4. Advantages of Digital TransmissionAdvantages of Digital Transmission
1. Noise Immunity of Digital Signals
2. Viability of Regenerative Repeaters in Digital Communicationy g p g
3. Digital signals can checked for errors.
4. A variety of services can afford over one line. For example, IpTV
connection can used to watch cable TV channels while browsing theconnection can used to watch cable TV channels while browsing the
Internet through a PC using same line. This line can also used to make a
phone call at the same time.
5 Digital data can be compressed and therefore possible to pass over5. Digital data can be compressed and therefore possible to pass over
higher bandwidths.
6. More secure. Digital data can be encrypt using an encryption method.
7 Supports data integrity Simple to integrate voice video and data7. Supports data integrity. Simple to integrate voice, video and data.
Digital transmission provides easier way to integrate different digital
formats.
8 Digital transmission provides higher maximum transmission rates via8. Digital transmission provides higher maximum transmission rates via
medium such as optical fibers.
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 4
7. Basic cause of ISI
⢠We need to transmit a pulse every Tb interval.
⢠The channel has a finite bandwidth.
i d t d t t th l lit d tl⢠we are required to detect the pulse amplitude correctly
(that is, without ISI).
⢠In our discussion so far, we are considering timeâlimited
pulses. Since such pulses cannot be bandâlimited, part of
their spectra is suppressed by a bandâlimited channel.
⢠This causes pulse distortion (spreading out) and,
consequently, ISI.q y,
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 7
8. How to eliminate ISIHow to eliminate ISI
⢠To eliminate ISI Nyquist proposed three⢠To eliminate ISI, Nyquist proposed three
different criteria for pulse shaping.
⢠We shall consider only the first two criteria.
The third is inferior to the first two, and,
hence, will not be considered here.
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 8
9. 1st Nyquist Criterion for Zero ISI
⢠In the first method, Nyquist achieves zero IS1 by choosing a
pulse shape that has a non zero amplitude at its center (say t
= 0) and zero amplitudes at t = (n = 1, 2, 3, . . .),bnTÂą) p ( , , , ),
⢠We can write such a pulse as:
bn
⢠There exists one (and only one) pulse that meets Nyquist's 1st
criterion and has a bandwidth Rb/2 Hz This pulse iscriterion and has a bandwidth Rb/2 Hz. This pulse isÂ
p(t)Â =Â sinc (nRbt)
⢠The Fourier transform of this is
⢠Using this pulse, we can transmit at a rate of Rb pulses per g p , p p
second without ISI, over a bandwidth of Rb/2.
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 9
11. Limitation of 1st criterion pulse
⢠Unfortunately, this pulse is impractical because it starts at ââ.
⢠We will have to wait an infinite time to generate it⢠We will have to wait an infinite time to generate it.
⢠Any attempt to truncate it would increase its bandwidth
/beyond Rb/2 Hz.
⢠But even if this pulse were realizable it has the undesirableBut even if this pulse were realizable, it has the undesirable
feature that it decays too slowly at a rate 1/t.
Thi i ti l bl⢠This causes some serious practical problems.
⢠For instance, if the nominal data rate of Rb bits required for, q
this scheme deviates a little, the pulse amplitudes will not
vanish at the other pulse centers and will cause ISILt Col A K Nigam, ITM University Gurgaon9/4/2013 11
12. 2nd Nyquist Criterion2nd Nyquist CriterionÂ
⢠The solution is to find a pulse p(t) thatThe solution is to find a pulse p(t) thatÂ
satisfies the condition specified but decaysÂ
faster than l / tfaster than l / t .
N i h d h h h l i⢠Nyquist had shown that such a pulse requiresÂ
a bandwidth of kRb/2, with 1 ⤠k ⤠2.
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 12
13. Roll Off factorRoll Off factor
⢠The bandwidth of P(w) is= / 2b xR W+( )
⢠where is the bandwidth in excess of the theoretical
b x
xW
minimum bandwidth.
⢠Let r (roll off factor) be the ratio of the excess bandwidth w,
to the theoretical minimum bandwidth thento the theoretical minimum bandwidth then
Excess BW
r =
2 /x
r
Theoretical Minimum BW
W
W R
=
= = 2 /
/ 2
x b
b
W R
R
= =
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 13
14. Observe that because wx is at most equal to wb/2 and
0 < r < l0 < r < l
The theoretical minimum bandwidth is Rb/2 Hz, andÂ
the excess bandwidth is thus fx = r Rb/2 Hz.
Th f th b d idth f P( ) iTherefore, the bandwidth of P(w) is
16. Equalization
The Need
⢠A pulse train is attenuated and distorted by the transmission
medium.
⢠The distortion is in the form of dispersion, which is caused
by an attenuation of highâfrequency components of theby an attenuation of highâfrequency components of the
pulse train.
⢠This need to be corrected for recovery of the signal at
receiver.
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 16
17. Characteristics for Equalizer
An equalizer should have a frequency characteristic that is the
inverse of that of the transmission medium
q
inverse of that of the transmission medium.
di i l i l h l li i i llFor digital signals, however, complete equalization is really not
necessary, because a detector has to make relatively simple
decisionsâsuch as whether the pulse is positive or negative (orp p g (
whether the pulse is present or absent)
A judicious choice of the equalization characteristics is a central
feature of all digital communication systems.
19. ZeroâForcing Equalizer
B i P i i lBasic Principle
⢠It eliminates or minimizes interference with
neighboring pulses at their respective samplingneighboring pulses at their respective sampling
instants only,
⢠This can be accomplished by the transversalâfilter⢠This can be accomplished by the transversalâfilter
equalizer which forces the equalizer output pulse to
have zero values at the sampling (decisionâmaking)p g ( g)
instants.
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 19
21. ⢠To begin with, set the tap gains co = 1 and ck = 0 for all other
values of K
⢠Thus the output of the filter will be the same but delayed by
NTb.NTb.
⢠We see that the pulse amplitudes a1 , aâ1, and a2 at Tb, âTb,
and 2Tb respectively are not negligibleand 2Tb, respectively, are not negligible.
⢠By adjusting the tap gains we generate additional shifted
pulses of proper amplitudes that will force the resultingpulses of proper amplitudes that will force the resulting
output pulse to have desired values at t = 0, Tb, 2Tb, âŚ.
⢠The output p0(t) is the sum of pulses thus
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 21
23. ⢠Substitution of this condition into Eq. yields a set of 2N + 1Â
i lt ti i 2N 1 i blsimultaneous equations in 2N + 1 variables :
The tapâgain ck's can be obtained by solving this set of equations.The tap gain ck s can be obtained by solving this set of equations.
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 23
25. Eye patternsEye patterns
⢠Shows combined effect of all the impairments on overallp
system performance.
⢠Is defined as the synchronized superposition of all possible
realizations of the signal of interest (e.g., received signal,
receiver output) viewed within a particular signalingp ) p g g
interval.
⢠An eye pattern provides a great deal of useful information
about the performance of a data transmission system,
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 25
28. Information obtained from Eye Diagram
⢠The width of the eye opening defines the time interval over which
the received signal can be sampled without error from interâg p
symbol interference
⢠The sensitivity of the system to timing errors is determined by the
rate of closure of the eye as the sampling time is varied.
⢠The height of the eye opening, at a specified sampling time,
d fi h i i f hdefines the noise margin of the system.
⢠In the case of an Mâary system, the eye pattern contains (M â 1)Â
e e openings Stacked p erticall one on the other here M iseye openings Stacked up vertically one on the other, where M isÂ
the number of discrete amplitude levels used to construct theÂ
transmitted signal.
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 28
29. Line Coding
⢠Digital data can be transmitted by various transmission or line
codes, such as onâoff, polar, bipolar, and so on.
⢠Each has its advantages and disadvantages.
⢠Among other desirable properties, a line code should have the
following properties:
1 T i i b d id h I h ld b ll ibl1. Transmission bandwidth: It should be as small as possible.
2. Power efficiency: For a given bandwidth and a specified
detection error probabilit the transmitted po er sho ld be asdetection error probability, the transmitted power should be as
small as possible.
Lt Col A K Nigam, ITM University Gurgaon9/4/2013 29
30. 3. Error detection and correction capability: It should be possible toÂ
detect, and preferably correct, detection errors. In a bipolar case,Â
for example a single error will cause bipolar violation and can easilyfor example, a single error will cause bipolar violation and can easilyÂ
be detected.
4. Favorable power spectral density: It is desirable to have zero PSDÂ
at w = 0 (dc), because ac coupling and transformers are used at theÂ
repeaters Significant power in low frequency components causesrepeaters. Significant power in lowâfrequency components causesÂ
dc wander in the pulse stream when ac coupling is used.
5. Adequate timing content: It should be possible to extract timingÂ
or clock information from the signal.
6. Transparency: It should be possible to transmit a digital signalÂ
correctly regardless of the pattern of 1's and 0âsIf the data are socorrectly regardless of the pattern of 1 s and 0 sIf the data are soÂ
coded that for every possible sequence of data the coded signal isÂ
received faithfully, the code is transparent.Lt Col A K Nigam, ITM University Gurgaon9/4/2013 30