Digital communication systems unit 1

Digital Communication SystemsCode: ECL303

Prof A K Nigam

Unit 1: SyllabusUnit 1: Syllabus

• Advantages of Digital Transmission,

• Inter symbol Interference,

• Equalization,

• Eye Patterns• Eye Patterns,

• Line Coding techniques and its properties (Reference Book Digital and Analog Communications Systems B P Lathi)(Reference Book Digital and Analog Communications Systems ‐ B P Lathi)

Lt Col A K Nigam, ITM University Gurgaon9/4/2013 2

Basic Digital Communication Block Diagram


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, IpTVconnection can used to watch cable TV channels while browsing theconnection can used to watch cable TV channels while browsing theInternet through a PC using same line. This line can also used to make aphone 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 overhigher 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 digitalformats.

8 Digital transmission provides higher maximum transmission rates via8. Digital transmission provides higher maximum transmission rates viamedium such as optical fibers.


Noise Immunity and Viability of Regenerative Repeaters in y y g pDigital Communication


Intersymbol interference (ISI)Intersymbol interference (ISI)

• Spreading of a pulse beyond its interval willTSpreading of a pulse beyond its interval will cause it to interfere with neighboring pulses

bT

• This is known as intersymbol interference (ISI) hi h i h(ISI), which can cause errors in the correct detection of pulses.


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 time‐limitedpulses. Since such pulses cannot be band‐limited, part oftheir spectra is suppressed by a band‐limited channel.

• This causes pulse distortion (spreading out) and,consequently, ISI.q y,


How to eliminate ISIHow to eliminate ISI

• To eliminate ISI Nyquist proposed three• To eliminate ISI, Nyquist proposed threedifferent 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.


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, . . .),bnT±) p ( , , , ),

• We can write such a pulse as:bn

• There exists one (and only one) pulse that meets Nyquist's 1stcriterion and has a bandwidth Rb/2 Hz This pulse iscriterion and has a bandwidth Rb/2 Hz. This pulse is

p(t) = sinc (nRbt)

• The Fourier transform of this is

• Using this pulse, we can transmit at a rate of Rb pulses per g p , p psecond without ISI, over a bandwidth of Rb/2.


1st Nyquist Criterion Pulse shape1 Nyquist Criterion Pulse shape


Limitation of 1st criterion pulse• Unfortunately, this pulse is impractical because it starts at ‐∞.

• 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 undesirablefeature 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, qthis scheme deviates a little, the pulse amplitudes will notvanish at the other pulse centers and will cause ISILt Col A K Nigam, ITM University Gurgaon9/4/2013 11

2nd Nyquist Criterion2nd Nyquist Criterion

• The solution is to find a pulse p(t) thatThe solution is to find a pulse p(t) that satisfies the condition specified but decays faster than l / tfaster than l / t .

N i h d h h h l i• Nyquist had shown that such a pulse requires a bandwidth of kRb/2, with 1 ≤ k ≤ 2.


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

xWminimum 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 BWr =

2 /x

rTheoretical Minimum BWW W R

=

= = 2 // 2 x b

b

W RR

= =


Observe that because wx is at most equal to wb/2 and0 < r < l0 < r < l

The theoretical minimum bandwidth is Rb/2 Hz, and 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

Pulses satisfying the Nyquist criterion.


EqualizationThe Need

• A pulse train is attenuated and distorted by the transmissionmedium.

• The distortion is in the form of dispersion, which is causedby an attenuation of high‐frequency components of theby an attenuation of high‐frequency components of thepulse train.

• This need to be corrected for recovery of the signal atreceiver.


Characteristics for Equalizer

An equalizer should have a frequency characteristic that is theinverse 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 notnecessary, because a detector has to make relatively simpledecisions‐such 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 centralfeature of all digital communication systems.

Types of EqualizationsTypes of Equalizations

• Zero‐Forcing Equalizer

• Least Mean Squared Error Equalizer

• Automatic and adaptive equalizationAutomatic and adaptive equalization


Zero‐Forcing Equalizer

B i P i i lBasic Principle

• It eliminates or minimizes interference withneighboring pulses at their respective samplingneighboring pulses at their respective samplinginstants only,

• This can be accomplished by the transversal‐filter• This can be accomplished by the transversal‐filterequalizer which forces the equalizer output pulse tohave zero values at the sampling (decision‐making)p g ( g)instants.



• To begin with, set the tap gains co = 1 and ck = 0 for all othervalues of K

• Thus the output of the filter will be the same but delayed byNTb.NTb.

• We see that the pulse amplitudes a1 , a‐1, and a2 at Tb, ‐Tb,and 2Tb respectively are not negligibleand 2Tb, respectively, are not negligible.

• By adjusting the tap gains we generate additional shiftedpulses of proper amplitudes that will force the resultingpulses of proper amplitudes that will force the resultingoutput pulse to have desired values at t = 0, Tb, 2Tb, ….

• The output p0(t) is the sum of pulses thus


• The samples of p0(t) at t = kTb are

• Or

(Where KTb is replaced by K which does not make any difference)

• The Nyquist criterion requires the samples =0 for k # 0, and = 1 for k = 0.

• If we specify the values of p,[k] only at 2N + 1 points as


• Substitution of this condition into Eq. yields a set of 2N + 1 i lt ti i 2N 1 i blsimultaneous equations in 2N + 1 variables :

The tap‐gain 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.



Eye patternsEye patterns

• Shows combined effect of all the impairments on overallpsystem performance.

• Is defined as the synchronized superposition of all possiblerealizations of the signal of interest (e.g., received signal,receiver output) viewed within a particular signalingp ) p g ginterval.

• An eye pattern provides a great deal of useful informationabout the performance of a data transmission system,




Information obtained from Eye Diagram

• The width of the eye opening defines the time interval over whichthe received signal can be sampled without error from inter‐g psymbol interference

• The sensitivity of the system to timing errors is determined by therate 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 M‐ary system, the eye pattern contains (M ‐ 1) e e openings Stacked p erticall one on the other here M iseye openings Stacked up vertically one on the other, where M is the number of discrete amplitude levels used to construct the transmitted signal.


Line Coding• Digital data can be transmitted by various transmission or line

codes, such as on‐off, polar, bipolar, and so on.

• Each has its advantages and disadvantages.

• Among other desirable properties, a line code should have thefollowing 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 specifieddetection error probabilit the transmitted po er sho ld be asdetection error probability, the transmitted power should be assmall as possible.


3. Error detection and correction capability: It should be possible to detect, and preferably correct, detection errors. In a bipolar case, for example a single error will cause bipolar violation and can easilyfor example, a single error will cause bipolar violation and can easily be detected.

4. Favorable power spectral density: It is desirable to have zero PSD at w = 0 (dc), because ac coupling and transformers are used at the repeaters Significant power in low frequency components causesrepeaters. Significant power in low‐frequency components causes dc wander in the pulse stream when ac coupling is used.

5. Adequate timing content: It should be possible to extract timing or clock information from the signal.

6. Transparency: It should be possible to transmit a digital signal correctly regardless of the pattern of 1's and 0‘sIf the data are socorrectly regardless of the pattern of 1 s and 0 sIf the data are so coded that for every possible sequence of data the coded signal is received faithfully, the code is transparent.Lt Col A K Nigam, ITM University Gurgaon9/4/2013 30

(a)On‐off (RZ). ( ) ( )

(b)Polar (RZ).

(c) Bipolar (RZ).

(d) On‐off (NRZ)(d) On‐off (NRZ).

( ) P l (NRZ)(e) Polar (NRZ).


On‐off (RZ) or Unipolar RZ

For the case of a half‐width rectangular pulse


Polar (RZ) ( )

• We shall consider a specific pulse shape to be a rectangular p p p gpulse of width Tb/2 (a half‐width rectangular pulse), that is,


PSD of Polar RZ signal


Bipolar (RZ)/ AMIBipolar (RZ)/ AMI

For the case of a half‐width rectangular pulse PSD is given by


Comparison of PSDComparison of PSD


Manchester EncodingManchester Encoding(Also called split‐phase/ twinned‐binary signal)

• Manchester code ensures frequent line voltage transitions, directly proportional to the clock rate; this helps clock recovery.

• The DC component of the encoded signal is not dependent• The DC component of the encoded signal is not dependent on the data and therefore carries no information, allowing the signal to be conveyed conveniently by media (e.g., h ) hi h ll dEthernet) which usually do not convey a DC component.


Manchester EncodingManchester Encoding


Manchester Coding PSDManchester Coding PSD


Engineering

Digital communication systems unit 1