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Communication System II
Chapter 3
Samrat SubediKantipur Engineering College
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Digital Data Communication
System
Communication System are Designed toTransmit Information.
The Purpose of Communication System isto transmit the output of Source toDestination.
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Two Fundamental Questions Of
Communication Theory are:
What is the rate at which given
source is emitting information.Information Theory
What is the maximum rate of
information transmitted over a noisychannel
Channel Capacity theorem
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Information Theory
A message is a sequence of Symbol
intended to reduce Uncertainty ofReceiver.
If a sequence of symbol does not change
the Uncertainty Level of the receiver, themessage does not contain anyinformation.
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Consider the following Cases
1. Tomorrow the Sun rises in the East.
2. United States invades Cuba.
3. Cuba invades United States
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From the Viewpoint of common sense
The first headline hardly contain Any information
The Second contain large amount of information
The third Convey the largest
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Therefore
The Information content of any messagesignal is closely related to
The past knowledge of Occurrence of event
andLevel of uncertainty it contains with respect to
the recipients of the message
Thus in general
The amount of information received fromknowledge of Occurrence of an event is relatedto the probability or the likelihood ofOccurrence of the Event.
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Measurement
Let m1,m2,m3mq be out of a possible
message emitted by a source withprobabilities p1,p2,pq Such that
p1+p2++pq=1
If I(mk) is the information Content of Kth
message Then,1. I(mk) > I(mj) for pk
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To Satisfy above Condition We canRelate I(mk) and pk
I(mk) = log (1/pk)
Unit of I(mk) depends on baseassigned to log
Base e nat
Base 10 Hartley or decitBase 2 bit
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Entropy
The average information content of asequence of symbol
Consider a memory less source( i.e. probability ofOccurrence of symbol does not depend upon previous and future Occurrence of
Symbol) emitting m possible Symbolss1,s2,s3sm with probabilities p1,p2,pmrespectively.
For a long message Sequence ContainingN Symbols, rate of Occurrence of siSymbol is
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P(si) = piN
And the information Content
I(si) = piNlog2(1/pi)
Then
Itot
=
We know entropy(H) is average information
contenti.e. Iavg =
=
m
i 1 pi)piNlog2(1/
N
Itot
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H = bits/Symbol
If Symbol rate(message rate) is Rsym then
information rate isRinfo = H X R sym
Bits/sec bits/ symbol symbol/sec
=
m
i 1pi)piNlog2(1/
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Baseband Digital Communication System
It refers to a system in which tx and Rx ofdigital Signal over a band limited channelwithout carrier modulation.
Since baseband Signal have sizablepower at low frequency, they are suitablefor transmission over a pair of cable,
coaxial cable, optical fiber etc.
Before Transmission some transformationin data waveform is needed.
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Baseband data communication system usingPAM have following Blocks
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The output of pulse generator is
x(t) = bk Pg(t- KTb)
Where Pg(t) is a basic Pulse whoseamplitude bK depends upon the input dataSequence
bk = +b if Kth bit is 1
bk = -b if Kth bit is 0
= -k
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The signal from pulse generator is thenpassed through Tx filter, Rx filter, The
channel with noise added at channel.
So the output of Receiver filter is
x(t) = Kc bk Pg(t- KTb-d) no(t)
Where,Kc is cumulative response of Tx filter, Channel and
Rx. Filter such that
Bk = Kc bK ; Pr(t) = Kc Pg(t) ;
dis time delay
=K
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For Simplicity , Let us take
no(t) = 0 and d =0
Therefore
x(t) = Kc bk Pg(t- KTb)
y(t) is then passed through decisionmaking device.
If y(t) is above threshold output is 1 else 0.
=k
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At Decision Making Instant
y(t=mTb) = Bk Pr(mTb- KTb)
= Bm + Pr(mTb- KTb)
The first Term is mth decoded bit and the secondterm represents the residue while decoding mth
bit due to all other transmitted bit called ISI
=k
=mk
k
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Design Criteria
ISI arises due to dispersion of pulse shapeby the filter and channel.
The major task of System Designer is to
optimally design transmitting and receivingfilter and the shape of basic pulse tominimize ISI.
Parameter Known to DesignerInput Bit StreamChannel Characteristics
Statistical Characteristics of Noise
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Selection Of Optimum HT(f)
Hc(f) Pg(t)
Criteria
Maximize data rate Optimize Bandwidth
Minimum Error Rate
Minimum Transmission Power
Maximize SNR
Simple Circuit Design
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Inter Symbol Interference (ISI)
Spreading of pulse beyond its interval Tb will
cause it to interfere with neighboring Pulse. Thisis called ISI
We need to Transmit a pulse every Time at
interval of Tb.We are considering a time limited pulse and
such pulse are not band limited.
Parts of their spectra are suppressed by bandlimited channel.
This cause pulse distortion and ConsequentlyISI
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Band Limited pulse can not be time
limited.
Pulse amplitude can be detected correctly
despite pulse spreading if there is no ISI atthe decision making Instant
This can be accomplished by properlyshaped band limited Pulse
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ISI Removing Methods
1. Nyquist Method
i. Ideal Solution (Zero ISI)
ii. Raised Cosine Spectrum Method
1. Correlative Coding (Partial ResponseSignaling)
i. Duobinary Signalling
ii. Modified Duobinary Signalling
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Nyquist Pulse Shaping Cr i t er ia / Nyquist Condi t ion for Zero I SI
We have;
= Bm + Pr(mTb- KTb)
For Zero ISI,
Pr [(m- K)Tb] = 1 k = m= 0 k = m
=mk
k
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i.e.
Pr (nTb) = 1 n = 0= 0 n = 0
In General
P(t) = 1 t = 0
= 0 t = nTb
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A Pulse Sat is fy ing above Cr i t er ia c auses Zero ISI at
Signal ing Instant
Sampling Instants
ISI occurs but,
NO ISI is present atthe sampling instants
0 Tb 2Tb
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Transmission of Rb bits/Sec require aminimum bandwidth of Rb/2 Hz.
The Pulse satisfying Nyquist criteria andhas B/W of Rb/2 Hz is
p(t) = sinc (2B0t) =Where,
B0 = 1 = Rb is absolute minimum B/W required
2Tb 2 for zero ISI
)2()2(
Bot
BotSin
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Although Nyquist Pulse Shaping shapes for p(t)achieves economy in B/W, it suffers from two majorproblem.
To generate a sync function Signal must
be passed through a Filter having flat
response from -B0 to +B0 and zero
elsewhere. This response are physicallyUnrealizable.
p(t) decreases too slowly at the
Rate of 1/t. If the nominal data rate of Rb bits/secrequired for this scheme deviates a little, the pulseamplitude will not vanish at other pulse centre. TheCumulative interference at any pulse centre from all theremaining pulse will be very high.
0f
P(f)
1/2B0
B0-B0
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Raised Cosine Approximation
The overall Frequency response P(f) decreases
towards zero gradually rather then abrupt. In particular p(f) consist of flat portion and roll off
portion that has the form of raised cosine function
as1/2B0 for 0 f f1
P(f)= 1+ cos (f- f1) for f1 f 2B0-f12B0-2f1
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Here, f1 and B0 are related as
= 1 f1/B0 , is roll off factor
For = 0;f1 = B0 is absolute minimum bandwidth required
for zero ISI (Nyquist B/W)
For =1 and taking Inverse Fourier Transform
P(t) = Sinc( 4B0t)
1- 16B02t2
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.
1 f/B 0
2B0P(f) =0
= 0.25
= 0.50= 0.75= 1.00
23/2
t
0
p(t)
-TbTb
1
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P(t)
1
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Characteristics of p(f)
For = 0, it is ideal case For = 0.5 & 1 p(f) cut off gradually and
hence it is physically implementable
Value of p(f) at f/B0 =1 will be half of itsmaximum value for any
P(f) is real i.e. non negative
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Characteristics of p(t)
At t= Tb/2, p(t) has half amplitude for =1 additional zero crossing at
+3Tb/2, +5Tb/2 in addition to Tb, 2Tb,.
These are used for generating timingsignal for Synchronization.
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Transmission Bandwidth Consideration
B/WPAM = B0 (B0= 1/2Tb)
Ideal Case For Raised Cosine
We have = 1 f1/B0
B= 2B0- f1= 2B0 B0(1- )
For =1
B/W = 2B0In general
B/WPAM =B0(1+ ) = Rb /2(1+ )35@Samrat Subedi
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Take an Example of T1 System
24 independent voice input based on 8 bit
PCM Word
Tb= 0.647 sec and Rb= 1.544 Mbps
Ideal solution B0= 1/2Tb = 772 KHz
Raised Cosine B= 1/Tb = 1.544 MHz
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Correlative-Level Coding
For Rb data Rate, the absolute min B/W as perNyquist Criteria is Rb/2 and with raised Cosine
minimum bandwidth is Rb.
By adding ISI to the transmitted signal in a
controlled manner, it is possible to achieve a signaling
rate equal to the Nyquist rate of 2Wsymbols/sec in a
channel of bandwidth WHz.
Correlative-level coding may be regarded as apractical method of achieving the theoretical
maximum signaling rate of 2 Wsymbols/sec in a
bandwidth ofWHz
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Data Rate Bandwidth ISI Condition
Rb B0(Rb/2)Zero Ideal
Rb 2B0(Rb) Zero Raised Cosine ( =1 )Rb B0(Rb/2)
Controlled ISI Correlative Coding
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DUOBINARY CODING
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DUOBINARY CODING
Duobinary signaling implies doubling the transmission
capacity in a straight binary system. This particular formof correlative-level coding is also called class I partialresponse.
Consider a binary input sequence {bk} applied to a pulse-
amplitude modulator to produce a two-level sequence{ak} :
+A if symbol bk is 1
ak = {-A if symbol bk is 0
When this sequence is applied to a duobinary encoder, it is
converted into a three-level output, namely, -2A, 0, and +2A. 39@Samrat Subedi
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We may express the duobinary coder output ckas the
sum of the present input pulse akand its previous value
ak-1, as shown by
ck = ak + ak-1
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+2A If ak & ak-1 are both 1
Ck = 0 If ak & ak-1 are different-2A If ak & ak-1 are both 0
And We have
HI(f) = HNyquist(f) . HDB(f)
For Tb seconds delay element having frequency response
exp(-j2fTb), the frequency response of the delay-line is
1 + exp(-j2fTb)
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Hence, the overall frequency response of this filterconnected in cascade with an ideal Nyquist channel is
HI(f) =HNyquist(f) [l + exp(-j2fTb)]
=HNyquist(f) [exp(jfTb) + exp(-jfTb)] exp(-jfTb)
= 2HNyquist(f) cos(fTb) exp(-jfTb)
For an ideal Nyquist channel of bandwidth W= 1/2Tb, we have
1 |f| < 1/2Tb (= B0)HNyquist(f) =
0 elsewhere
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The overall frequency response of the duobinarysignaling scheme has the form of a half-cycle cosinefunction, as
2cos(fTb) exp(-jfTb) |f| < 1/2Tb (=B0)
HI(f) =
0 otherwise
AND
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Frequency response of the duobinary conversionfilter. (a) Magnitude response. (b) Phase response.
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Ifckis received without error and if the previousestimate ak-1 corresponds to a correct decision, thenthe current estimate akwill be correct too.
A major drawback of this detection procedure is thatonce errors are made, they tend to propagate throughthe output because a decision on the current akdepends on the correctness of the decision made onthe previous a
k-1. 45@Samrat Subedi
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A means to avoid the error-propagation is to useprecoding before the duobinary coding
The precoding operation performed on the binary datasequence {bk} converts it into another binary sequence{dk} defined by
dk = bkdk-1 Ck = dk + dk-1
+A If it is 1dk = {
-A If it is 046@Samrat Subedi
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dK
If kth input bit bk=0Then dk=dk-1
Soif b
k
=0 Ck
= +2A or -2Aif bk =1 bk is complement of bk-1 ck=0
0 if data symbol bkis 1ck =
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Take an Example
Input bit Sequence{bk}
0 0 1 0 1 0
dk1
(let)1 1 0 0 1 1
Representation of dk +A +A +A -A -A +A +A
Output of DB
Encoder{ck=dk+dk-1}
+2A +2A 0 -2A 0 +2
ADecoded Bit 0 0 1 0 1 0
Put dk-1 =0 anddo again
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MODIFIED DUOBINARY SIGNALING
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MODIFIED DUOBINARY SIGNALING
If we observe the frequency response of duobinary
signalling, we see that it has non zero frequency responseat t=0
This is not Suitable for circuitary with no DC path. Hencewe use Modified DB.
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The overall frequency response of the delay-line
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The overall frequency response of the delay linefilter connected with an ideal Nyquist channel, as inFigure 4.16, is given by
HIV(f) =HNyquist(f) [l - exp(-j4fTb)]
= 2j HNyquist(f) sin(2fTb) exp(-j2fTb)
2jsin(2fTb) exp(-j2fTb), |f| < 1/2TbHIV(f) = {
0, elsewhere
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Baseband M-ary Signalling
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Baseband M-ary Signalling
In a basebandM-ary PAM system, the pulse-amplitude
modulator produces one ofMpossible amplitude levelswithM> 2.
A signal alphabet inM-ary PAM system containsMequally likely and statistically independent symbols, withsymbol duration T seconds.
The signaling rate 1/T is expressed in symbols persecond, or bauds.
This form of pulse modulation is illustrated in Figure4.20a for the case of quaternary (M= 4) system and thebinary data sequence 0010110111.
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Signaling Rate and B/W Requirement:
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Signaling Rate and B/W Requirement:-
Let Rs(Symbol per sec or Baud) be the Symbol rate
emitted by the source If M symbols are emitted that are equiprobable and
spastically independent
Entropy (H) = pilog
2(1/p
i)
Since M are equiprobable pi = 1/MTherefore
H = log2MAnd
Information Rate(Rinfo) =Rs x H Rslog2M bps
Absolute B/W required is Rs/2 --------
=
m
i 1
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For Binary
M=2
SO Rinfo = Rb = Rslog22= Rs bps
B/W = Rs/2 ---------
From Equation 1 & 2 we see
B/W requirement for Mary andbinary system is same
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Eye Diagram/ Eye Pattern
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Eye Diagram/ Eye Pattern
When the Sequence is transmitted over abaseband binary data transmissionsystem, the signal obtained at the outputYr(t) is a continuous time signal
1 1110 0
bT
bT2
bT3
bT40 bT5
ResultantChannel OutputWaveform
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If the received Signal is cut in each interval Tb and placeover one another, the diagram obtained is known as eyeDiagram as it looks like an eye.
Data 1
bT 0 bT0bT bT
Data 0
bT 0 bT0bT bT
Channel Input
Pulse width Tb
Channel Output
Pulse width Tb
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If the received Signal is cut in each interval Tb and placeover one another, the diagram obtained is known as eyeDiagram as it looks like an eye.
This pattern can also be obtained on CRO if Yr(t) is appliedto vertical input and a saw tooth signal with duration T=Tb
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Information Of Eye Diagram
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Information Of Eye Diagram
60@S S b di