COE 341: Data

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COE 341 Data Computer Communications
(T081)Dr. Marwan Abu-Amara

• Chapter 3 Data Transmission

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Agenda

• Concepts Terminology
• Decibels and Signal Strength
• Fourier Analysis
• Analog Digital Data Transmission
• Transmission Impairments
• Channel Capacity

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Terminology (1)

• Transmitter
• Receiver
• Medium
• Guided medium
• e.g. twisted pair, optical fiber
• Unguided medium
• e.g. air, water, vacuum

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Terminology (2)

• Direct link
• No intermediate devices
• Point-to-point
• Direct link
• Only 2 devices share link
• Multi-point
• More than two devices share the link

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Terminology (3)

• Simplex
• One direction
• e.g. Television
• Half duplex
• Either direction, but only one way at a time
• e.g. police radio
• Full duplex
• Both directions at the same time
• e.g. telephone

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Frequency, Spectrum and Bandwidth

• Time domain concepts
• Analog signal
• Varies in a smooth way over time
• Digital signal
• Maintains a constant level then changes to
  another constant level
• Periodic signal
• Pattern repeated over time
• Aperiodic signal
• Pattern not repeated over time

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Analogue Digital Signals
8
PeriodicSignals
T
Temporal Period
S (tnT) S (t) Where t is time T is the
waveform period n is an integer
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Sine Wave s(t) A sin(2?ft ?)

• Peak Amplitude (A)
• maximum strength of signal
• unit volts
• Frequency (f)
• rate of change of signal
• unit Hertz (Hz) or cycles per second
• Period time for one repetition (T) 1/f
• Phase (?)
• relative position in time
• unit radians
• Angular Frequency (w)
• w 2 ?/T 2 ?f
• unit radians per second

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Varying Sine Wavess(t) A sin(2?ft ?)
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Wavelength (?)

• Distance occupied by one cycle
• Distance between two points of corresponding
  phase in two consecutive cycles
• Assuming signal velocity v
• ? vT
• ?f v
• For an electromagnetic wave,
• v speed of light in the medium
• In free space, v c 3108 m/sec

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Frequency Domain Concepts

• Signal usually made up of many frequencies
• Components are sine waves
• Can be shown (Fourier analysis) that any signal
  is made up of component sine waves
• Can plot frequency domain functions

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Addition of FrequencyComponents(T1/f)
Fundamental Frequency
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FrequencyDomainRepresentations
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Spectrum Bandwidth

• Spectrum
• range of frequencies contained in signal
• Absolute bandwidth
• width of spectrum
• Effective bandwidth
• Often just bandwidth
• Narrow band of frequencies containing most of the
  energy
• DC Component
• Component of zero frequency

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Signal with a DC Component
t
1V DC Level
t
1V DC Component
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Bandwidth for these signals
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Bandwidth and Data Rate

• Any transmission system supports only a limited
  band of frequencies for satisfactory transmission
• system includes TX, RX, and Medium
• Limitation is dictated by considerations of cost,
  number of channels, etc.
• This limited bandwidth degrades the transmitted
  signals, making it difficult to interpret them at
  RX
• For a given bandwidth Higher data rates
  More degradation
• This limits the data rate that can be used with
  given signal and noise levels, receiver type, and
  error performance
• More about this later!!!

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Bandwidth Requirements
1,3
Larger BW needed for better representation
BW 2f
More difficult reception with more limited BW
f
3f
1
1,3,5
BW 4f
5f
f
3f
2
1,3,5,7
BW 6f
7f
f
5f
3f
3

BW ?
1,3,5,7 ,9,?
?
f
5f
7f
3f
4
Fourier Series for a Square Wave
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Decibels and Signal Strength

• Decibel is a measure of ratio between two signal
  levels
• NdB number of decibels
• P1 input power level
• P2 output power level
• Example
• A signal with power level of 10mW inserted onto a
  transmission line
• Measured power some distance away is 5mW
• Loss expressed as NdB 10log(5/10)10(-0.3)-3 dB

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Decibels and Signal Strength

• Decibel is a measure of relative, not absolute,
  difference
• A loss from 1000 mW to 500 mW is a loss of 3dB
• A loss of 3 dB halves the power
• A gain of 3 dB doubles the power
• Example
• Input to transmission system at power level of 4
  mW
• First element is transmission line with a 12 dB
  loss
• Second element is amplifier with 35 dB gain
• Third element is transmission line with 10 dB
  loss
• Output power P2
• (-1235-10)13 dB 10 log (P2 / 4mW)
• P2 4 x 101.3 mW 79.8 mW

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Relationship Between Decibel Values and Powers of
10
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Decibel-Watt (dBW)

• Absolute level of power in decibels
• Value of 1 W is a reference defined to be 0 dBW
• Example
• Power of 1000 W is 30 dBW
• Power of 1 mW is 30 dBW

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Decibel Difference in Voltage

• Decibel is used to measure difference in voltage.
• Power PV2/R
• Decibel-millivolt (dBmV) is an absolute unit with
  0 dBmV equivalent to 1mV.
• Used in cable TV and broadband LAN

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Fourier Analysis
Signals
Aperiodic
Periodic (fo)
Discrete Continuous
Discrete Continuous
DFS
FS
FT
Finite time
Infinite time
DTFT
DFT
FT Fourier Transform DFT Discrete Fourier
Transform DTFT Discrete Time Fourier
Transform FS Fourier Series DFS Discrete
Fourier Series
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Fourier Series (Appendix B)

• Any periodic signal of period T (f0 1/T) can be
  represented as sum of sinusoids, known as Fourier
  Series

fundamental frequency
DC Component
If A0 is not 0, x(t) has a DC component
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Fourier Series

• Amplitude-phase representation

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Fourier Series Representation of Periodic Signals
- Example
x(t)
1
1/2
-1/2
1
3/2
-3/2
-1
2
-1
T
Note (1) x( t)x(t) ? x(t) is an even
function (2) f0 1 / T ½
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Fourier Series Representation of Periodic Signals
- Example
Replacing t by t in the first integral sin(-2pnf
t) - sin(2pnf t)
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Fourier Series Representation of Periodic Signals
- Example
Since x( t)x(t) as x(t) is an even function,
then Bn 0 for n1, 2, 3,
Cosine is an even function
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Another Example
x(t)
x1(t)
1
1
-1
2
-2
-1
T
Note that x1(-t) -x1(t) ? x(t) is an odd function
Also, x1(t)x(t-1/2)
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Another Example
Sine is an odd function
Where
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Fourier Transform

• For a periodic signal, spectrum consists of
  discrete frequency components at fundamental
  frequency its harmonics.
• For an aperiodic signal, spectrum consists of a
  continuum of frequencies (non-discrete
  components).
• Spectrum can be defined by Fourier Transform
• For a signal x(t) with spectrum X(f), the
  following relations hold

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Fourier Transform Example
x(t)
A
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Fourier Transform Example
Sin (x) / x sinc function
Study the effect of the pulse width ?
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The narrower a function is in one domain, the
wider its transform is in the other domain
The Extreme Cases
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Power Spectral Density Bandwidth

• Absolute bandwidth of any time-limited signal is
  infinite
• However, most of the signal power will be
  concentrated in a finite band of frequencies
• Effective bandwidth is the width of the spectrum
  portion containing most of the signal power.
• Power spectral density (PSD) describes the
  distribution of the power content of a signal as
  a function of frequency

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Signal Power

• A function x(t) specifies a signal in terms of
  either voltage or current
• Assuming R 1 W,
• Instantaneous signal power V2 i2 x(t)2
• Instantaneous power of a signal is related to
  average power of a time-limited signal, and is
  defined as
• For a periodic signal, the averaging is taken
  over one period to give the total signal power

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Power Spectral Density Bandwidth

• For a periodic signal, power spectral density is
• where ?(f) is
• Cn is as defined before on slide 27, and f0
  being the fundamental frequency

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Power Spectral Density Bandwidth

• For a continuous valued function S(f), power
  contained in a band of frequencies f1 lt f lt f2
• For a periodic waveform, the power through the
  first j harmonics is

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Power Spectral Density Bandwidth - Example

• Consider the following signal
• The signal power is

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Fourier Analysis Example

• Consider the half-wave rectified cosine signal
  from Figure B.1 on page 793
• Write a mathematical expression for s(t)
• Compute the Fourier series for s(t)
• Write an expression for the power spectral
  density function for s(t)
• Find the total power of s(t) from the time domain
• Find a value of n such that Fourier series for
  s(t) contains 95 of the total power in the
  original signal
• Determine the corresponding effective bandwidth
  for the signal

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Example (Cont.)

• Mathematical expression for s(t)

Where f0 is the fundamental frequency, f0
(1/T)
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Example (Cont.)

• Fourier Analysis

f0 (1/T)
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Example (Cont.)

• Fourier Analysis (cont.)

f0 (1/T)
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Example (Cont.)

• Fourier Analysis (cont.)

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Example (Cont.)

• Fourier Analysis (cont.)

Note cos2q ½(1 cos 2q)
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Example (Cont.)

• Fourier Analysis (cont.)

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Example (Cont.)

• Fourier Analysis (cont.)

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Example (Cont.)

• Fourier Analysis (cont.)

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Example (Cont.)

• Power Spectral Density function (PSD)
• Or more accurately

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Example (Cont.)

• Power Spectral Density function (PSD)

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Example (Cont.)

• Total Power

Note cos2q ½(1 cos 2q)
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Example (Cont.)

• Finding n such that we get 95 of total power

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Example (Cont.)

• Finding n such that we get 95 of total power

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Example (Cont.)

• Finding n such that we get 95 of total power
• Effective bandwidth with 95 of total power
• Beff fmax fmin
• 2f0 0 2f0

Beff
?
f
2f0
0
f0
3f0
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Data Rate and Bandwidth

• Any transmission system has a limited band of
  frequencies
• This limits the data rate that can be carried
• Example on pages 74 76 of textbook

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Bandwidth and Data Rates
Data Element, Signal Element
Period T 1/f
T/2
Bsys (Bsig 4f)
Data rate 1/(T/2) 2/T bits
per sec 2f
B
0
0
1
1
Given a bandwidth B, Data rate 2f 2(B/4) B/2
Two ways to double the data rate To double the
data rate you need to double f
1. Double the transmission system bandwidth, with
the same receiver and error rate (same
received waveform)
(Bsys 2B) (Bsig 4f)
2B
1
1
1
1
0
0
0
0
New bandwidth 2B, Data rate 2f 2(2B/4) B
f
3f
5f
2. Same transmission system bandwidth, B, with a
better receiver, higher S/N, or by tolerating
more error (poorer received waveform)
1
(Bsys B) (Bsys 2f)
1
1
1
0
0
0
0
B
Bandwidth B, Data rate 2f 2(B/2) B
3f
f
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Bandwidth and Data Rates

• Increasing the data rate (bps) with the same BW
  means working with inferior waveforms at the
  receiver, which may require
• Better signal to noise ratio at RX (larger signal
  relative to noise)
• Shorter link spans
• Use of more repeaters/amplifiers
• Better shielding of cables to reduce noise, etc.
• More sensitive ( costly!) receiver
• Dealing with higher error rates
• Tolerating them
• Adding more efficient means for error detection
  and correction- this also increases overhead!.

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Bandwidth and Data Rates
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Analog and Digital Data Transmission

• Data
• Entities that convey meaning
• Signal
• Electric or electromagnetic representations of
  data
• Transmission
• Communication of data by propagation and
  processing of signals

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Analog and Digital Data Transmission

• Data
• Can be either Analog data or Digital data
• Signal
• Can use either Analog signal or Digital signal to
  convey the data
• Transmission
• Can use either Analog transmission or Digital
  transmission to carry the signal

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Analog and Digital Data

• Analog
• Continuous values within some interval
• e.g. sound, video
• Digital
• Discrete values
• e.g. text, integers

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Acoustic Spectrum (Analog)
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Analog and Digital Signals

• Means by which data are propagated
• Analog
• Continuously variable
• Various media
• wire, fiber optic, space
• Speech bandwidth 100Hz to 7kHz
• Telephone bandwidth 300Hz to 3400Hz
• Video bandwidth 4MHz
• Digital
• Use two DC components

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Advantages Disadvantages of Digital Signals

• Advantages
• Cheaper
• Less susceptible to noise
• Disadvantages
• Greater attenuation
• Pulses become rounded and smaller
• Leads to loss of information

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Attenuation of Digital Signals
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Components of Speech

• Frequency range (of hearing) 20Hz-20kHz
• Speech 100Hz-7kHz
• Easily converted into electromagnetic signal for
  transmission
• Sound frequencies with varying volume converted
  into electromagnetic frequencies with varying
  voltage
• Limit frequency range for voice channel
• 300-3400Hz

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Conversion of Voice Input into Analog Signal
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Video Components

• USA - 483 lines scanned per frame at 30 frames
  (scans) per second
• 525 lines but 42 lost during vertical retrace
• So 525 lines x 30 frames (scans) 15750 lines
  per second
• 63.5?s per line
• 11?s for retrace, so 52.5 ?s per video line
• Max frequency if line alternates black and white
• Horizontal resolution is about 450 lines giving
  225 cycles of wave in 52.5 ?s
• Max frequency (for black and white video) is
  4.2MHz

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Binary Digital Data

• From computer terminals etc.
• Two dc components
• Bandwidth depends on data rate

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Conversion of PC Input to Digital Signal
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Data and Signals

• Usually use digital signals for digital data and
  analog signals for analog data
• Can use analog signal to carry digital data
• Modem
• Can use digital signal to carry analog data
• Compact Disc audio

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Analog Signals Carrying Analog and Digital Data
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Digital Signals Carrying Analog and Digital Data
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Four Data/Signal Combinations
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Analog Transmission

• Analog signal transmitted without regard to
  content
• Analog signal may be analog or digital data
• Attenuated over distance
• Use amplifiers to boost signal
• Also amplifies noise

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Digital Transmission

• Concerned with content
• Integrity endangered by noise, attenuation etc.
• Repeaters used
• Repeater receives signal
• Extracts bit pattern
• Retransmits
• Attenuation is overcome by a repeater by
  reconstructing the signal
• Noise is not amplified

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Four Signal/Transmission Mode Combinations
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Advantages of Digital Transmission

• Digital technology
• Low cost LSI/VLSI technology
• Data integrity
• Longer distances over lower quality lines
• Capacity utilization
• High bandwidth links economical
• High degree of multiplexing easier with digital
  techniques
• Security Privacy
• Encryption
• Integration
• Can treat analog and digital data similarly

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Transmission Impairments

• Signal received may differ from signal
  transmitted
• Analog signal - degradation of signal quality
• Digital signal - bit errors
• Caused by
• Attenuation and attenuation distortion
• Delay distortion
• Noise

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Attenuation

• Signal strength falls off with distance
• Depends on medium (guided vs. unguided)
• Attenuation affects received signal strength
• received signal strength must be enough to be
  detected
• received signal strength must be sufficiently
  higher than noise to be received without error
• signal strength can be achieved by using
  amplifiers or repeaters
• Attenuation is an increasing function of
  frequency
• Different frequency components of a signal get
  attenuated differently ? Signal distortion
• Particularly significant with analog signals
• for digital signals, strength of signal falls of
  rapidly with frequency
• Can overcome signal distortion using equalizers

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Delay Distortion

• Only in guided media
• Propagation velocity varies with frequency
• Highest at center frequency (minimum delay)
• Lower at both ends of the bandwidth (larger
  delay)
• Effect Different frequency components of the
  signal arrive at slightly different times!
  (Dispersion)
• Badly affects digital data due to bit spill-over
  (intersymbol interference)
• major limitation to max bit rate over a
  transmission channel
• Can overcome delay distortion using equalizers

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Noise

• Additional unwanted signals inserted between
  transmitter and receiver
• The most limiting factor in communication systems
• Noise categories
• Thermal
• Intermodulation
• Crosstalk
• Impulse

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Thermal (White) Noise

• Due to thermal agitation of electrons
• Uniformly distributed across the bandwidth
• Power of thermal noise present in a bandwidth B
  (Hz) is given by
• T is absolute temperature in kelvin and k is
  Boltzmanns constant (k 1.38?10-23 J/K)

Example at T 21 ?C (T 294 ?K) and for a
bandwidth of 10 MHz N -228.6 10 log 294
10 log 107 -133.9 dBW
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Intermodulation

• Occurs when signals at different frequencies
  share same transmission medium
• Produces signals that are the sum and/or the
  difference of original frequencies sharing the
  medium
• f1, f2 ? (f1f2) and (f1-f2)
• Caused by nonlinearities in the medium and
  equipment, e.g. due to overdrive and saturation
  of amplifiers
• Resulting frequency components (i.e. f1f2 and
  f1-f2) may fall within valid signal bands, thus
  causing interference

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Crosstalk Impulse

• Crosstalk
• A signal from one channel picked up by another
  channel
• e.g. Coupling between twisted pairs, antenna pick
  up, leakage between adjacent channels in FDM,
  etc.
• Impulse
• Irregular pulses or spikes
• Short duration
• High amplitude
• e.g. External electromagnetic interference
• Minor effect on analog signals but major effect
  on digital signals, particularly at high data
  rates

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Channel Capacity

• Channel capacity Maximum data rate usable under
  given communication conditions
• How BW, signal level, noise and other
  impairments, and the amount of error tolerated
  limit the channel capacity?
• Max data rate
• Function (BW, Signal wrt noise, Error rate
  allowed)
• Max data rate Max rate at which data can be
  communicated, bits per second (bps)
• Bandwidth BW of the transmitted signal as
  constrained by the transmission system, cycles
  per second (Hz)
• Signal relative to Noise, SNR signal
  power/noise power ratio (Higher SNR ? better
  communication conditions)
• Error rate bits received in error/total bits
  transmitted. Equal to the bit error probability

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1. Nyquist Bandwidth (Noise-free, Error-free)

• Idealized, theoretical
• Assumes a noise-free, error-free channel
• Nyquist If rate of signal transmission is 2B
  then a signal with frequencies no greater than B
  is sufficient to carry that signalling rate
• In other words Given bandwidth B, highest
  signalling rate possible is 2B signals/s
• Given a binary signal (1,0), data rate is same as
  signal rate ? Data rate supported by a BW of
  B Hz is 2B bps
• For the same B, data rate can be increased by
  sending one of M different signal levels
  (symbols) as a signal level now represents log2M
  bits
• Generalized Nyquist Channel Capacity, C 2B
  log2M bits/s (bps)

bits/signal
Signals/s
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Nyquist Bandwidth Examples

• C 2B log2M bits/s
• C Nyquist Channel Capacity
• B Bandwidth
• M Number of discrete signal levels (symbols)
  used
• Telephone Channel B 3400-300 3100 Hz
• With a binary signal (M 2)
• C 2B log2 2 2B 6200 bps
• With a quandary signal (M 4)
• C 2B log2 4 2B x 2 4B 12,400 bps
• Practical limit larger M makes it difficult for
  the receiver to operate, particular with noise

1
11
0
10
01
00
93
2. Shannon Capacity Formula (Noisy, Error-Free)

• Assumes error-free operation with noise
• Data rate, noise, error A given noise burst
  affects more bits at higher data rates, which
  increases the error rate
• So, maximum error-free data rate increases with
  reduced noise
• Signal to noise ratio SNR signal / noise levels
• SNRdB 10 log10 (SNR) dBs
• Shannon Capacity C B log2(1SNR)
• Highest data rate transmitted error-free with a
  given noise level
• For a given BW, the larger the SNR the higher the
  data rate I can use without errors
• C/B Spectral (bandwidth) efficiency, BE,
  (bps/Hz) (gt1)
• Larger BEs mean better utilizing of a given B for
  transmitting data fast.

Caution! Log2 Not Log10
Caution! Ratio- Not log
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Shannon Capacity Formula Comments

• Formula says for data rates ? calculated C, it
  is theoretically possible to find an encoding
  scheme that gives error-free transmission.
• But it does not say how
• It is a theoretical approach based on thermal
  (white) noise only
• However, in practice, we also have impulse noise
  and attenuation and delay distortions
• So, maximum error-free data rates obtained in
  practice are lower than the C predicted by this
  theoretical formula
• However, maximum error-free data rates can be
  used to compare practical systems The higher
  that rate the better the system is

95
Shannon Capacity Formula Comments Contd.

• Formula suggests that changes in B and SNR can be
  done arbitrarily and independently but
• In practice, this may not be the case!
• High SNR obtained through excessive amplification
  may introduce nonlinearities distortion and
  intermediation noise!
• High Bandwidth B opens the system for more
  thermal noise (kTB), and therefore reduces SNR!

96
Shannon Capacity Formula Example

• Spectrum of communication channel extends from 3
  MHz to 4 MHz
• SNR 24dB
• Then B 4MHz 3MHz 1MHz
• SNRdB 24dB 10 log10 (SNR)
• SNR 251
• Using Shannons formula C B log2 (1 SNR)
• C 106 log2(1251) 106 8 8 Mbps
• Based on Nyquists formula, determine M that
  gives the above channel capacity
• C 2B log2 M
• 8 106 2 (106) log2 M
• 4 log2 M
• M 16

97
3. Eb/N0 (Signal Energy per Bit/Noise Power
density per Hz) (Noise and Error Together)

• Handling both noise and error together
• Eb/N0 A standard quality measure for digital
  communication system performance
• Eb/N0 Can be independently related to the error
  rate
• Expresses SNR in a manner related to the data
  rate, R
• Eb Signal energy per bit (Joules)
• Signal power (Watts) x bit interval Tb
  (second)
• S x (1/R) S/R
• N0 Noise power (watts) in 1 Hz kT

98
Eb/N0 Example 1

• Given Eb/No 8.4 dB (minimum) is needed to
  achieve a bit error rate of 10-4
• Given
• The effective noise temperature is 290oK (room
  temperature)
• Data rate is 2400 bps
• What is the minimum signal level required for the
  received signal?
• 8.4 S(dBW) 10 log 2400 228.6 dBW 10
  log290
• S(dBW) (10)(3.38) 228.6
  (10)(2.46)
• S -161.8 dBW

99
Eb/N0 (Cont.)
Lower Error Rate larger Eb/N0

• Bit error rate for digital data is a decreasing
  function of Eb/N0 for a given signal encoding
  scheme
• Which encoding scheme is better A
  or B?
• ? Get Eb/N0 to achieve a desired error rate, then
  determine other parameters from formula, e.g. S,
  SNR, R, etc. (Design)
• Error performance of a given system (Analysis)
• Effect of S, R, T on error performance

B
A
Better Encoding
100
Eb/N0 (Cont.)

• From Shannons formula
• C B log2(1SNR)
• We have
• From the Eb/N0 formula
• With R C, substituting for SNR we get
• Relates achievable spectral efficiency C/B
  (bps/Hz) to Eb/N0

101
Eb/N0 (Cont.) Example 2

• Find the minimum Eb/N0 required to achieve a
  spectral efficiency (C/B) of 6 bps/Hz
• Substituting in the equation above
• Eb/N0 (1/6) (26 - 1) 10.5 10.21 dB