Data Transmission Overview

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Data Transmission - Overview

• Signals
• Frequency domain representation of periodic
  signals
• Frequency domain representation of aperiodic
  signals
• Concept of bandwidth
• Relationship between data rate and bandwidth

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Electromagnetic Signals

• Continuous signal
• Various in a smooth way over time
• Discrete 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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PeriodicSignals

• A signal is periodic if and only if
• s(tT) s(t) for all t
• where T is a constant and is denoted as the
  period of of the signal
• Example
• s(t) A sin (2pf1t ?)
• A amplitude
• f1 frequency
• ? phase which denotes the relative position in
  time

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Addition of FrequencyComponents
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Frequency Domain Representation of Periodic
Signals - Key idea

• Any periodic signal can be shown to be made-up of
  component sine and cosine waves. This is called
  the Fourier series representation of a periodic
  signal
• Sinusoidal representation is useful because of
  the following characteristics
• A sine wave when subjected to a linear
  time-invariant operation, results in another sine
  wave of the same frequency.
• While in reality communication systems are not
  linear and time-invariant, the goal is to design
  system that are linear and time-invariant.

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Fourier Series

• Given any periodic signal s(t), the Fourier
  series representation is given by
• Where

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Fourier Series (Cont.)

• Thus the Fourier series representation of the
  periodic square pulse signal is given by
• X(f) (4k/p) sin 2pf0t 1/3 sin 2p(3f0)t 1/5
  sin 2p(5f0)t 1/7 sin 2p(7f0)t
• Only odd harmonics
• Amplitude of the nth harmonic is multiplied by a
  factor of (1/n)
• Note that in our case f0 1/2p

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Examples

• A tool to show Fourier series approximation can
  be found at
• http//www.jhu.edu/signals/fourier2/
• Example

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Spectrum Bandwidth

• Spectrum
• range of frequencies contained in signal
• Examples
• (1) for s(t) sin(2?f1t) 1/3 sin(2p(3f1)t) the
  spectrum is from f1 to 3f1
• (2) for s(t) square wave of time period T
  (1/f) the spectrum is f to ?
• Absolute bandwidth
• width of spectrum
• Examples
• (1) absolute bandwidth is 2f1
• (2) absolute bandwidth is ?

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Example 1

• Periodic signal have discrete spectrum
• Aperiodic signals have continuous spectrum

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Example 2

• Signal with a DC component
• Component with 0 frequency

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Power Spectrum Bandwidth

• The function s(t) specifies the signal in terms
  of voltage or current
• We would like to know the signal power as a
  function of the frequency -- power spectral
  density
• Effective bandwidth
• Often just bandwidth
• band of frequencies containing most of the power
• Half-power bandwidth
• Range of frequencies at which the power has
  dropped to half of its maximum value

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Relationship Between Data Rate and Bandwidth

• Just like the signal has a bandwidth, any
  transmission system has a bandwidth
• the transmission medium accommodates a limited
  band of frequencies
• This limits the data rate that can be carried
• Consider a periodic square wave s(t) of period T
• Using Fourier series the square wave can be
  expressed as
• s(t) (4?/k) ? n odd n1 -gt ? (1/n)sin(2?nf1t)
  
• where f11/T is the period of the signal

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Relationship Between Data Rate and Bandwidth

• This waveform has infinite number of harmonics
  and hence infinite bandwidth
• The peak amplitude of the kth component is 1/k
  that of the fundamental frequency
• Most of the power will be concentrated in the
  first few harmonics

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Example

• Let us consider that the square wave is very well
  approximated by the first three harmonics. I.e.,
• s(t) 4/p (sin 2pft 1/3 sin 2p 3f t 1/5 sin
  2p 5f t)
• Let T 1 microsecond. f 1 Mhz
• Data rate 2 Mbps
• Bandwidth required 4 Mhz
• If T 0.5 microsecond. f 2Mhz
• Data rate 4 Mbps
• Bandwidth required 8 Mhz

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Analog and Digital Data Transmission

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

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Data

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

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Analog (Stream) Date

• Voice, video occur in steady stream
• The data can take continuous values

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Block (Digital) Data

• Examples
• Text files
• Scanned color documents

Figure 3.1
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Video Data
_at_ 30 frames/sec 10.4 x 106 pixels/sec
_at_ 30 frames/sec 67 x 106 pixels/sec
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Transmission Medium

• Type
• Guided medium - e.g. twisted pair, optical fiber
• Unguided medium - e.g. air, water, vacuum
• Characteristic
• Simplex
• signal is transmitted in only one direction
• Half-duplex
• both station may transmit but only one at a time
• Full-duplex
• both stations may transmit simultaneously. The
  medium is carrying signals in both directions.

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Analog and Digital Transmission

• (a) Analog transmission all details must be
  reproduced accurately

• e.g. AM, FM, TV transmission

(b) Digital transmission only discrete levels
need to be reproduced
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A Generic Long-Distance Link

• Over distance
• Signal is attenuated
• Noise (thermal and electromagnetic) noise gets
  added.
• Repeaters regenerate signal

Figure 3.7
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An Analog Repeater

• Amplify the signal
• Eliminate distortion using the equalizer
• Different frequency components are
• Attenuated differently
• Delayed differently
• Noise accumulates

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A Digital Repeater

• Amplifier and equalizer mitigate some of the
  channel distortion
• Goal is not to regenerate the signal but to
  determine the original pulse
• Regenerate a fresh pulse
• Noise does not accumulate

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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 - degradation of signal quality
• Digital - 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
• Received signal strength
• must be enough to be detected
• must be sufficiently higher than noise to be
  received without error
• Attenuation is an increasing function of
  frequency

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Delay Distortion

• Only in guided media
• Propagation velocity varies with frequency

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Noise (1)

• Additional signals inserted between transmitter
  and receiver
• Thermal
• Due to thermal agitation of electrons
• Uniformly distributed
• White noise
• Intermodulation
• Signals that are the sum and difference of
  original frequencies sharing a medium

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Noise (2)

• Crosstalk
• A signal from one line is picked up by another
• Impulse
• Irregular pulses or spikes
• e.g. External electromagnetic interference
• Short duration
• High amplitude

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Signal to Noise Ratio
signal noise
signal
noise
Figure 3.12
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Nyquist Signaling Rate

• The Nyquist rate rmax is the maximum signaling
  rate that is achievable through an ideal low-pass
  channel with no inter-symbol interference
• If B is the bandwidth of the filter then
• rmax 2B signals/sec
• For example if B 4Khz then pulses can be sent
  every T 1/8000 125 microsecond
• If each signal is m bits, then
• rmax 2Bm bits/sec
• If a signal can take M levels, m log2M

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Impact of noise on Multi-level Encoding

• Multilevel transmission result in higher bit
  rate each signal now correspond to more bits
• R 2Bm bits/second
• More number of levels imply more decision errors
  and hence higher bit error rate
• Higher bit rate imply an impulse noise will
  corrupt more bits

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Shannon Channel Capacity

• What is the maximum achievable bit rate at which
  reliable communication is possible over an ideal
  channel of bandwith W and a given SNR?
• Result
• C Wlog2(1 SNR) bit/second
• If the transmission rate R is less than C then it
  is possible to design an encoding scheme that
  will result in error free transmission. Hence, it
  is the maximum possible transmission rate.

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Attenuation

• Reduction in signal power
• It is expressed in db
• Attenuation 10 log10(Pin/Pout)
• Power of a sinsoidal signal with amplitude A is
  A2/2

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Channel Characterization

• The channel can be characterized by two functions
• Amplitude-response function A(f)
• Phase shift function ?(f)

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Example of Amplitude Response Function

• Low pass channel
• Allows low frequency components to go through

1
f
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Attenuation

• Reduction in signal power
• It is expressed in db
• Attenuation 10 log10(Pin/Pout)
• Power of a sinsoidal signal with amplitude A is
  A2/2

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Channel Bandwidth

• The range of frequency that the channel allows
• Low pass channel allows frequency components
• Bandpass channel allows frequency component
  between f1 and f2

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Overview

• Guided - wire
• Unguided - wireless
• Characteristics and quality determined by medium
  and signal
• For guided, the medium is more important
• For unguided, the bandwidth produced by the
  antenna is more important
• Key concerns are data rate and distance

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Design Factors

• Bandwidth
• Higher bandwidth gives higher data rate
• Transmission impairments
• Attenuation
• Interference
• Number of receivers
• In guided media
• More receivers (multi-point) introduce more
  attenuation

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Guided Transmission Media

• Twisted Pair
• Coaxial cable
• Optical fiber

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Transmission Characteristics of Guided Media
 
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Twisted Pair
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Attenuation as a function of frequency of twisted
pair
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Twisted Pair - Transmission Characteristics

• Analog
• Amplifiers every 5km to 6km
• Digital
• Use either analog or digital signals
• repeater every 2km or 3km
• Limited distance
• Limited bandwidth (1MHz)
• Limited data rate (100MHz)
• Susceptible to interference and noise

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Twisted Pair - Applications

• Most common medium
• Telephone network
• Between house and local exchange (subscriber
  loop)
• Within buildings
• To private branch exchange (PBX)
• For local area networks (LAN)
• 10Mbps or 100Mbps

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Twisted Pair - Pros and Cons

• Cheap
• Easy to work with
• Low data rate
• Short range

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Coaxial cable
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Attenuation as a function of frequency
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Coaxial Cable - Transmission Characteristics

• Analog
• Amplifiers every few km
• Closer if higher frequency
• Up to 500MHz
• Digital
• Repeater every 1km
• Closer for higher data rates

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Coaxial Cable Applications

• Television distribution
• Ariel to TV
• Cable TV
• Long distance telephone transmission
• Can carry 10,000 voice calls simultaneously
• Being replaced by fiber optic
• Short distance computer systems links
• Local area networks

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Optical fiber
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Attenuation as a function of wavelength
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Optical Fiber - Transmission Characteristics

• Act as wave guide for 1014 to 1015 Hz
• Portions of infrared and visible spectrum
• Light Emitting Diode (LED)
• Cheaper
• Wider operating temp range
• Last longer
• Injection Laser Diode (ILD)
• More efficient
• Greater data rate
• Wavelength Division Multiplexing

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Optical Fiber - Benefits

• Greater capacity
• Data rates of hundreds of Gbps
• Smaller size weight
• Lower attenuation
• Electromagnetic isolation
• Greater repeater spacing
• 10s of km at least

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Wireless Propagation

• Signal travels along three routes
• Ground wave
• Follows contour of earth
• Up to 2MHz
• AM radio
• Sky wave
• Amateur radio, BBC world service, Voice of
  America
• Signal reflected from ionosphere layer of upper
  atmosphere
• (Actually refracted)
• Line of sight
• Above 30Mhz
• May be further than optical line of sight due to
  refraction

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Ground Wave Propagation
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Sky Wave Propagation
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Line of Sight Propagation
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Refraction

• Velocity of electromagnetic wave is a function of
  density of material
• 3 x 108 m/s in vacuum, less in anything else
• As wave moves from one medium to another, its
  speed changes
• Causes bending of direction of wave at boundary
• Towards more dense medium
• Index of refraction (refractive index) is
• Sin(angle of incidence)/sin(angle of refraction)
• Varies with wavelength
• May cause sudden change of direction at
  transition between media
• May cause gradual bending if medium density is
  varying
• Density of atmosphere decreases with height
• Results in bending towards earth of radio waves

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Optical and Radio Horizons
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Line of Sight Transmission

• Free space loss
• Signal disperses with distance
• Greater for lower frequencies (longer
  wavelengths)
• Atmospheric Absorption
• Water vapour and oxygen absorb radio signals
• Water greatest at 22GHz, less below 15GHz
• Oxygen greater at 60GHz, less below 30GHz
• Rain and fog scatter radio waves
• Multipath
• Better to get line of sight if possible
• Signal can be reflected causing multiple copies
  to be received
• May be no direct signal at all
• May reinforce or cancel direct signal
• Refraction
• May result in partial or total loss of signal at
  receiver

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Multipath Interference
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Line Encoding

• Encoding data into signals
• Digital data into digital signal
• Analog data into digital signal
• Digital data into analog signal
• Analog data into analog signal

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Analog and Digital Data Transmission

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

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Data

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

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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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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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Encoding digital data into digital signal
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Key Design Issues

• Bandwidth
• Timing information
• Immunity to noise
• Signal power
• Error detection

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Power spectrum of different encoding schemes

• NRZ has spectrum that is concentrated at the
  lower frequencies
• Bipolar codes are designed for bandpass channels
• Manchester encoding requires higher bandwidth

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Differential Encoding

• Detecting transitions is more immune to noise
• Differential encoding
• The signal level or the transition depends on the
  preceding sequence of bits
• Error occur in pairs

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Bit Error Rate and Eb/No

• Different encoding schemes need different amount
  signal power for a given probability of bit
  error.

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Analog Signals Carrying Analog and Digital Data
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Encoding Digital Data into Analog Signals
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Modulating a signal
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Multilevel PSK
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Other constellation
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Analog Data to Digital Signals

• Analog data is digitized to digital data codec
  (coder/decoder)
• Digital data can be encoded to digital signals
• Digital data can also be encoded into analog
  signal

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Pulse Amplitude Modulation

• The signal is sampled at a rate higher than twice
  the maximum frequency Nyquist Sampling Theorem

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Pulse Code Modulation

• Pulse amplitude modulation
• Quantization
• Quantization error for n bit quantized sample
• SNR(db) 6.02n 1.76bB

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Nonlinear Encoding

• In linear encoding the quantization levels are
  equally spaced
• Lower amplitude values have higher errors
• Companding (Compressing-expanding)

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Delta Modulation