energy required fortransmission over Rayleigh channel. We alsoobserved that the BER for transmission overAWGN channel is lesser than that for Rayleighchannel. From our results, it is evident thatQPSK modulation is preferred in cases wherewe need to consider small amounts oftransmitting energy. The main reason is thatthe QPSK offers acceptable BER whiletransmitting signals of relatively low energy.This work further focuses on the ways toreduce BER and thus increase powerefficiency. This in turn, results in thetransmission of signals of specified quality witha smaller transmit power.

FUTURE WORKThe work in this project is Bit Error Rate andthe Eb/N0 vs BER for BPSK modulation overRayleigh Fading channel and the AWGN foruncoded signal. The future work is bit error rateand the Eb/N0 vs BER for BPSK modulationover Rayleigh Fading channel and the AWGNfor coded signal using convolution codes andThe Viterbi Algorithm.

Figure 6: BER for QPSK Modulationin Rayleigh Channel

SIMULATIONS RESULTThe simulations in this work are carried outusing MATLAB software. The performance is

16


REFERENCES1. Andrew J Viterbi (1967), “Error Bounds

for Convolutional Codes and anAsymptotically Optimum DecodingAlgorithm”, IEEE Transactions onInformation Theory, Vol. IT-13, April,pp. 260-269.

2. “BER Performance Analysis of a RealData Communication Through WiMAX-PHY Layer Over an AWGN and FadingChannels”, International Journal ofElectrical & Computer Sciences IJECS-IJENS, Vol. 10, No. 04, p. 13.

3. Bernard Sklar (1997), “Rayleigh FadingChannel in Mobile DigitalCommunication System Part 1:Characterization”, IEEE CommunicationMagazine, July , pp. 90-100.

4. Dennis Roddy and John Coolen (2003),Electronics Communications, 4th Edition,Prentice-Hall of India, New Delhi.

5. John Proakis (2007), DigitalCommunication, 5th Edition, McGraw-HillScience/Engineering/Math.

6. Jon W Mark and Weihua Zhuang (2005),“Wireless Communications andNetworking”, Prentice-Hall India, NewDelhi.

7. Mclane P J, Wittke P H, Mo P K and LooC (1988), “PSK and DPSK Trellis Codesfor Fast Fading, Shadowed MobileSatellite Communication Channels”, IEEETransactions on Communications ,Vol. 36, No. 11.

8. Simon Haykin (1988), “DigitalCommunication”, Wiley, India.

9. Theodore S Rappaport (2002), WirelessCommunication: Principle and Practice,2nd Edition, Pearson EducationalInternational.

Documents

BER PERFORMANCE OF BPSK AND QPSK OVER RAYLEIGH …