Ceyhan Kasap Presentation

7/30/2019 Ceyhan Kasap Presentation

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PERFORMANCE ANALYSIS

OF VARIOUS DIGITALMODULATION METHODSFOR DIGITAL

COMMUNICATIONS

Prepared by :

Ceyhan Kasap 2007704389


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Agenda

INTRODUCTION

DIGITAL MODULATION BASICS

DIGITAL MODULATION METHODS Pulse Amplitude Modulation (PAM) Phase Modulated Signals (Phase Shift Keying) (PSK) Quadrature Amplitude Modulated Signals (QAM)

OPTIMUM RECEIVERS FOR DIGITAL MODULATION FORADDITIVE WHITE GAUSSIAN NOISE CHANNELS

Optimum Correlation Receiver

SIMULATIONS

SIMULATION RESULTS

CONCLUSIONS


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INTRODUCTION Communication system: a composite system

of subunits that make the exchange ofinformation possible between two or more

parties.


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Source:message originator

Transmitter unit: modifies the message signal forefficient transmission

Channel: the physical medium, through whichthe message signal is sent to the destination.

Receiver: message destination


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The main problem of all communication systems:The message signal attenuated or contaminated bynoise through transmission process on the channel.

The ultimate goal of every communicationsystemis to eliminate the noise and attenuation effectsin order to guarantee reliable exchange of information.

If there was no noise or channel attenuation, there

would be no need for telecommunication engineers!!!


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Digital communicationsrefers to the transmission ofa sequence of digital messages (a bit stream) or adigitized analog signal.

The messages are represented by a limited set ofanalogue wave forms, using a digital modulationmethod .

Digital modulation is the key to todays

high speed data transfer


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DIGITAL MODULATION BASICSIn simplest terms, an M-ary digital modulator

takes k bits of information and maps them toone of the M possible analog waveforms. In thatsense modulation is a mapping from the bits toanalog waveforms. These M waveforms areusually chosen by modulating either theamplitude, frequency or a hybrid combination ofthe two

Un

{ 0 1 0 0 0 . }

Incoming bits are

grouped into blocks of k

bits

SERIAL TO

PARALEL

CONVERTER

SYMBOL LEVEL

MAPPER

Un_1

Un_2

Un_k-1

Un_k

MODULATOR


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Usually the modulators that are used in practice arequite complex. Generally non-linear modulators withmemory are used. For example the European digital

cellular communication system, named GSM (GlobalSystem for Mobile communications), uses Gaussianminimum shift keying type modulation which is a non-linear modulation method

To understand the basic principles of digital modulation;we will examine linear, memoryless modulation methodsin this project


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DIGITAL MODULATION

METHODSa) Pulse Amplitude Modulation (PAM) In pulse amplitude modulation, the M-ary pulse

amplitude modulator output is one of the M possiblewaveforms, each differing from each other in their

discrete amplitudes.

For PAM, the m-th signal waveform defined for aduration of time period T may be represented as:


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An orthogonal signal expansion on the amplitudemodulated signals reveals that the set has dimensionality

of 1 (A single function spans the whole set)

Ex:The constellation diagram(*) for a digital PAM with M = 4

(*)Constellation diagram: The representation of a signal modulated by acertain digital modulation scheme


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Time domain representation of a pulse amplitudemodulated signal

Note the change in the amplitude of the carrier (modulated signal) as themodulating digital data sequence changes


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b) Phase Modulated Signals (Phase ShiftKeying) (PSK)

In phase shift keying, the M-ary pulse amplitude modulator outputis one of the M possible waveforms, each differing from each otherin their discrete phases.(It is the phase of the carrier that ismodulated)

For PSK, the m-th signal waveform defined for a duration of timeperiod T may be represented as:


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An orthogonal signal expansion on phase modulatedsignals reveals that the set has dimensionality of 2 (One

for the sine term and onether one for the cosine term)

Ex:The constellation diagram for a digital PSK with M = 8


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Time domain representation of a phase modulatedsignal

Note the abrupt change in the phase of the carrier (shown in gray) as themodulating signal (shown in blue) changes


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c) Quadrature Amplitude Modulated Signals(QAM)

It is possible to employ PAM on both a cosine and a sine signal so as toincrease the overall bandwidth efficiency. This is achieved bysimultaneously impressing two seperate k-bit symbols from informationsequence an on two quadrature carriers cos 2fct and sin 2fct. Theresulting modulation technique is called QAM (In some literature QAM is

also called quadrature PAM) .

For QAM, the m-th signal waveform defined for a duration of timeperiod T may be represented as:


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An orthogonal signal expansion on QAM modulated signalsreveals that the set has dimensionality of 2

Ex:The constellation diagram for a digital QAM with M = 16


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QAM signal waveforms may also be viewed as acombined amplitude and phase modulation.

This is apparent if we express the signalwaveforms as:

This means, we may select any combination of M1- levelPAM and M2- level PSK to construct an M = M1 . M2combined PAM-PSK constellation. This is actually anotherform for representation of the QAM signals.

OPTIMUM RECEIVERS FOR DIGITAL


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OPTIMUM RECEIVERS FOR DIGITALMODULATION FOR ADDITIVE

WHITEGAUSSIAN NOISE CHANNEL

Noise is present in every communication processand that is the actual reason for using digitalmodulation.

Since noise is not a deterministic phenomena,

statistical methods and models must be used todeal with it


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The noise sources in the communication channel such asthe magnetic effects of the electronic circuitry at the

transmitter and receiver, the weather conditions for thewireless channels and etc are many and and independent ofeach other.

The central limit theorem states that the sum of many

independent random variables converges to a gaussiandistribution. This permits us to model the total noise by aGaussian distribution.


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Optimum Correlation

Receiver The function of the receiver is to separate the signal content

from the noise content. For this reason the receiver isseparated into two blocks. The first block demodulates thereceived signal according to the modulation scheme usedand the second block makes a decision on the demodulatedsignal.

FIRST BLOCK>>In order to demodulate the received signal,the receiver first converts the received waveform r(t) into Ndimensional vector r where N is the dimensionality of thetransmitted signal waveforms (For example N=1 for PAM and

N=2 for PSK and QAM)


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SECOND BLOCK BLOCK>> The detector block aims tomake a decision on the transmitted signal in each signal

interval based on the observation of the vector r in eachinterval such that the probability of a correct decision ismaximized.

In other words, the detector bases its decision on theposterior probabilities

Prob( signal sm was transmitted| r), for m = 1, 2, . . . ,M

and chooses the one with maximum probability.


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Gaussanity assumption enables to determine theprobabilities and to make a decision based on the

minimum distance metric.

The Block Diagram of an Optimum Correlation Receiver


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For simulations, several digital modulationmethods are implemented in MATLAB code.

In the transmitter end, the modulation

methods of pulse amplitude modulation, phaseshift keying and quadrature amplitudemodulation are implemented. For optimumdetection, a correlation type demodulator that

makes a decision based on the minimumdistance metric is used.

The channel noise is modeled as whiteGaussian noise

SIMULATIONS


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Simulations are run to obtain the simulated errorprobabilities of the modulation methods. In simulations,

the bit/symbol error probability performance of themodulation methods are measured at different signal tonoise ratios. The bit/symbol error-rate (BER/SER) aredefined as:


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In order to minimize symbol error for single bitdifferences, Gray encoding is utilized in all constellations.

The length of the simulations are arranged to be longenough to ensure a smooth BER curve reaching 10^(-6)

The simulation interval is arranged according to the

complexity of the simulations. For example thecomputational complexity of BPSK is low so an SNRinterval of 0.5 dB is chosen for it. On the other handcomputational complexity of QAM is much higher so anSNR interval of 2 dB is chosen for it.

Theoretical error probabilities are also calculated for eachscheme


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SIMULATION RESULTS

a) BPSK Modulation (PAM with M=2)


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b) QPSK Modulation (PSK with M=4)


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c) 8PSK Modulation (PSK with M=8)


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d) 16QAM Modulation (QAM with M=16)


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COMPARISON OF THE IMPLEMENTED METHODS


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The above graph that puts all the simulated BER curves togetherfor all the implemented modulation methods, reveals that BPSK isbest in terms of error probability whereas 16-QAM is the worst. It

must also be noted that there is only a small difference betweenthe performances of BPSK and QPSK.

In terms of error probability the methods can be ordered from thebest to worst as follows:

BPSK>QPSK>8-PSK>16-QAM

However this does not necessarily mean that BPSK is thebest and 16QAM is the worst. When designing an actualsystem, all considerations like algorithm complexity,energy considerations and channel noise effects must betaken into account.


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In this work: Some of the widely used digital modulation methods are

introduced

The optimum demodulation techniques for these methods arepresented under Gaussian noise assumption

The performance analysis of the introduced digital modulationmethods are done using MATLAB

Final words:

Nearly all of todays state of the art communication systems usedigital communication. Digital modulation is an indispensable partof these systems.

It seems as if the academic interest on the area will continue atleast for a few more decades.

CONCLUSIONS


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Thank you !!!

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