dc digital communication part1
DESCRIPTION
A property of MVG_OMALLOORBy H V KumaraswamyTRANSCRIPT
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Digital communication
H V KUMARASWAMY
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Course: Digital Communication (EC61)
Course instructors:
1. Mr. H. V.KumaraSwamy, RVCE,Bangalore
2. Mr. P.Nagaraju, RVCE, Bangalore
3. Ms. M.N.Suma, BMSCE, Bangalore
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Digital Communication
TEXT BOOK:
Digital Communications
Author: Simon Haykin
Pub: John Wiley Student Edition, 2003
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Reference Books
1. “Digital and Analog Communication Systems” – K. Sam Shanmugam, John Wiley, 1996.
2. “An Introduction to Analog and Digital Communication”- Simon Haykin, John Wiley, 2003.
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Digital Communication- Topics
• Chapter 1: Introduction
• Chapter 2: Sampling Process
• Chapter 3: Waveform Coding Techniques
• Chapter 4: Base-band shaping
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Digital Communication- Topics
• Chapter 5: Digital Modulation Techniques
• Chapter 6: Detection and Estimation
• Chapter 7: Spread Spectrum Modulation.
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Communication System
The purpose of a Communication System is to transport an information bearing signal from a source to a user destination via a communication channel.
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MODEL OF A COMMUNICATION SYSTEM
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Basic Blocks
1. Transmitter
2. Channel
3. Receiver
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Communication
Types of Communication:
1. Analog Communication
2. Digital Communication
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DCS - Block diagram
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Digital Communication- Blocks
• Information Source
• Source Encoder and Decoder
• Channel Encoder and Decoder
• Modulator and Demodulator
• Channel
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Block diagram with additional blocks
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Additional Blocks
• Encryptor
• Decryptor
• Multiplexer
• Demultiplexer.
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Digital Communication- Advantages
• Less Distortion, Low noise & interference.
• Regenerative Repeaters can be used.
• Digital Circuits are more reliable.
• Hardware implementation is more flexible.
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Digital Communication- Advantages
• Secrecy of information.
• Low probability of error due to error detection and error correction.
• Multiplexing- ( TDM )
• Signal Jamming is avoided.
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Digital Communication- Disadvantages
• Large Bandwidth
• Synchronization
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Channels for Digital Communication
Channel Characteristics:
• Bandwidth
• Power
• Linear or Non-linear
• External interference
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Types of Channels
1. Telephone Channels
2. Coaxial Cables
3. Optical fibers
4. Microwave radio
5. Satellite Channel
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1. Telephone Channels
• Provides voice grade Communication.
• Good for data communication over long distances.
• Frequency range: 300Hz – 3400Hz.
• High SNR – about 30dB.
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1. Telephone Channels contd..
• Flat amplitude response for voice signals.
• For data & image transmissions EQUALIZERS are used.
• Transmission rate = 16.8kb/s
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2. Coaxial Cable
• Single-wire conductor inside an outer Conductor with dielectric between them.
• Wide Bandwidth
• Low external Interference.
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2. Coaxial Cable contd..
• Closely spaced Repeaters are required.
• Transmission rate = 274 Mb/s.
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3.Optical fibers
• Communication is by light rays.
• Fiber consists of Inner core and an outer core called CLADDING.
• Refractive Index of Cladding is less.
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3.Optical fibers
• Larger Bandwidth.
• Immune to cross talk and EMI.
• More secure.
• Low cost.
• Date rate = Terra bits/sec.
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4. Microwave radio
• Transmitter & Receiver With antennas.
• Works on Line-of-sight principle.
• Point to Multipoint communication.
• Reliable & High Speed of Transmission.
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4. Microwave Radio
• Operating Frequency - (1 – 30)GHz
• System Performance degrades due to meteorological variations.
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5. Satellite Channel.
• Repeater in the sky.
• Placed in geo-stationary orbit.
• Long distance transmission.
• High Bandwidth.
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5. Satellite Channel
• Operates in microwave frequency.
• Uplink frequency is more than down link frequency
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Topics in this session:– Geometric interpretation of signal– Response of bank of correlators to
noisy input– Detection of known signals in
noise
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Geometric interpretation of signal
Using N orthonormal basis functions we can represent M signals as
MiTttStSN
jjiji ,.....,2,10)()(
1
Coefficients are given by
Nj
MidtttSS j
T
iij
,.....,2,1
,.....,2,1)()(0
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Mi
S
S
S
S
iN
i
i
i ,.....,2,1
.
.
.2
1
Visualizing signal vectors as a set of M points in an N dimensional Euclidean space, which is also called signal space
The squared-length of any vector si is given by inner product
N
jijiii SSSS
1
22),(
The vector si is called signal vector
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Two vectors are orthogonal if their inner product is zero
The energy of the signal is given by
dttSET
ii )(0
2
T N
kkik
N
jjiji dttStSE
0 11
)]([)]([
T
kj
N
jik
N
kiji dtttSSE
01 1
)()(
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T
kj
N
jik
N
kiji dtttSSE
01 1
)()(
N
jiji SE
1
2
dttStS
SSSS
k
T
i
N
jkjijki
2
0
1
22
)]()([
)(
ki SS Is a Euclidean distance between vectors
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Response of bank of correlators
to noisy input
Mi
TttWtStX i
.,......3,2,1
0)()()(
Received Signal X(t) is given by
NjWS
dtttXX
jij
T
o
jj
,........2,1
)()(
W(t) is AWGN with Zero Mean and PSD N0/2
Output of each correlator
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T
jiij dtttSS0
)()(
First Component
Second Component
T
o
jj dtttWW )()(
N
jjj tXtXtX
1
)()()('
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N
i ij j jj=1
N
j jj=1
X'(t) =S (t)+W(t)- (S + W )φ (t)
= W(t)- W φ (t)
= W'(t)
N
j jj=1
N
j jj=1
X(t) = X φ (t)+X'(t)
= X φ (t)+W'(t)
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Mean and variance
ij
jij
jji
jjx
S
WES
WSE
XEm
][
][
][
][
])[(
][
2
2
2
j
ijj
jjx
WE
SXE
XVar
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T T2
x j j j
0 0
T T
j j
0 0
σ = E W(t)φ (t)dt W(u)φ (u)du
= E φ (t)φ (u)W(t)W(u) dtdu
T T2
x j j j
0 0
T T
j j w
0 0
σ = φ (t)φ (u)E[ W(t)W(u) ] dtdu
= φ (t)φ (u)R (t,u)dtdu
),( utRw = autocrrelation function
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)(2
),( 0 utN
utRw
T
j
T T
jjjx
dttN
dudtututN
0
20
0 0
02
)(2
)()()(2
jallforN
jx2
02
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kj
dtutN
dudtututN
dudtutRut
duuuWdtttWE
WWE
SXSiXE
mXmXEXXCov
kj
T
T T
kj
T T
wkj
T T
kj
kj
ikkjj
kxkjxjkj
0
)()(2
)()()(2
),()()(
)()()()(
][
)])([(
)])([(][
0
0
0 0
0
0 0
0 0
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Detection of known signals in
noise
Mi
TttwtStx i
.....,,.........3,2,1
0)()()(
MiwSx i ,,.........3,2,1
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Detection of known signals in noise
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Digital communication
H V KUMARASWAMY
Assistant Professor
Dept of Telecommunication & P G Studies
R V College of Engineering
Bangalore-59
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Topics to be coveredI Digital Carrier Modulation Schemes• Optimum receiver for Binary Modulation
Schemes• Binary ASK, PSK, FSK.
• Comparison of digital modulation schemes, • M-ary signaling schemes • Synchronization methods
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Topics to be covered (cont.)
II Detection and Estimation
Gram-Schmidt Orthogonalization procedure.
Geometric interpretation of signals. Response of bank of correlators to noisy
input. Detection of known signals in noise.
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Topics to be covered (cont.)
Probability of error.
Correlation receiver.
Matched filter receiver.
Detection of signals with unknown phase in noise.
Maximum likelihood estimation
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Topics in this session: Detection & Estimation
1 Model of digital communication system
2 Gram-schmidt orthogonalization procedure
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Fundamental Issues in digital communications
1.Detection
2.Estimation
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Detection theory deals with the design and evaluation of decision – making processor that observes the received signal and guesses which particular symbol was transmitted according to some set of rules.
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Estimation Theory deals with the design and evaluation of a processor that uses information in the received signal to extract estimates of physical parameters or waveforms of interest.
The results of detection and estimation are always subject to errors
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Model of digital communication system
Message source
Vectortransmitter
modulatorWaveformchannel
detectorVector
receiver
noise
Receiver
{mi} {Si} {Si(t)}
X(t)
X
Transmitter
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Model (cont..)Consider a source that emits one symbol every T
seconds, with the symbols belonging to an alphabet of M symbols which we denote
m1, m2, . . . . . . mM.
We assume that all M symbols of the alphabet are equally likely. Then
iallforM
emittedmPp ii
1
)(
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Mi
S
S
S
S
iN
i
i
i ,.....,2,1
.
.
.2
1
The output of the message source is presented to a vector transmitter producing vector of real number
Where the dimension N ≤ M.
The modulator then constructs a distinct signal si(t) of duration T seconds. The signal si(t) is necessarily of finite energy
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Channel: Channel is linear, with a bandwidth that is
large enough to accommodate the transmission of the modulator output si(t) without distortion.
The transmitted signal si(t) is perturbed by an additive, zero-mean, stationary, white, Gaussian noise process.
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GRAM – SCHMIDT ORTHOGONALIZATION
PROCEDURE:In case of Gram-Schmidt Orthogonalization procedure,
any set of ‘m’ energy signals {Si(t)} can be represented by a linear combination of ‘N’ orthonormal basis functions where N≤m. That is we may represent the given set of real valued energy signals S1(t), S2(t). . . . . . . Sm(t) each of duration T seconds in the form
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)(........)()()( 12121111 tStStStS NN
)(........)()()( 22221212 tStStStS NN
)(........)()()( 2211 tStStStS NmNmmm
mi
TttStS
N
jjiji ......3,2,1
0)()(
1
nj
mittStS
T
jiij ......3,2,1
.....3,2,1)()()(
0
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The co-efficient Sij may be viewed as the jth
element of the N – dimensional Vector Si
iN
i
i
i
S
S
S
S
'
'
'
'2
1
i = 1,2,3 . . . . . . m
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Let )(4)(3 211 ttS
)(2)( 212 ttS
4
31S
2
12SVector
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)(2
2)( 11 tEtfCos
T
EtS bc
b
b
)(22
)2(2
)( 12 tEtfCosT
EtfCos
T
EtS bc
b
bc
b
b
for Symbol ‘1’
for Symbol ‘0’
PSK
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)(2
2)( 11 tEtfCos
T
EtS bc
b
b
0)(2 tS
for Symbol ‘1’
for Symbol ‘0’
ASK
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)(2
2)( 111 tEtfCos
T
EtS b
b
b
)()2(2
)( 222 tEtfCosT
EtS b
b
b
for Symbol ‘1’
for Symbol ‘0’
FSK
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Digital communication
H V KUMARASWAMY
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Topics in this session:– Optimum transmitter &
receiver
– Correlative receiver
– Matched filter
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Optimum transmitter & receiver
Probability of error depends on signal to noise ratio
As the SNR increases the probability of error decreases
An optimum transmitter and receiver is one which maximize the SNR and minimize the probability of error.
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Correlative receiver
ObservationVector x
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Receiver consists of a bank of M product-integrator or correlators
Φ1(t) ,Φ2(t) …….ΦM(t) orthonormal function
The bank of correlator operate on the received signal x(t) to produce observation vector x
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Implemented in the form of maximum
likelihood detector
Operates on observation vector x to produce an estimate of the transmitted symbol
Inner products {(x,sk)} k= 1, 2 ..M
The largest in the resulting set of numbers is selected
The optimum receiver is commonly referred as a correlation receiver
![Page 72: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/72.jpg)
MATCHED FILTER
dthxty jj )()()(
)()( tTt jj h
dtTxty jj )()()(
dxTy jj )()()(
![Page 73: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/73.jpg)
T
jj dxTy0
)()()(
00)( tth j
Yj(t) = xj where xj is the j th correlator output
The impulse response of the matched filter is time-reversed and delayed version of the input signal
For causal system
![Page 74: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/74.jpg)
![Page 75: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/75.jpg)
MAXIMIZATION OF OUTPUT SNR
Tttwttx 0)()()(
)()()( 0 tntty
h(t) = impulse response = input signalW(t) =white noise
)(t
![Page 76: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/76.jpg)
Impulse Response h(t)
SampleAt t = T
Outputφ(t) Known Signal
White Noise w(t)
+
MATCHED FILTER
![Page 77: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/77.jpg)
)]([
)()(
2
2
00 tnE
TSNR
dfftjffHt )2exp()()()(0
2
2
0 )2exp()()()(
dffTjffHT
20 )(2
)( fHN
fS N
![Page 78: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/78.jpg)
dffHN
dffStnE N
20
2
)(2
)()]([
dffH
N
dffTjffH
SNR20
2
0
)(2
)2exp()()(
)(
dffdffHdffTjffH22
2
)()()2exp()()(
Schwarz’s inequality
![Page 79: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/79.jpg)
dffN
SNR2
00 )(
2)(
dffdtt22
)()(
dffN
SNR2
0max,0 )(
2)(
Rayleigh’s energy theorem
![Page 80: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/80.jpg)
)2exp()(*)( fTjffH opt
)()(* ff
dftTfjfthopt )](2exp[)(*)(
)(
)](2exp[)()(
tT
dftTfjfthopt
![Page 81: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/81.jpg)
Digital communication
H V KUMARASWAMY
![Page 82: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/82.jpg)
Topics in this session:– Matched filter (cont..)
– Properties of Matched filter
– Problems
![Page 83: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/83.jpg)
Impulse Response h(t)
SampleAt t = T
OutputΦ(t) Known Signal
White Noise w(t)
+
MATCHED FILTER
![Page 84: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/84.jpg)
Φ(t) = input signalh(t) = impulse responseW(t) =white noise
00)( tth j
The impulse response of the matched filter is time-reversed and delayed version of the input signal
)()( tTt h
For causal system
![Page 85: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/85.jpg)
•Matched filter properties
PROPERTY 1
The spectrum of the output signal of a matched filter with the matched signal as input is, except for a time delay factor, proportional to the energy spectral density of the input signal.
![Page 86: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/86.jpg)
)2exp()(
)2exp()()(*
)()()(
2
0
fTjf
fTjff
ffHf opt
![Page 87: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/87.jpg)
PROPERTY 2
The output signal of a Matched Filter is proportional to a shifted version of the AutoCorrelation Function of the input signal to which the filter is matched.
)()(0 TtRt
ERT )0()(0
At time t = T
![Page 88: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/88.jpg)
PROPERTY 3
The output Signal to Noise Ratio of a Matched filter depends only on the ratio of the signal energy to the power spectral density of the white noise at the filter input.
![Page 89: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/89.jpg)
)]([
)()(
2
2
00 tnE
TSNR
dfftjffHt )2exp()()()(0 2
2
0 )2exp()()()(
dffTjffHT
20 )(2
)( fHN
fS N
SNR at the output of matched filter is
![Page 90: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/90.jpg)
dffHN
dffStnE N
202 )(2
)()]([
dffH
N
dffTjffH
SNR20
2
0
)(2
)2exp()()(
)(
dffdffHdffTjffH22
2
)()()2exp()()(
Schwarz’s inequality
![Page 91: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/91.jpg)
dffN
SNR2
00 )(
2)(
dffdtt22
)()(
0
2
0max,0
2
)(2
)(
N
E
dffN
SNR
Rayleigh’s energy theorem
![Page 92: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/92.jpg)
PROPERTY 4
The Matched Filtering operation may be separated into two matching conditions; namely spectral phase matching that produces the desired output peak at time T, and the spectral amplitude matching that gives this peak value its optimum signal to noise density ratio.
![Page 93: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/93.jpg)
In polar form
)(exp)()( fjff
fTjfjfHfH 2)(exp)()(
dfTtfjffH
dfftjffHt
)](2exp[)()(
)2exp()()()('0
Spectral phase matched
![Page 94: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/94.jpg)
dffHfTt
)()()()( '0
'0
)()( ffH
At time t = T, output is maximum
For spectral amplitude matching
![Page 95: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/95.jpg)
Digital communication
H V KUMARASWAMY
![Page 96: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/96.jpg)
Topics in this session:– Digital modulation techniques
– Digital modulation formats
– Coherent binary modulation techniques
– Coherent binary PSK [BPSK]
![Page 97: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/97.jpg)
SHIFT KEYING METHODS Amplitude shift keying [ASK] Frequency shift keying [FSK] Phase shift keying [PSK]
Digital modulation techniques
![Page 98: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/98.jpg)
Digital modulation formats
ASK
PSK
FSK
![Page 99: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/99.jpg)
Hierarchy of digital modulation technique
![Page 100: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/100.jpg)
TYPES OF DIGITAL
MODULATION SYSTEM
1.COHERENT
2.NON- COHERENT
![Page 101: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/101.jpg)
BPSK
TRANSMITTER
![Page 102: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/102.jpg)
BPSK
RECEIVER
![Page 103: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/103.jpg)
If x1 > 0, the receiver decides in favour of symbol 1.
If x1 < 0, the receiver decides in favour of symbol 0.
BPSK DECISION
![Page 104: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/104.jpg)
tfCosT
EtS c
b
b 22
)(1
tfCosT
EtfCos
T
EtS c
b
bc
b
b 22
)2(2
)(2
Where Eb= Average energy transmitted per bit
210 bb
b
EEE
Representation of BPSK
![Page 105: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/105.jpg)
bcb
TttfCosT
t 022
)(1
In BPSK system
)()( 11 tEtS b
)()( 12 tEtS b
![Page 106: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/106.jpg)
b
T
EdtttSSb
)()( 1
0
111
b
T
EdtttSSb
)()( 1
0
221
BPSK CO-EFFECIENTS
![Page 107: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/107.jpg)
Digital communication
H V KUMARASWAMY
![Page 108: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/108.jpg)
Topics in this session:– Digital modulation techniques
– Design goals
– Coherent binary modulation techniques
– Coherent binary PSK [BPSK]
– Coherent binary FSK [BFSK]
![Page 109: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/109.jpg)
DESIGN GOALS Maximum data rate Minimum probability of symbol error Minimum transmitted power Minimum channel bandwidth Maximum resistance to interfering signals Minimum circuit complexity
Digital modulation techniques
![Page 110: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/110.jpg)
Digital modulation formats
ASK
PSK
FSK
![Page 111: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/111.jpg)
BPSK
TRANSMITTER
![Page 112: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/112.jpg)
BPSK
RECEIVER
![Page 113: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/113.jpg)
If x1 > 0, the receiver decides in favour of symbol 1.
If x1 < 0, the receiver decides in favour of symbol 0.
BPSK DECISION
![Page 114: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/114.jpg)
tfCosT
EtS c
b
b 22
)(1
tfCosT
EtfCos
T
EtS c
b
bc
b
b 22
)2(2
)(2
Where Eb= Average energy transmitted per bit
210 bb
b
EEE
Representation of BPSK
![Page 115: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/115.jpg)
bcb
TttfCosT
t 022
)(1
Probability of Error Calculation
In BPSK system
)()( 11 tEtS b
)()( 12 tEtS b
![Page 116: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/116.jpg)
b
T
EdtttSSb
)()( 1
0
111
b
T
EdtttSSb
)()( 1
0
221
![Page 117: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/117.jpg)
The observation vector x1 is related to the
received signal x(t) by
dtttxxT
0
11 )()(
The error is of two types1) Pe(0/1) i.e. transmitted as ‘1’ but received as ‘0’ 2) Pe(1/0) i.e. transmitted as ‘0’ but received as ‘0’
![Page 118: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/118.jpg)
1
02
21
2 2
)(exp
2
1)0/1( dx
xPe
Error of 1st kind is given by
μ = mean value = for the transmission of symbol ‘0’
= Variance = for additive white Gaussian noise.Threshold Value λ = 0. [Indicates lower limit in integration]
bE
2 20N
![Page 119: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/119.jpg)
Probability of Error Calculation [Contd..]
1
0 0
21
0
0
)(exp
1)0/1( dx
N
Ex
NPP bee
0
1
N
ExZ b
dzZPPNE
ee
b
)/(
20
0
)(exp1
)0/1(
02
1)0/1(
N
EerfcP b
e
![Page 120: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/120.jpg)
02
1)1/0(
N
EerfcP b
e
similarly
The total probability of error
assuming probability of 1’s and 0’s are equal.
)1()1/0()0()0/1( eeeee PPPPP
)]1/0()0/1([2
1eee PPP
02
1
N
EerfcP b
e
![Page 121: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/121.jpg)
Coherent Binary FSK
tfCosT
EtS
b
b11 2
2)(
tfCosT
EtS
b
b22 2
2)(
for symbol 1
for symbol 0
tfCosT
tb
11 22
)(
Basic orthogonal functions
OtherwiseZeroandTtfortfCosT
t bb
022
)( 22
![Page 122: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/122.jpg)
01
bES
bES
02
coefficients
M = 2 N = 2
Transmitter
![Page 123: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/123.jpg)
Receiver
![Page 124: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/124.jpg)
The correlator outputs are the subtracted one from the other and resulting a random vector ‘l’ (l=x1-x2). The output ‘l’ is compared with
threshold of zero volts.
If l > 0, the receiver decides in favour of symbol 1.
l < 0, the receiver decides in favour of symbol 0.
![Page 125: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/125.jpg)
Probability of Error Calculation
bb
TttfCosT
t 022
)( 11
bb
TttfCosT
t 022
)( 22
The transmitted signals S1(t) and S2(t) are given by
)()( 11 tEtS b
)()( 22 tEtS b
for symbol 1
for symbol 0
![Page 126: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/126.jpg)
![Page 127: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/127.jpg)
The observation vector x1 and x2
bT
dtttxx0
11 )()(
bT
dtttxx0
22 )()(
Assuming zero mean additive white Gaussian noise with input
PSD =N0/2 hence variance = N0/2
The new observation vector ‘l’ is the difference of two random variables x1 & x2.
l = x1 – x2
![Page 128: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/128.jpg)
b
b
E
E
xE
xE
lE
0
11121
conditional mean of random variable ‘l’ for symbol 1 was transmitted
similarly for ‘0’ transmission
bEl
E
0
![Page 129: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/129.jpg)
0
21 ][][][
N
xVarxVarlVar
dlN
El
NPP bee
0 0
2
0
0 2
)(exp
2
1)0/1(
02N
ElZ blet
0
2
20
22
1
)exp(1
0
N
Eerfc
dzzP
b
N
E
e
b
![Page 130: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/130.jpg)
01 22
1
N
EerfcP b
e
similarly
The total probability of error = ][2
110 ee PP
022
1
N
EerfcP b
e
![Page 131: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/131.jpg)
Digital communication
H V KUMARASWAMY
![Page 132: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/132.jpg)
Topics in this session:– Digital modulation techniques
(Contd..)
– ASK [or Binary ASK]
– QPSK
![Page 133: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/133.jpg)
BASK
Transmitter
![Page 134: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/134.jpg)
BASK Receiver
![Page 135: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/135.jpg)
bcb
TttfCosT
t 022
)(1
1)()( 11 SymbolfortEtS b
00)(2 SymbolfortS
022
1
N
EerfcP b
e
422
0
2
2
2
10 b
b
bbb
TATA
EEE
Probability of error
![Page 136: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/136.jpg)
BPSK
TRANSMITTER
![Page 137: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/137.jpg)
BPSK
RECEIVER
![Page 138: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/138.jpg)
COHERENT QUADRIPHASE – SHIFT KEYING [QPSK]
Transmitter
![Page 139: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/139.jpg)
QPSK Receiver
![Page 140: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/140.jpg)
elsewhere
TtitfT
Ets c
i
0
04
)12(2cos2
)(
elsewhere
TttfiT
E
tfiT
E
ts c
c
i
0
0)2sin(4
)12(sin2
)2cos(4
)12(cos2
)(
![Page 141: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/141.jpg)
114
72cos
2)(
014
52cos
2)(
00.4
32cos
2)(
104
2cos2
)(
4
3
2
1
dibitinputfortT
Et
dibitinputfortT
Et
dibitinputfortT
Et
dibitinputfortT
Et
fS
fS
fS
fS
c
c
c
c
Transmitted signals
E = the transmitted signal energy per symbol.T = Symbol duration.
![Page 142: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/142.jpg)
Tttt
Tttt
fT
fT
cb
cb
02sin2
)(
02cos2
)(
2
1
Basic functions
4,3,2,1
412sin
412cos
i
iE
iE
Si
Message points
![Page 143: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/143.jpg)
Signal vectors, Si1 & Si2
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Signal Space Representation
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4,3,2,1
0)()()(
i
Tttwtstx i
1
0
11
4)12(cos
)()(
wiE
dtttxxT
2
0
22
4)12(sin
)()(
wiE
dtttxxT
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Probability of error
-The signal energy per bit 2
E
-The noise spectral density is
20N
N
N
Eerfc
EEE
erfcP
2 0
0
1
2
1
22
2
1
![Page 148: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/148.jpg)
No
Eerfc
No
Eerfc
No
Eerfc
PPC
24
1
21
22
11
1
2
2
21
No
Eerfc
No
Eerfc
PP Ce
24
1
2
1
2
No
EerfcPe 2
No
Eerfc
b
eP 2or
In QPSK E = 2 Eb
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Digital communication
H V KUMARASWAMY
![Page 150: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/150.jpg)
Topics in this session:– Probability of error in QPSK
– Non coherent ASK, FSK
– DPSK
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Probability of error
-The signal energy per bit 2
E
-The noise spectral density is
20N
N
N
Eerfc
EEE
erfcP
2 0
0
1
2
1
22
2
1
![Page 152: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/152.jpg)
No
Eerfc
No
Eerfc
No
Eerfc
PPC
24
1
21
22
11
1
2
2
21
No
Eerfc
No
Eerfc
PP Ce
24
1
2
1
2
No
EerfcPe 2
No
Eerfc
b
eP 2or
In QPSK E = 2 Eb
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BASK
Transmitter
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BASK Receiver
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Non coherent ASK
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Transmitter
Coherent FSK
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Coherent FSK
Receiver
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Non coherent FSK
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BPSK
TRANSMITTER
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Coherent BPSK
RECEIVER
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DPSK [Differential PSK]
Non-coherent PSK
Transmitter
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Receiver
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Input Binary Sequence {bK} 1 0 0 1 0 0 1 1
{b’K} 0 1 1 0 1 1 0 1
{dK-1} 1 1 0 1 1 0 1 1
{d’K-1} 0 0 1 0 0 1 0 0
{bKdK-1} 1 0 0 1 0 0 1 1
{b’Kd’K-1} 0 0 1 0 0 1 0 0
Differentially Encoded 1 sequence {dK}
1 0 1 1 0 1 1 1
Transmitted Phase 0 0 Π 0 0 Π 0 0 0
Received Sequence(Demodulated Sequence)
1 0 0 1 0 0 1 1
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Input Binary Sequence {bK} 1 0 0 1 0 0 1 1
Differentially Encoded 1 sequence {dK}
1 0 1 1 0 1 1 1
Transmitted Phase 0 0 Π 0 0 Π 0 0 0
Received Sequence(Demodulated Sequence)
1 0 0 1 0 0 1 1
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Digital communication
H V KUMARASWAMY
![Page 168: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/168.jpg)
Topics to be covered in this session
I Minimum shift keying
II M-ary FSK
III M-ary PSK
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Minimum shift keying
Proper utilization of phase during detection, for improving noise performance
Complexity increasesCPFSK (Continuous-phase frequency-shift keying)
.
0])0(2[2
1])0(2[2
)(
2
1
SymbolfortfCosT
E
SymbolfortfCosT
E
ts
b
b
b
b
θ(0) denotes the value of the phase at time t=0
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])(2[2
)( ttfCosT
Ets c
b
b
An angle-modulated wave
θ(t) is the phase of s(t), continuous function of time.
)(2
121 fff c Carrier frequency
Phase bb
TttT
ht 0)0()(
)ff(Th 21b Deviation ratio
Measured with respect to bit rate 1/Tb
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At time t=Tb
0
1)0()(
Symbolforh
SymbolforhTb
Phase Tree
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Phase Trellis, for sequence 1101000
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)2()]([2
)2()]([2
)( tfSintSinT
EtfCostCos
T
Ets c
b
bc
b
b
In terms of In phase and Quadrature Component
bb
TttT
t 02
)0()(
+ Sign corresponds to symbol 1
- Sign corresponds to symbol 0
h=1/2
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bbbb
b
bb
b
b
b
TtTtT
CosT
E
tT
CosCosT
E
tCosT
Ets
2
2
2])0([
2
])([2
)(1
For the interval of bb TtT
Half cosine pulse
In phase components
+ Sign corresponds to θ(0) =0- Sign corresponds to θ(0) = п
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bbb
b
bb
b
b
b
bQ
TttT
CosT
E
tT
CosTSinT
E
tSinT
Ets
202
2
2])([
2
])([2
)(
Quadrature components
+ Sign corresponds to θ(Tb) =п/2- Sign corresponds to θ(Tb) = -п/2
Half sine pulse
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Four possibilities
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bbcbb
TtTtfCostT
CosT
t
)2(
2
2)(1
bcbb
TttfSintT
SinT
t 20)2(2
2)(2
bTttststs 0)()()( 2211
Basic functions
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bbb
T
T
TtTCosE
dtttssb
b
)0(
)()( 11
bbb
T
TtTSinE
dtttssb
b
20)(
)()(2
0
22
coefficients
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Signal Space Characterization of MSK
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bb
T
T
TtTws
dtttxxb
b
11
11 )()(
b
T
Ttws
dtttxxb
20
)()(
22
2
0
22
0
2
0 4
1
N
Eerfc
N
EerfcP bb
e
0N
EerfcP b
e
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MSK receiver
Q-channel
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Sketch the waveform of the MSK signal for the sequence for the 101101.Assume that the carrier frequencya) Is 1.25 times the bit rate. b) Equal to the bit
Solution (a) fc =(f1+f2)/2 =1.25/ Tb OR f1+f2=2.5/Tb
Also f1-f2=1/(2Tb)
Solving f1=1.5/Tb f2=1/Tb
(b) fc=1/Tb f1+f2=2/Tb f1-f2=1/(2Tb)\
Solving f1=1.25/Tb f2=0.75/Tb
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Digital communication
H V KUMARASWAMY
![Page 187: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/187.jpg)
Topics in this session:
M-ary Modulation Technique
M-ary PSK and FSK
Problems
Bandwidth calculation
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1....,..........,.........2,1,02
22
)(
Mi
M
itfCos
T
Ets ci
TttfCosT
t c 022
)(1
TttfSinT
t c 022
)(2
M - ary PSK
Orthogonal Functions
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Signal Constellation for octaphase – shift - keying
M=8
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Receiver for Coherent M-ary PSK
The decision making process in the phase discriminator is based on the noisy inputs
1..........1,02
1..........1,02
MiwM
iSinEx
MiwM
iCosEx
II
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M - ary QAM
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Block Diagram of M –ary QAM System - Transmitter
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Block Diagram of M –ary QAM System - Receiver
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Signalling Constellation M=16
M-ary QPSK M-ary QAM
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Serial to Parallel
D / A VCOBinary Data M-ary FSK
M-ary FSK
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Problems
A bandpass data transmission scheme uses a PSK signalling scheme with
bcbc T
TttACostS 10
,0,)(2
mSecTTttACostS bbc 2.0,0,)(1
The Carrier Amplitude at the receiver input is 1mV and the PSD of the Additive white gaussian Noise at the input is 10-11 Watts/Hz. Assume that an ideal correlation receiver is used. Calculate average bit error rate of the receiver.
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3
3
11
323
0
2
0
110
107.0
1044.12
1)236.2(
2
1
52
1
)102(*2
10*2.0*)10(
2
1
22
1
2
1
/102
1
12.0
erfc
erfcerfc
N
TAerfc
N
EerfcP
HzWattN
mVA
RmSecT
bbe
c
bb
Using erfc function
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3
0
2
107.000069.0)2.3(
10
Q
QN
TAQP b
e
Using Q function
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Bandwidth calculation
1 ASK BW=2rb
2 PSK BW=2rb
3 FSK BW>2rb
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Digital communication
H V KUMARASWAMY
![Page 204: DC Digital Communication PART1](https://reader037.vdocument.in/reader037/viewer/2022102410/5474ed45b4af9f985d8b456d/html5/thumbnails/204.jpg)
Topics in this session:
Synchronization Carrier synchronizationSymbol synchronizationApplications
1 Voice-grade modem2 Digital radio3 Digital communication by satellite
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Synchronization
1 carrier recovery or Carrier Synchronization
2 Clock recovery or Symbol Synchronization
3 Word Synchronization
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•Carrier Synchronization
Mth power loop
Square loop ( M = 2 )
Costas loop
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Mth power loop
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Costas loop
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•Symbol Synchronization
1 Transmitting clock along with the data-bearing signal
[ multiplexed form ]
- waste of clock power
2 Use a noncoherent detector to extract clock
3 Clock is extracted from the demodulated base band signal
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•Matched filter
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•Early-late gate synchronizer
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•Applications
1 Voice-grade ModemsVoice frequency range- 300-3400 Hz
A/DMod
Dem
Mod
Dem D/A
Modem Modem
Telephone channelvoice voice
FSK modem operating at 1200bps, commonly used frequencies 1300Hz & 2100Hz
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16 QAM
Phase jitter in M-ary PSK & DPSK
DPSK limited to 4800bps
M-ary QAM
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•Digital radio
- Information originating from a source is transmitted to its destination by means of digital modulation techniques over an appropriate number of microwave radio links.
- LOS [ Line Of Sight ] propagation.- 64kbps PCM is used- M-ary QAM [ M=64, M=256 ]- Multipath fading- Diversity Techniques
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LOS [ Line Of Sight ] propagation
Reflected wave
Building
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Digital Communication by Satellite
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-TDMA-Transmission are organized into frames-A frame contain N bursts-Preamble , Post amble, guar time
Digital Communication by Satellite
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Digital Communication by Satellite
M-ary PSK
Coherent MSK
QPSK for BW saving
-Power efficiency is increased by using TWT near saturation
-Independent simultaneous provisions for carrier and clock recovery, overhead recovery time is minimized