Lecture 10 Passband Modulation Techniques

College of Telecommunication – MCSNational University of Sciences and

Technology - NUST

Instructor: Dr. M. Arif [email protected]

AdvanceDigital Communications

mailto:[email protected]

206:35 PM

What are we studying ?

Adv Digital Comm - Dr. M. Arif Wahla

Digital Communications Systems

• Base Band Modulation Schemes Sampling (PAM) . . . Baseband & Bandpass

Systems Quantization (PCM) . . . Uniform and Non-

uniform PCM Waveforms . . . Line Coding Time Division Multiplexing T1/E1 Standards

Baseband Detection/Demodulation Matched Filter and Correlators Threshold Detection ISI and Equalization• Band pass Modulation Techniques

306:35 PMAdv Digital Comm - Dr. M. Arif Wahla

ModulationModulation is the process of facilitating the transfer of information over a medium

Amplitude Shift Keying (ASK)

Frequency Shift Keying (FSK)

Phase Shift Keying (PSK)

On-Off Keying (OOK)

Ai

0( ) ( ) cos[ ( ) cos[ ( )] General forms t A t t A t t t


The study of signal spaces provides us with a geometric method of conceptualizing the modulation process.

Signal Spaces

In a physical space when we describe a vector by its coordinates (x, y); the vector is being described by a linear combination of two functions (1, 0) and (0, 1).

Any vector can be written as a linear combination of these two functions. These functions are called ‘Basis functions’ and are orthogonal to each other.

Basis functions should

Have unit energyshould be orthogonal to

every other function


Basis Functions

An important example of terrific basis functions is the pair of sine and cosine waves of unit amplitude. This special basis set is used as carriers in all real communications systems.

Sine and cosine, two orthogonal functions are the basis set for all modern communications

Sine Cosine


Basis FunctionsThe concept of I and Q Channels

I and Q projections Polar form


Binary Phase Shift Keying (BPSK) modulationLet’s give these two symbols names of s1 and s2. Simplest thing is to have the symbol stand for just one bit. We define two little packets of the cosine wave, one with zero phase and second one with a 180 degree different phase.

Symbol Energy =


Creating a BPSK carrierA bit sequence 0111 0101 0010 1011

s1 s2 s2 s2 s1 s2 s1 s2 s1 s1 s2 s1 s2 s1 s2 s2

16 symbols are required since each BPSK symbol stands for one bit

What is a transition?


Quadrature Phase Shift Keying (QPSK) modulationThe dimensionality of a modulation is defined by the number of basis functions used.Therefore, QPSK a two-dimensional signal. Not because it sends two bits per symbol,but because it uses two independent signals (a sine and a cosine) to create the symbols.

QPSK signal is an extension of the BPSK signal. Both of these are a type of M-ary signals.

M = 2, makes this a BPSK, M = 4 is QPSK, M = 8, 8PSK and so on.

M-PSK modulations, a. BPSK, b. QPSK, c. also QPSK, d. 8PSK

2 2 ( 1)( ) cos , 0 , 0,1,2,.... 1i c

E is t t t T and i M

T M

• Analytical expression can be written as

where– m(t) = transmitting signal pulse shape– A = amplitude of the signal– = carrier phase

• The range of the carrier phase can be determined using

• For a rectangular pulse, we obtain

( ) ( ) cos[ ( )], 0 , 1, 2,....,i c i bs t Am t t t t T i M

2( ) , 0 ;m t t T and assume A E

T

2 ( 1)( ) 0,.... 1i

it i M

M

Adv Digital Comm - Dr. M. Arif Wahla 1006:35 PM

2 2 ( 1)( ) cos , 0 , 0,1,2,.... 1i c


T M

• We can now write the analytical expression as

• In PSK the carrier phase changes abruptly at the beginning of each signal interval while the amplitude remains constant

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carrier phase changes abruptly at the beginning of each signal interval

Constant envelope

2 2 ( 1)( ) cos , 0 , 0,1,2,.... 1i c


T M


• Also can be written as

• Furthermore, si(t) may be represented as a linear combination of two orthogonal functions ψ1(t) and ψ2(t) as follows

Where

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M

it

T

Ets ci

)1(2cos

2)(

2 2 ( 1) 2 ( 1)cos cos sin sinc c

E i it t

T M M

)()1(2

sin)()1(2

cos)( 21 tM

iEt

M

iEtsi

]sin[2

)(]cos[2

)( 21 tT

tandtT

t cc


• Using the concept of the orthogonal basis function, we can represent PSK signals as a two dimensional vector

• For M-ary phase modulation M = 2k, where k is the number of information bits per transmitted symbol

• In an M-ary system, one of M ≥ 2 possible symbols, s1(t), …, sm(t), is transmitted during each Ts-second signaling interval

• The mapping or assignment of k information bits into M = 2k possible phases may be done in many ways, e.g. for M = 4

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1 2

2 ( 1) 2 ( 1)( ) cos , sini

i is t E E

M M


• A preferred assignment is to use “Gray code” in which adjacent phases differ by only one binary digit such that only a single bit error occurs in a k-bit sequence

• It is also possible to transmit data encoded as the phase change (phase difference) between consecutive symbols– This technique is known as Differential PSK (DPSK)

• There is no non-coherent detection equivalent for PSK

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𝜙𝜙4


• Two BPSK in phase quadrature• QPSK (or 4PSK) is a modulation technique that transmits 2-bit of

information using 4 states of phases• For example

• General expression:

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2-bit Information ø

00 0

01 π/2

10 π

11 3π/2

Each symbol corresponds

to two bits

scs

sQPSK Tti

M

itf

T

Ets

04,3,2,1,)1(2

2cos2

)(



M-ary PSK modulation . . .

Modulation equation called the quadrature form

• So a phase modulated signal is a combination of two quadrature signals, the amplitude of which changes in response to the phase change. The modulating signal can be seen as a vector with I and Q as its x and y components

• We need a way to create a signal packet of a particular phase when needed out of a free-running sine or cosine. This is where Quadrature Modulation with I and Q channels come into play. • I and Q channels are not just concepts but also how modulators are designed. However, the signal created by I and Q channels is not what is transmitted, it is the sum or the difference (makes no difference as long the polar form is consistent) of these two, and that is the real modulated signal.

1 2

2 ( 1) 2 ( 1)( ) cos , sini

i is t E E

M M


M-ary PSK modulation . . .How the bits are mapped to the possible phases ?Number the bits such a way that each adjacent phase means just one bit difference. So that when a phase mistake is made and the most likely one is the nearest phase, then only one bit is decoded incorrectly. This is called Gray coding.



Constellation diagram


0 3 2 0 3 3 2

1 -1 1 1 -1 -1 1

1 -1 -1 1 -1 -1 -1




The quadrature form of modulation using I and Q channels


8 PSK modulation . . .


16 QAMIn PSK all points lie on a circle so the I and Q values are related to each other. PSK signals are constant envelope and all points have the same amplitude. If we allow the amplitude to change from symbol to symbol, then we get a modulation called Quadrature amplitude modulation (QAM).

M = 16, so that we have 16 symbols, eachrepresenting a four bit word

The signal points lie in rectangle instead of a circle

1 2

2 ( 1) 2 ( 1)( ) cos , sini

i is t E E

M M


16 QAM . . .


3

3

-3

31 3

-3

1

-1 -3 -3

1

-1 -3

16 QAM . . .

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Amplitude Shift Keying

• Modulation Process– In Amplitude Shift Keying (ASK),

the amplitude of the carrier is switched between two (or more) levels according to the digital data

– For BASK (also called ON-OFF Keying (OOK)), one and zero are represented by two amplitude levels A1 and A0

cos( ), 0 1( )

0, 0 0i o

i

A t t T binarys t

t T binary

0( ) ( ) cos[ ( ) cos[ ( )] General forms t A t t A t t t

• Adv Digital Comm - Dr. M. Arif Wahla

2606:35 PM

• 4.2.4 ASK - Analytical Expression:

where Ai = peak amplitude

Hence,

where

)cos(2)cos(2)cos()( 02

00 tAtAtAtsrmsrms

0 0

22 cos( ) cos( )

EP t t

T

0

2 ( )cos( ), 0 1

( ) , 1,2,......

0, 0 0

i

i

E tt t T binary

s t i MTt T binary

1,......2,0,)(0

2 MidttsET

i

cos( ), 0 1( )

0, 0 0i o

i

A t t T binarys t

t T binary


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• Where for binary ASK (also known as ON OFF Keying (OOK))

• Mathematical ASK Signal Representation– The complex envelope of an ASK signal is:

– The magnitude and phase of an ASK signal are:

– The in-phase and quadrature components are:

the quadrature component is wasted.

1( ) ( ) cos( ), 0 1o os t A m t t t T binary

( ) ( )og t A m t

00,0)(0 binaryTtts

( ) ( ), ( ) 0oA t A m t t

( ) ( )ox t A m t

,0)( ty


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• It can be seen that thebandwidth of ASK

modulated is twice thatoccupied by the source

baseband stream

• Bandwidth of ASK– Bandwidth of ASK can be found from its power spectral density– The bandwidth of an ASK signal is twice that of the unipolar NRZ line

code used to create it., i.e.,

• This is the null-to-null bandwidth of ASKb

b TRB

22


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• If raised cosine rolloff pulse shaping is used, then the bandwidth is:

• Spectral efficiency of ASK is half that of a baseband unipolar NRZ line code– This is because the quadrature component is wasted

• 95% energy bandwidth

2(1 ) bB r R

bb

RT

B 33


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4.2.3 Frequency Shift Keying (FSK)

• In FSK, the instantaneous carrier frequency is switched between 2 or more levels according to the baseband digital data– data bits select a carrier at one of two frequencies– the data is encoded in the frequency

• Until recently, FSK has been the most widely used form of digital modulation;Why?– Simple both to generate and detect– Insensitive to amplitude fluctuations in the channel

• FSK conveys the data using distinct carrier frequencies to represent symbol states• An important property of FSK is that the amplitude of the modulated wave is

constant• Waveform

2( ) cos( ), 1,....i i

Es t t i M

T


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Binary FSK

• In BFSK, 2 different frequencies, f1 and f2 = f1 + ∆ f are used to transmit binary information

• Data is encoded in the frequencies• That is, m(t) is used to select between 2 frequencies:• f1 is the mark frequency, and f2 is the space frequency

0 1

2( ) cos 2 ( ), 0b

bb

Es t f t T

T

1 2

2( ) cos 2 ( ), 0b

bb

Es t f t T

T

𝜙𝜙


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1

2

cos( ), ( ) 1 1( )

cos( ), ( ) 1 0c n

c n

A t when m t or Xs t

A t when m t or X

• Binary Orthogonal Phase FSK

• When w1 an w2 are chosen so that f1(t) and f2(t) are orthogonal, i.e.,

– form a set of K = 2 basis orthonormal basis functions1 2( ) ( ) 0t t

𝜙

𝜙

2 ( )t¿ ¿

¿ ¿


% Matlab script for generating FM via Phase modulation

clear all;close all;

t0=.15; % signal duration

ts=0.0005; % sampling interval

fc=200; % carrier frequency

kf=100; % Modulation index

fs=1/ts; % sampling frequency

t=[0:ts:t0]; % time vector

df=0.25; % required frequency resolution

%message signal

m=[ones(1,t0/(3*ts)),-1*ones(1,t0/(3*ts)),ones(1,t0/(3*ts)+1)];

int_m(1)=0;

for i=1:length(t)-1 % Integral of m

int_m(i+1)=int_m(i)+m(i)*ts;

end

u=cos(2*pi*fc*t+2*pi*kf*int_m); % phase modulating with the % integral of the signal


0 0.05 0.1 0.15-1

-0.5

0

0.5

1

The message signal

0 0.05 0.1 0.15

-1

-0.5

0

0.5

1

Time

The modulated signal


Lecture 10 Passband Modulation Techniques

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