digital communication.pdf

digital communication bsics

1. MUTHAYAMMAL ENGINEERING COLLEGE
RASIPURAM-637408
COURSE CODE & TITLE –
19ECC10/Digital Communication
Systems

2. Contents
Introduction, sampling process.
Quantization, quantization noise, conditions for optimality of
quantizer, encoding.
Pulse-Code Modulation (PCM),Line codes, Differential encoding,
Regeneration, Decoding & Filtering.
Noise considerations in PCM systems.
Time-Division Multiplexing (TDM), Synchronization.
Delta modulation (DM).
Differential PCM (DPCM), Processing gain Adaptive DPCM
(ADPCM)
Comparison of the above systems.

3. Introduction
Source: analog or digital
Transmitter:transducer,amplifier,modulator,
oscillator, power amp., antenna
Channel: e.g. cable, optical fibre, free space
Receiver:antenna, amplifier,
demodulator, power amplifier, transducer
oscillator,
Recipient:e.g.person,(loud)speaker,computer
3

4. Types of information:
Voice, data, video, music, email etc.
Types of communication systems:
Public Switched Telephone Network
(voice,fax,modem)
Satellite systems
Radio,TV broadcasting Cellular phones
Computer networks (LANs, WANs, WLANs)
4

5. InformationRepresentation
Communicationsystemconvertsinformationintoelectrical
electromagnetic/opticalsignalsappropriateforthe
transmissionmedium.
Analogsystemsconvertanalogmessageintosignalsthatcan
propagatethroughthechannel.
Digitalsystemsconvertbits(digits,symbols)intosignals
•Computers naturally generate information as characters/bits
•Most information can be converted into bits
•Analog signals converted to bits by sampling and quantizing
(A/D conversion)
5

6. WHYDIGITAL?
Digitaltechniquesneedtodistinguishbetweendiscrete
symbols allowing regeneration versus amplification
Goodprocessingtechniques are
availablefordigital signals, such as medium.
•Data compression (or source coding)
•Error Correction (or channel coding)(A/D conversion)
•Equalization
•Security
Easy to mix signals and data using digital techniques
6

7. 7

8. 8

9. InformationSourceandSinks
Information Source and Input Transducer:
The source of information can be analog or digital,
Analog: audio or video signal,
Digital: like teletype signal.
In digital communication the signal produced by this source is
converted into digital signal consists of 1′s and 0′s.
Output Transducer:
The signal in desired format analog or digital at the output
9

10. Channel
The communication channel is the physical medium that is used
for transmitting signals from transmitter to receiver
•Wireless channels: Wireless Systems
•Wired Channels: Telephony
Channeldiscriminationonthebasisoftheir
property and characteristics, like AWGN channel
etc.
10

11. SourceEncoderAndDecoder
SourceEncoder
Indigitalcommunicationweconvertthesignalfromsource
intodigitalsignal.
SourceEncodingorDataCompression:theprocessof
efficientlyconvertingtheoutputofwitheranalogordigital
sourceintoasequenceofbinarydigitsisknownassource
encoding.
SourceDecoder
Attheend,ifananalogsignalisdesiredthensourcedecoder
triestodecodethesequencefromtheknowledgeoftheencoding
algorithm.
11

12. ChannelEncoderAnd Decoder
ChannelEncoder:
Theinformationsequenceispassedthroughthechannel
encoder.Thepurposeofthechannelencoderistointroduce,in
controlledmanner,someredundancyinthebinaryinformation
sequencethatcanbeusedatthereceivertoovercometheeffects
ofnoiseandinterferenceencounteredinthetransmissiononthe
signalthroughthechannel.
ChannelDecoder:
Channeldecoderattemptstoreconstructtheoriginal
informationsequencefromtheknowledgeofthecodeusedby
thechannelencoderandtheredundancycontainedinthe
receiveddata
12

13. DigitalModulatorAndDemodulator
DigitalModulator:
Thebinarysequenceispassedtodigitalmodulatorwhich
inturnsconvertthesequenceintoelectricsignalssothat
wecantransmitthemonchannel.Thedigitalmodulator
mapsthebinarysequencesintosignalwaveforms.
DigitalDemodulator:
Thedigitaldemodulatorprocessesthechannelcorrupted
transmittedwaveformandreducesthewaveformtothe
sequenceofnumbersthatrepresentsestimatesofthe
transmitteddatasymbols.
13

14. WhyDigitalCommunications?
Easy to regenerate the distorted signal
Regenerative repeaters along the transmission path can detect a
digital signal and retransmit a new, clean (noise free) signal
These repeaters prevent accumulation of noise along the path
This is not possible with analogcommunication systems
Two-state signal representation
The input to a digital system is in the form of a sequence of
bits (binary or M-ary)
Immunity to distortion and interference
Digitalcommunication is ruggedin the
sense thatitismore
immune to channel noise and distortion
14

15. Hardware is more flexible
Digital hardware implementation is flexible and permits the
use of microprocessors, mini-processors, digital switching
and VLSI
Shorter design and production cycle
Low cost
The use of LSI and VLSI in the design of components and
systems have resulted in lower cost
Easier and more efficient to multiplex several digital
signals
Digital multiplexing techniques –Time & Code Division
Multiple Access -are easier to implement than analog
techniques such as Frequency Division Multiple Access
15

16. Can combine different signal types –data, voice, text, etc.
Data communication in computers is digital in nature
whereas voice communication between people is analog in
nature
Using digital techniques, it is possible to combine both
format for transmission through a common medium
Encryption and privacy techniques are easier to
implement
Better overall performance
Digital communication is inherently more efficient than
analog in realizing the exchange of SNR for bandwidth.
Digital signals can be coded to yield extremely low rates
and high fidelity as well as privacy.
16

17. Disadvantages:
Requiresreliable“synchronization”
RequiresA/Dconversionsathighrate
Requireslargerbandwidth
Nongracefuldegradation
PerformanceCriteria
ProbabilityoferrororBitErrorRate
17

18. SamplingProcess
Sampling is converting a
continuous time signal into a
discrete time signal.
There three types of sampling
Impulse (ideal) sampling
Natural Sampling
Sample and Hold operation
18

19. Quantization
Quantization is a non linear transformation which maps
elements from a continuous set to a finite set.
19

20. QuantizationNoise
20

21. Uniform&Non-UniformQuantization
Non uniform Quantization Used to reduce quantization error
and increase the dynamic range when input signal is not
uniformly distributed over its allowed range of values.
Uniformquantization
21
Non-Uniform
quantization

22. 22

23. 23

24. Encoding
24

25. PulseCodeModulation
PulseCode
conversion.
Itconsists
Modulation(PCM)isaspecialformofA/D
ofsampling,quantizing,andencodingsteps.
1.Usedforlongtimeintelephonesystems
2.Errorscanbecorrectedduringlonghaultransmission
3.Canusetimedivisionmultiplexing
4.Inexpensive
25

26. PCMTransmitter
26

27. PCMTransmissionPath
27

28. PCMReceiver
Reconstructedwaveform
28

29. BandwidthofPCM
Assume w(t) is band limited to B hertz.
Minimum sampling rate = 2B samples / second
A/D output = n bits per sample (quantization level M=2
n)
Assume a simple PCM without redundancy.
Minimum channel bandwidth = bit rate /2
Bandwidth of PCM signals:
B
PCM nB (with sinc functions as orthogonal basis)
B
PCM 2nB (with rectangular pulses as orthogonal basis)
 For any reasonable quantization level M, PCM
requires much higher bandwidth than the original w(t).
29

30. AdvantagesofPCM
Relatively inexpensive. Easily multiplexed.
Easily regenerated.
Better noise performance than analog system.
Signals may be stored and time-scaled efficiently.
Efficient codes are readily available.
Disadvantage
Requires wider bandwidth than analog signals
30

31. LineCodes
31

32. CategoriesofLineCodes
Polar-Sendpulseornegativeofpulse
Unipolar-Sendpulseora0
Bipolar-Represent1byalternatingsignedpulses
GeneralizedPulseShapes
NRZ-Pulselastsentirebitperiod
PolarNRZ
BipolarNRZ
RZ -ReturntoZero-pulselastsjusthalfofbitperiod
PolarRZ
BipolarRZ
ManchesterLineCode
Send a2-pulseforeither1(highlow)or0(lowhigh)
Includesrisingand fallingedgeineachpulse
No DCcomponent
32

33. DifferentialEncoding
33

34. 34

35. 35

36. NoiseConsiderationsInPCM
36

37. TimeDivisionMultiplexing(TDM)
37

38. Synchronization
38

39. DeltaModulation
Types of noise
Quantization noise: step
size takes place of smallest
quantization level.
too small: slope
overload noise
too large: quantization noise
and granular noise
39

40. DeltaModulatorTransmitter&Receiver
40

41. ADM
41

42. ADMTransmitter&Receiver
42

43. DPCM
Often voice and video signals do not
change much from one
sample to next.
-Such signals has energy concentrated
in lower frequency.
-Sampling faster than necessary
generates redundant information.
Can save bandwidth by not sending all
samples.
*Send true samples occasionally.
*In between, send only change
from previous value.
*Change values can be sent using
a fewer number of bits
than true samples.
43

44. DPCMTransmitter
44

45. DPCMReceiver
45

46. ProcessingGain
In a spread-spectrumsystem, the process gain (or
"processing gain") is the ratio of the spread (or RF)
bandwidth to the unspread (or baseband) bandwidth.
It is usually expressed in decibels(dB).
For example, if a 1 kHz signal is spread to 100 kHz, the
process gain expressed as a numerical ratio would be
100000/1000 = 100. Or in decibels, 10 log
10(100) = 20
dB.
46

47. AdaptiveDPCM
47

48. Comparisons
48

49. VEMUINSTITUTEOFTECHNOLOGY
(ApprovedbyAICTE,New Delhi&AffiliatedtoJNTUA,Ananthapuramu)
P.Kothakota,Puthalapattu(M),ChittoorDist–517112AP,India
Department of Electronics and Communication Engineering
Digital Communication Systems
Unit-2
Baseband Pulse Transmission
By
B SAROJA
Associate Professor Dept. of . ECE

50. Contents
Introduction
Matched filter, Properties of Matched filter,Matched filter for
rectangular pulse, Error rate due to noise
Inter-symbol Interference(ISI)
Nyquist‟s criterion for distortion less baseband binary
transmission Ideal Nyquis tchannel
Raised cosine filter & its spectrum
Correlative coding–Duo binary & Modified duo binary signaling
schemes, Partial response signaling
Baseband M-array PAM transmission Eye diagrams

51. 3

52. MatchedFilter
Itpassesallthesignalfrequencycomponentswhile
suppressinganyfrequencycomponentswherethereis
onlynoiseandallowstopassthemaximumamountof
signalpower.
Thepurposeofthematchedfilteristomaximizethesignal
tonoiseratioatthesamplingpointofabitstreamandto
minimizetheprobabilityofundetectederrorsreceived
fromasignal.
ToachievethemaximumSNR,wewanttoallowthroughall
thesignalfrequencycomponents.
4

53. MatchedFilter:
⦁Considerthereceivedsignalas avectorr,andthetransmittedsignalvectorass
⦁Matchedfilter“projects”therontosignalspacespannedbys(“matches”it)
Filtered signal can now be safely sampled by the receiver at the correct sampling instants,
resulting in a correct interpretation of the binary message
Matched filter is the filter that maximizes the signal-to-noise ratioit can be shown that it
also minimizes the BER: it is a simple projection operation
5

54. ExampleOf MatchedFilter(RealSignals)
T t T t T t0 2T
y(t)s
i(t)h
opt(t)
A
2s (t)
opt
t t T t
y(t)s
i(t)h
opt(t)
A
2s (t)
i opt
0T/2 3T/22TT/2T T/2T
2

A
2
i
A
h(t)
A
h(t)
A
A
T
A
T
A
6

55. PropertiesoftheMatchedFilter
1.The Fourier transform of a matched filter output with the matched signal as
input is, except for a time delay factor, proportional to the ESDof the input
signal.
orrelationfunctionof theinputsignaltowhichthefilter
Z ( f ) | S( f ) |
2
exp(j2fT)
2.The output signal of a matched filter is proportional to a shifted version of the
autocis matched.
z(t) R
s (t T ) z(T ) R
s (0) E
s
3.The output SNR of a matched filter depends only on the ratio of the signal energy
to the PSD of the white noise at the filter input.
0
N/2
E
s

N

T
max
S

7

56. MatchedFilter:FrequencydomainView
SimpleBandpassFilter:
excludesnoise,butmissessomesignalpower
8

57. MatchedFilter:FrequencyDomainView(Contd
Multi-BandpassFilter:includesmoresignalpower,butaddsmore noisealso!
MatchedFilter:includesmore signalpower,weightedaccordingtosize
=>maximalnoise rejection!
9

58. MatchedFilterForRectangularPulse
Matched filter for causal rectangular pulse has an impulse
response that is a causal rectangular pulse
Convolve input with rectangular pulse of duration T sec and
sample result at T sec is same as to
First, integrate for T sec
Second, sample at symbol period T sec
Third,resetintegrationfor nexttimeperiod
Integrateanddumpcircuit
T
10
Sampleanddump

59. 11

60. Inter-symbolInterference(ISI)
ISI in the detection process due to the filtering effects of
the system
Overall equivalent system transfer function
H ( f ) H( f ) H
creates echoes and hence time dispersion
causes ISI at sampling time
ISI effect
z
k s
k n
k 
is
i
ik
12

61. Inter-symbolInterference(ISI):MODEL
Basebandsystemmodel
n(t
r(t)
Detector
k
z
t kT
kxˆx
k
x
1x
2
3
x
T
T
EquivalentHm(ofd)el
t
Tx filter
h
t (t)
Rx.filter
h
r(t)
H
r(f)
Channel
h
c (t)
H
c ( f )
z(t
Detector
k
z
t kT
kxˆx
k
x
1x
2
x
3
T
T
Equivalentsystem
h(t)
H
nˆ(t
filterednoise
13
H(f)H
t(f)H
c(f)H
r(f)

62. 14

63. 15

64. 16

65. 17

66. Equiv System: Ideal Nyquist Pulse
(FILTER)
18
2T
1
2T
1
T
f t
0T2T2TT0
2T
W
1
Ideal Nyquist filter
H ( f )
Ideal Nyquist pulse
h(t) sinc( t / T )
1

67. NyquistPulses(FILTERS)
Nyquist pulses (filters):
Pulses (filters) which result in no ISI at the sampling time.
Nyquist filter:
Itstransferfunctioninfrequencydomainisobtainedby
convolvingarectangularfunctionwithanyrealeven-
symmetricfrequencyfunction
Nyquistpulse:
Itsshapecanberepresentedbyasinc(t/T)functionmultiply
byanothertimefunction.
ExampleofNyquistfilters:Raised-Cosinefilter
19

68. RaisedCosineFilter&ItsSpectrum
2
Baseband
sSB
s
R
W(1r)
r1
r
r1
r
131
2T4TT
131
T4T2T
| H ( f ) || H
RC ( f )
|
1
0.5
0
h(t) h
RC (t)
1
0.5
0
r 0.5
r 
T2T
3T
20
T2T3T
PassbandW
DSB(1r)R
s

69. RAISEDCOSINEFILTER&ITSSPECTRUM
Raised-CosineFilter
ANyquistpulse(NoISIatthesamplingtime)

for|f|W

0
for2WW|f|W
4WW
1
0
0
0
H(f)cos
2

for|f|2W
0W
|f|W2W
Excessbandwidth:WW
0
r
WW
Roll-off factor
0 r 1
0
0
cos[2
1[4(WW)t]
2
h(t)2W
0(sinc(2W
0t))
(WW)t]
21

70. Correlative Coding –DUO
BINARY SIGNALING

71. ImpulseResponseofDuobinaryEncoder

72. EncodingProcess
1)a
n = binary input bit; a
n ∈ {0,1}.
2)b
n = NRZ polar output of Level converter in the precoder
and is given by,
bn={−d,if an=0+d,if an=1
3)y
n can be represented as
The duobinary encoding correlates present sample a
n and the
previous input sample a
n-1.

73. DecodingProcess
Thereceiverconsistsofaduobinarydecoderanda
postcoder.
b^n=yn−b^n−1
Thisequationindicatesthatthedecodingprocessisprone
toerrorpropagationastheestimateofpresentsample
reliesontheestimateofprevioussample.
Thiserrorpropagationisavoidedbyusingaprecoder
beforeduobinaryencoderatthetransmitteranda
postcoderaftertheduobinarydecoder.
Theprecodertiesthepresentsampleandprevioussample
andthepostcoderdoesthereverseprocess.

74. Correlative Coding –Modified Duobinary
Signaling

75. ModifiedDuobinarySignalingisanextensionofduobinary
signaling.
ModifiedDuobinarysignalinghastheadvantageofzeroPSDat
lowfrequencieswhichissuitableforchannelswithpoorDC
response.
Itcorrelatestwosymbolsthatare2Ttimeinstantsapart,
whereasinduobinarysignaling,symbolsthatare1Tapart
arecorrelated.
ThegeneralconditiontoachievezeroISIisgivenby
p(nT)={1,n=00,n≠0

76. Inthecaseofmodifiedduobinarysignaling,theabove
equationismodifiedas
p(nT)={1,n=0,20,otherwise
whichstatesthattheISIislimitedtotwoalternate
samples.
Hereacontrolledor“deterministic”amountofISIis
introducedandhenceitseffectcanberemovedupon
signaldetectionatthereceiver.

77. Impulse Response Of A Modified
Duobinary Encoder

79. PartialResponseSignalling
31

80. 32

81. EyePattern
33timescale
amplitude
scale
Sensitivityto
timingerror
Eye pattern:Display on an oscilloscope which sweeps the system
response to a baseband signal at the rate 1/T (T symbol duration)
Distortion due to ISI
Noise margin
Timingjitter

82. ExampleOfEyePattern:
BINARY-PAM,SRRCPULSE
Perfectchannel(nonoiseandnoISI)
34

83. EyeDiagramFor4-PAM
35

84. VEMUINSTITUTEOFTECHNOLOGY
(ApprovedbyAICTE,NewDelhi&AffiliatedtoJNTUA,Ananthapuramu)
P.Kothakota,Puthalapattu(M),ChittoorDist–517112AP,India
Department of Electronics and Communication Engineering
Digital Communication Systems
Unit-3
Signal Space Analysis
By
B SAROJA
Associate Professor
Dept. of . ECE

85. Contents
Introduction
Geometric representation of signals
Gram-Schmidt orthogonalization procedure
Conversion of the Continuous AWGN channel into a vector
channel Coherent detection of signals in noise
Correlation receiver
Equivalence of correlation and Matched filter receivers
Probability of error
Signal constellation diagram

86. Introduction:signalSpace
What is a signal space?
Vector representations of signals in an N-dimensional orthogonal
space
Why do we need a signal space?
It is a means to convert signals to vectors and vice versa.
It is a means to calculate signals energy and Euclidean distances
between signals.
Why are we interested in Euclidean distances between
signals?
For detection purposes: The received signal is transformed to a
received vectors.
The signal which has the minimum distance to the received
signal
is estimated as the transmitted signal.

87. i
0
(5.2)
Transmitter takes the symbol (data) m
i (digital
message source output) and encodes it into a
distinct signal s
i(t).
The signal s
i(t) occupies the whole slot T allotted to
symbol m
i.
s
i(t) is a real valued energy signal (???)
T
i
Es
2
(t)dt,i=1,2,....,M
4

88. i
0
(5.2)
Transmitter takes the symbol (data) m
i (digital message
source output) and encodes it into a distinct signal s
i(t).
The signal s
i(t) occupies the whole slot T allotted to symbol
m
i.
s
i(t) is a real valued energy signal (signal with finite energy)
T
i
Es
2
(t)dt,i=1,2,....,M
5

89. GeometricRepresentationofSignals
Objective: To represent any set of M energy
signals
{s
i(t)} as linear combinations of N orthogonal
basis functions, where N ≤ M
Real value energy signals s
1(t), s
2(t),..s
M(t),
each of
durationTsec
(5.5)
N
i ijj
s(t),
0tT
s(t)  
i==1,2,....,M

j1
Orthogonalbasis
function
coefficient
Energy signal
6

90. Coefficients:
Real-valuedbasisfunctions:
0
i=1,2,....,M
(5.6)
j=1,2,....,M

 
T
ij i j
s(t)(t)dt,s
i
(5.7)
j ij
(t)
1ifij
(t)dt 
0if ij 
T

0
7

91. A)SYNTHESIZERFORGENERATINGTHESIGNALS
I(T).
B)ANALYZERFORGENERATINGTHESETOFSIGNAL
VECTORSS
I.
8

92. Each signal in the set s
i(t) is completely determined by the
vector of its coefficients
s
i1 
(5.8)

s

s
i 
.

i 2 
.
,i 1,2,....,M

.

s
iN
9

93. The signal vector s
i concept can be extended to 2D, 3D etc. N-
dimensional Euclidian space
Provides mathematical basis for the geometric representation
of energy signals that is used in noise analysis
Allows definition of
Length of vectors (absolute value)
Angles between vectors
Squared value (inner product of s
i with itself)
i
2
= (5.9)
ii
N
s
2
s
T
s
s ,i1,2,....,Mij
j 1
Matrix
Transposition
10

94. ILLUSTRATING THE
GEOMETRIC
REPRESENTATION OF
SIGNALS FOR THE CASE
WHEN N 2 AND M 3.
(TWO DIMENSIONAL
SPACE, THREE
SIGNALS)
11

95. …start with the definition
of average energy in a
signal…(5.10)
Wheres
i(t)isasin(5.5):
i
0
(5.10)
T
i
Es
2
(t)dt
(5.5)
N
s
i (t) s
ij
j (t),
j1
What is the relation between the vector representation of a
signal and its energy value?
12

96. Aftersubstitution:
Afterregrouping:
T

N

N

0j1 k1
E
is
ij
j(t)s
ik
k(t)

dt
T
0
(5.11)
N N
j1k1
E
i s
ijs
ik

j(t)
k(t)dt
2
i i
=s (5.12)
N
ij
s
2
j1
E
Φ
j(t) is orthogonal,
so finally we
have:
The energy of a signal is equal to the
squared length of its vector
13

97. Formulas for Two Signals
Assume we have a pair of signals: s
i(t)
and s
j(t), each represented by its vector,
Then:
0
(5.13)
ij i k ik
T
T
ss(t)s(t)dtss
Inner product of the signals
is equal to the inner product
of their vector
representations [0,T]
Inner product is invariant
to the selection of basis
functions
14

98. EuclidianDistance
The Euclidean distance between two points represented by
vectors (signal vectors) is equal to
||s
i-s
k|| and the squared value is given by:
N
2
=
j1
i
2
0
(5.14)
=
k
ss
ijkj
(s-s)
2
T
i k
(s(t)s(t))dt
15

99. ANGLE BETWEEN TWO SIGNALS
The cosine of the angle Θ
ik between two signal vectors
s
i and s
k is equal to the inner product of these two
vectors, divided by the product of their norms:
Sothetwo signalvectorsareorthogonaliftheirinner
product s
i
Ts
kiszero(cosΘ
ik=0)
s
T
s
(5.15)
s
is
k
cos
ik
ik
16

100. SchwartzInequality
Definedas:
acceptwithoutproof…
 
2
2 2
1 2 1 2
s(t)dts(t)dt(5.16)
  
  
s(t)s(t)dt  
17

101. Gram-schmidtOrthogonalizationProcedure
1.Define the first basis
function starting with s
1 as:
(where E is the energy of the
signal) (based on 5.12)
2.Then express s
1(t) using the
basis function and an energy
related coefficient s
11 as:
3. Later using s
2 define the
coefficient s
21 as:
1
1
1
s(t)
(t) (5.19)
E
1
E
1
1(t)=s
11
1(t)(5.20)s(t)
18
21 2 1
0
(5.21)
T
s(t)(t)dts
Assumeaset of Menergysignalsdenoted bys
1(t),s
2(t), .. ,s
M(t).

102. 4.If we introduce the
intermediate function g
2 as:
5.We can define the second
basis function φ (t) as:
2
6.Which after
substitution of
g
2(t) using s
1(t) and
s
2(t) it
becomes:
Note that φ
1(t) and φ
2(t) are
orthogonalthatmeans:
g
2(t)
2
2
0
(t) (5.23)
T
g
2(t)dt
s
2(t)s
21
1(t)
2
Es
2
2 21
(t) (5.24)
1 2
0
T
(t)(t)dt0
2
2
0
(t)dt1
T

g
2(t)s
2(t)s
21
1(t)(5.22)
Orthogonaltoφ
1(t)
19
(Lookat5.23)

103. AND SO ON FOR N DIMENSIONAL
SPACE…,
In general a basis function can be defined using the
following
formula:
0
(5.26)
T
ij
s
i(t)
j(t)dt,s j1,2,.....,i1
i1
g
i(t)s
i(t)s
ij-
j(t)
j1
(5.25)
•wherethecoefficientscanbedefinedusing:
20

104. SpecialCase:
For the special case of i = 1 g
i(t) reduces to s
i(t).
General case:
•Given a function g
i(t) we can define a set of basis functions,
which form an orthogonal set, as:
i
2
0
T
g
i(t)
g
i(t)dt
(t) ,i1,2,.....,N (5.27)

21

105. 22

106. AdditiveWhiteGaussianNoise(AWGN)
23
Thermalnoiseis describedbyazero-meanGaussianrandom process,
n(t)thatADDSontothesignal=>“additive”
ItsPSD is flat,hence,itiscalledwhitenoise.
Autocorrelationisaspikeat0:uncorrelatedatanynon-zerolag
Probabilitydensityfunction
(gaussian)
[w/Hz]
Power spectral
Density
(flat => “white”)
Autocorrelation
Function
(uncorrelated)

107. 24

108. CoherantDetectionofSignalsinNoise:
Assumingbothsymbolsequallylikely:u
Aischosen if
“likelihoods”
Log-Likelihood=>
25
Asimpledistancecriterion!

109. EffectofNoiseInSignalSpace
Thecloudfallsoffexponentially(gaussian).
Vectorviewpointcanbeusedinsignal space,witharandomnoisevectorw
26

110. CorrelatorReceiver
Thematchedfilteroutputatthesamplingtime,canbe
realizedas thecorrelatoroutput.
Matchedfiltering,i.e.convolutionwiths
*(T-)simplifiestoi
integration w/ s
i
*(), i.e. correlation or inner product!

*
r(
0
i
z(T ) h
opt (T ) r(T )
T
)s()dr(t),s(t)
Recall: correlation operation is the projection of the received
signal onto the signal space!
Key idea: Reject the noise (N) outside this space as irrelevant:
=> maximize S/N

111. ACorrelationReceiver
Threshold device
(A\D)
integrator
integrator
-
+
Sampl
eevery
Tb
seconds
T
b

0
T
b

0
S
1(t)
S
2(t)



2S (t)n(t)
S
1(t)n(t)
V(t)

or
28

112. 29

113. ProbabilityOfError
30

114. SignalConstellationDiagram
Aconstellationdiagramisarepresentationofasignalmodulated
byadigitalmodulationschemesuchasquadratureamplitude
modulationorphase-shiftkeying.
Itdisplaysthesignalasatwo-dimensionalxy-planescatter
diagraminthecomplexplaneatsymbolsamplinginstants.
31

115. 32

116. VEMU INSTITUTE OF TECHNOLOGY
(Approved by AICTE, New Delhi & Affiliated to JNTUA,
Ananthapuramu)
P.Kothakota, Puthalapattu (M), Chittoor Dist –517 112 AP, India
Department of Electronics and Communication Engineering
Digital Communication Systems
Unit-4
Passband Transmission Model
By
B SAROJA
Associate Professor Dept. of . ECE

117. Contents
Introduction, Pass band transmission model Coherent
phase-shift keying –BPSK, QPSK Binary Frequency
shift keying (BFSK)
Error probabilities of BPSK, QPSK, BFSK
Generation and detection of Coherent PSK, QPSK, &
BFSK
Power spectra of above mentioned modulated signals
M-array PSK, M-array QAM
Non-coherent orthogonal modulation schemes -DPSK,
BFSK,
Generation and detection of non-coherent BFSK, DPSK
Comparison of power bandwidth requirements for all
the above
schemes.

118. Introduction:
Baseband Vs Bandpass
Bandpass model of detectionprocess
is equivalentto baseband
model because:
The receivedbandpasswaveformis first
transformed to a baseband waveform.
Equivalence theorem:
Performing bandpasslinearsignal processing
followedby
heterodying the signal to the baseband, …
… yields the same results as …
… heterodying the bandpass signal to the baseband , followed by a
baseband linear signal processing.
3

119. PASSBANDTRANSMISSIONMODEL
4

120. TypesOf DigitalModulation
Amplitude Shift Keying (ASK)
The most basic (binary) form of ASK involves the process of switching
the carrier either on or off, in correspondence to a sequence of digital
pulses that constitute the information signal. One binary digit is
represented by the presence of a carrier, the other binary digit is
represented by the absence of a carrier. Frequency remains fixed
Frequency Shift Keying (FSK)
The most basic (binary) form of FSK involves the process of varying
the frequency of a carrier wave by choosing one of two frequencies
(binary FSK) in correspondence to a sequence of digital pulses that
constitute the information signal. Two binary digits are represented
by two frequencies around the carrier frequency. Amplitude remains
fixed
Phase Shift Keying (PSK)
Another form of digital modulation technique which we will not
discuss
5

121. BINARYPHASESHIFTKEYING(PSK)
Baseband
Data
BPSK
modulated
signal
1
6
10 0
where s
0 =-Acos(
ct) and s
1 =Acos(
ct)
Major drawback –rapid amplitude change between
symbols due to phase discontinuity, which requires
infinite bandwidth. Binary Phase Shift Keying
(BPSK) demonstrates better performance than ASK
and BFSK
BPSK can be expanded to a M-ary scheme,
employing multiple phases and amplitudes as
different states
s
1 s
0 s
0 s
1

122. BPSKTRANSMITTER
7

123. BINARY TO
BIPOLAR
CONVERSION
8

124. COHERENTBPSKRECEIVER
9

125. BPSKWAVEFORM
10

126. 11

127. QPSK
⚫Quadrature Phase Shift Keying (QPSK) can be interpreted
as two independent BPSK systems (one on the I-channel
and one on Q-channel), and thus the same performance
but twice the bandwidth (spectrum) efficiency.
⚫QuadraturePhaseShiftKeyinghastwicethebandwidth
efficiencyofBPSKsince2bitsaretransmittedinasingle
modulationsymbol
⚫Quadrature Phase Shift Keying (QPSK) has twice the
bandwidth efficiency of BPSK, since 2 bits are transmitted
in a single modulation symbol.
12

128. SymbolandcorrespondingphaseshiftsinQPSK
13

129. QPSK
QPSK→QuadraturePhaseShiftKeying
Fourdifferentphasestatesinonesymbolperiod
Twobitsofinformationineachsymbol
Phase: 0π/2π3π/2 → possible phase
values
Symbol:00011
1
10
Note that we choose binary representations so an error between two
adjacent points in the constellation only results in a single bit
error
For example, decoding a phase to be π instead of π/2 will result in a "11"
when it should have been "01", only one bit in error.
14

130. 15

131. Nowwehavetwobasisfunctions
E
s= 2E
bsince2 bitsaretransmittedpersymbol
I=in-phasecomponentfroms
I(t).
Q=quadrature componentthatiss
Q(t).
16

132. QPSKTransmitter
ANOFFSETQPSKTRANSMITTER
17

133. QPSKWaveforms
18

134. QPSKReceiver
19

135. TypesofQPSK
⚫Conventional QPSKhastransitionsthrough zero(i.e.180
0phasetransition).Highlylinear
amplifiersrequired.
⚫InOffsetQPSK,thephasetransitionsarelimitedto90
0,thetransitionsontheIandQ
channelsarestaggered.
⚫In /4QPSKthesetofconstellation pointsaretoggled eachsymbol, sotransitionsthrough
zero cannotoccur.Thisscheme producesthelowestenvelopevariations.
⚫AllQPSKschemes requirelinearpoweramplifiers
I
Q
I
Q
I
Q
ConventionalQPSK
20
OffsetQPSK /4QPSK

136. FrequencyShiftKeying(FSK)
Baseband
Data
BFSK
modulated
signal
f
1 f
0 f
0 f
1
wheref
0=Acos(
c-)tandf
1=Acos(
c+)t
Example:The ITU-TV.21modemstandardusesFSK
FSKcanbeexpandedtoaM-aryscheme,employingmultiplefrequencies
asdifferentstates
1 10 0
21

137. Generation&Detection ofFSK
22

138. AmplitudeShiftKeying(ASK)
Baseband
Data
ASK
modulated
signal
Acos(t)Acos(t)
Pulse shaping can be employed to remove spectral spreading
ASK demonstrates poor performance, as it is heavily affected
by noise,
fading, and interference
23
1 10 0 0

139. ErrorProbabilitiesof PSK,QPSK,BFSK
24

140. PowerSpectralDensity(PSD)
In practical, pulse shaping should be considered for a precise bandwidth
measurement and considered in the spectral efficiency calculations.
Power spectral density (PSD) describes the distribution of signal power in the
frequency domain. If the baseband equivalent of the transmitted signal
sequence is given as


k
sk
aptkTgt
a
k
:Basebandmodulationsymbol
T
s
:Signalintervalpt:Pulseshape
ag
Pfff
21
T
s
thenthePSDofg(t)isgivenas
a
2
RnEaa
kkn
*


1
n
PfFpt

afR
ane
j2fnTs
where

141. M-ARYPhaseShiftKeying(MPSK)
In M-aryPSK,thecarrierphasetakesonone oftheM
possiblevalues,namely
i=2 * (i-1)/M
wherei=1,2,3, …..M.
Themodulatedwaveformcanbeexpressedas
where E
sis energy per symbol =(log
2 M) E
b
T
sis symbol period = (log
2 M) T
b.
26

142. TheaboveequationintheQuadratureformis
Bychoosingorthogonalbasissignals
definedovertheinterval 0t T
s
27

143. M-arysignalsetcanbeexpressedas
Sincethereareonlytwobasissignals,theconstellation
ofM-aryPSKis twodimensional.
TheM-arymessagepointsareequallyspacedona
circleof radiusE
s,centeredattheorigin.
Theconstellationdiagramofan8-aryPSKsignalsetis
showninfig.
28

144. M-ARYPSKTransmitter
29

145. CoherentM-ARYPSKReceiver
30

146. M-ARY Quadrature
Amplitude Modulation
(QAM)It’saHybridmodulation
Asweallowtheamplitudetoalsovarywiththephase,a
newmodulationschemecalledquadratureamplitude
modulation(QAM)isobtained.
The constellation diagram of 16-ary QAM consists of a
square lattice of signal points.
Combines amplitude and phase modulation
One symbol is used to represent n bits using one symbol
BER increases with n,
31

147. Thegeneral formofan M-aryQAMsignalcan be
definedas
where
E
min is the energy of the signal with the lowest amplitude
and
a
i and b
i are a pair of independent integers chosen
according to the location of the particular signal point.
In M-ary QAM energy per symbol and also distance
between possible symbol states is not a constant.
32

148. M-PSKANDM-QAM
M-PSK(CircularConstellations)
16-PSK
an
bn
4-PSK
16-QAM
4-PSK
an
33
M-QAM (Square Constellations)
bn
Tradeoffs
–Higher-ordermodulations(Mlarge)aremorespectrally
efficientbut less powerefficient (i.e.BERhigher).
–M-QAMismorespectrallyefficient thanM-PSKbut
alsomoresensitivetosystemnonlinearities.

149. QAMConstellationDiagram
34

150. DifferentialPhaseShiftKeying(DPSK)
•DPSK is a non coherent form of phase shift keying which
avoids the need for a coherent reference signal at the
receiver.
Advantage:
•Non coherent receivers are easy and cheap to build,
hence widely used in wireless communications.
•DPSK eliminates the need for a coherent reference signal
at the receiver by combining two basic operations at the
transmitter:
35

151. DPSKWaveforms
36

152. Transmitter/Generatorof DPSKSignal
37

153. Non-coherentDetection
38

154. Non-coherentDPSKReceiver
39
DPSKReceiver
Dpskreceiverusing
correlator

155. Non-coherentBFSKReceiver
40

156. ComparisonsBetweenModulationTechniques
41

157. VEMUINSTITUTEOFTECHNOLOGY
(ApprovedbyAICTE,New Delhi&AffiliatedtoJNTUA,Ananthapuramu)
P.Kothakota,Puthalapattu(M),ChittoorDist–517112AP,India
Department of Electronics and Communication Engineering
Digital Communication Systems
Unit-5
ChannelCoding
By
B SAROJA
Associate Professor
Dept. of . ECE

158. Contents
Error Detection & Correction
Repetition & Parity Check Codes, Interleaving Code
Vectors and Hamming Distance Forward Error
Correction (FEC) Systems
Automatic Retransmission Query (ARQ) Systems
Linear Block Codes –Matrix Representation of
Block Codes
Convolutional Codes –Convolutional Encoding,
Decoding Methods.

159. Introduction
: Types of
Errors
3

160. Single bit errors are the least likely type of errors in serial data
transmission because the noise must have a very short duration which
is very rare. However this kind of errors can happen in parallel
transmission.
Example:
If data is sent at 1Mbps then each bit lasts only 1/1,000,000 sec. or 1 μs.
For a single-bit error to occur, the noise must have a duration of only 1
μs, which is very rare.
4

161. BurstError
5

162. 6

163. The term burst error means that two or more bits in the data unit have
changed from 1 to 0 or from 0 to 1.
Burst errors does not necessarily mean that the errors occur in
consecutive bits, the length of the burst is measured from the first
corrupted bit to the last corrupted bit. Some bits in between may not
have been corrupted.
7

164. Burst error is most likely to happen in serial transmission since the duration of
noise is
normally longer than the duration of a bit.
The number of bits affected depends on the data rate and duration of noise.
Example:
??????If data is sent at rate = 1Kbps then a noise of
1/100 sec can affect 10 bits.(1/100*1000)
??????If same data is sent at rate = 1Mbps then a
noise of 1/100 sec can affect 10,000
bits.(1/100*10
6
)
8

165. ErrorDetection
Error detection means to decide whether the received data is correct or not
without having a copy of the original message.
Error detection uses the concept of redundancy, which means adding extra bits
for detecting
errors at the destination.
9

166. ErrorCorrection
Itcanbehandledintwoways:
1)
2)
receiver can have the sender retransmit the entire data unit.
The receiver can use an error-correcting code, which
automatically corrects certain errors.
10

167. Single-bitErrorCorrection
To correct an error, the receiver reverses
the value of the altered bit. To do so, it
must know which bit is in error.
Number of redundancy bits needed Let
data bits = m
Redundancy bits = r
Total message sent = m+r
The value of r must satisfy the following
relation:
2
r
≥ m+r+1
11

168. ErrorCorrection
12

169. Repetetion
Retransmission is a very simple concept. Whenever one
party sends something to the other party, it retains a
copy of the data it sent until the recipient has
acknowledged that it received it. In a variety of
circumstances the sender automatically retransmits
the data using the retained copy.
13

170. ParityCheckCodes
information bits transmitted =
k bits actually transmitted = n
= k+1 Code Rate R = k/n =
k/(k+1)
Error detecting capability = 1
Error correcting capability = 0
14

171. Parity Codes–Example1
Even parity
(i) d=(10110) so,
c=(101101)
(ii)d=(11011)so,
c=(110110)
15

172. ParityCodes–Example2
Codingtablefor(4,3)evenparitycode
0 0 0 0 00 0
0 0 1 0 01 1
0 1 0 0 10 1
0 1 1 0 11 0
1 0 0 1 00 1
1 0 1 1 01 0
1 1 0 1 10 0
1 1 1 1 11 1
16
Dataword Codeword

173. ParityCodes
Todecode
Calculate sum of received bits in block (mod 2)
If sum is 0 (1) for even (odd) parity then the dataword is the first k bits of the received
codeword
Otherwise error
Codecandetectsingleerrors
Butcannotcorrecterrorsincetheerrorcouldbeinany
bit
Forexample,ifthereceiveddatawordis(100000)the
transmitteddatawordcouldhavebeen(000000)or
(110000)withtheerrorbeinginthefirstorsecond
placerespectively
Noteerrorcouldalsolieinotherpositionsincludingthe
paritybit.
17

174. Interleaving
Interleaving is a process or methodology to make a system more efficient, fast and
reliable by arranging datain a non contiguous manner. There are many uses for
interleaving at the system level, including:
Storage: As hard disks and other storage devices are used to store user and system
data, there is always a need to arrange the stored data in an appropriate way.
Error Correction: Errors in data communication and memory can be corrected
through interleaving.
18

175. CodeVectors
In practice, we have a message (consisting of words,
numbers, or symbols) that we wish to transmit. We
begin by encoding each “word” of the message as a
binary vector.
A binary code is a set of binary vectors (of the same
length) called code vectors.
The process of converting a message into code vectors is
called encoding, and the reverse process is called
decoding.
19

176. HammingDistance
Hamming distance is a metric for comparing two binary data strings.
While comparing two binary strings of equal length, Hamming distance is
the number of bit positions in which the two bits are different.
The Hamming distance between two strings, a and b is denoted as d(a,b).
It is used for error detection or error correction when data is transmitted
over computer networks. It is also using in coding theory for comparing
equal length data words.
Example :
Suppose there are two strings 1101 1001 and 1001 1101.
11011001 ⊕ 10011101 = 01000100. Since, this contains two 1s, the
Hamming distance, d(11011001, 10011101) = 2.
20

177. FECSystem
21

178. Forwarderrorcorrection(FEC)orchannel
techniqueused
transmissionover
channels.
forcontrollingerrorsin
codingisa
data
unreliableornoisycommunication
Thecentralideaisthesenderencodesthemessagein
aredundantwaybyusinganerror-correctingcode(ECC).
FECgivesthereceivertheabilitytocorrecterrorswithout
needingareversechanneltorequestretransmissionof
data,butatthecostofafixed,higherforwardchannel
bandwidth.
FEC is therefore applied in situations where
retransmissions
are costly or impossible, such as one-way communicationlinksandwhentransmittingtomultiplereceivers
in multicast.
22

179. AutomaticRepeatRequest(ARQ)
Automatic Repeat reQuest (ARQ), also known as Automatic Repeat
Query, is an error-controlmethod for data transmissionthat uses
acknowledgementsand timeoutsto achieve reliable data
transmission over an unreliable service.
If the sender does not receive an acknowledgment before the
timeout, it usually re-transmitsthe frame/packet until the sender
receives an acknowledgment or exceeds a predefined number of
re-transmissions.
The types of ARQ protocols include Stop-and-wait ARQ
Go-Back-N ARQ
Selective Repeat ARQ
All three protocols usually use some form of sliding window
protocolto tell the transmitter to determine which (if any)
packets need to be retransmitted.
23

180. ARQSystem
24

181. BlockCodes
Data is grouped Into Blocks Of Length k bits
(dataword)
Each dataword is coded into blocks of length n bits
(codeword), where in general n>k
This is known as an (n,k) block code
A vector notation is used for the datawords and
codewords,
Dataword d = (d
1 d
2….d
k)
Codeword c = (c
1 c
2……..c
n)
The redundancy introduced by the code is
quantified by the code rate,
Code rate = k/n
i.e., the higher the redundancy, the lower the code rate
25

182. BlockCode-Example
Data word length k = 4 Codeword length
n = 7
This is a (7,4) block code with code rate
= 4/7 For example, d = (1101), c =
(1101001)
26

183. Linear Block Codes:Matrix
Representation
parity bits n-k (=1 for Parity
Check) Message m = {m
1 m
2 …
m
k} Transmitted Codeword c =
{c
1 c
2 … c
n}
A generator matrix G
kxn
c mG
27

184. LinearBlockCodes
Linearity
Example:4/7HammingCode
k=4,n=7
4messagebitsat(3,5,6,7)
3paritybitsat(1,2,4)
Errorcorrectingcapability=1
Errordetectingcapability=2
c
1m
1G,
c
2m
2G
c
1c
2(m
1m
2)G
28

185. LinearBlockCodes
Iftherearekdatabits,allthatisrequiredistoholdklinearly
independentcodewords,i.e.,asetofkcodewordsnoneof
whichcanbeproducedbylinearcombinationsof2ormore
codewordsintheset.
Theeasiestwaytofindklinearlyindependentcodewordsisto
choosethosewhichhave‘1’injustoneofthefirstk
positionsand‘0’intheotherk-1ofthefirstkpositions.
29

186. LinearBlockCodes
Forexamplefor a(7,4) code,onlyfourcodewordsare
required,e.g.,
1000110
0100101
0010011
0001111
30
•So, to obtain the codeword for dataword 1011, the first, third
and fourth codewords in the list are added together, giving
1011010
•This process will now be described in more detail

187. An (n,k) block code has code vectors
d=(d
1 d
2….d
k) and c=(c
1 c
2……..c
n)
The block coding process can be written as
c=dG
where G is the Generator Matrix

31



k
2
a
a
a1
...

G
knk1
a
2n

a
1na
12...
a
22...
....
aak 2...
a
a
11

a
21

188. Thus,
k
32
c d
i a
i
i1
•a
i must be linearly independent, i.e., Since codewords
are given by summations of the a
i vectors, then to avoid
2 datawords having the same codeword the a
i vectors
must be linearly independent.
•Sum (mod 2) of any 2 codewords is also a codeword,
i.e.,
Since for datawords d
1 and d
2 we have;
d
3d
1 d
2

189. d
2i)a
i
k
d
2i a
i
i1
k
d
1i a
i
i1
k
(d
1i
i1
k
c
3 d
3i a
i
i1
So,
c
3c
1c
2
0isalwaysacodeword,i.e.,
Sinceallzerosisadatawordthen,
k
c0a
i0
i1
33

190. DecodingLinearCodes
One possibility is a ROM look-up table
In this case received codeword is used as an address
Example –Even single parity check code;
Address Data
000000 0
000001 1
000010 1
000011 0
……… .
Data output is the error flag, i.e., 0 –
codeword ok, If no error, dataword is first k
bits of codeword
For an error correcting code the ROM can
also store datawords. 34

191. ConvolutionalCodes
Block codes require a
buffer Example
k = 1
n = 2
Rate R = ½
35

192. ConvolutionalCodes:Decoding
Encoder consists of shift registers forming a finite state machine
Decoding is also simple –Viterbi Decoder which works by tracking
these states First used by NASA in the voyager space programme
Extensively used in coding speech data in mobile phones
36