Chapter 3

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Chapter 3 Data Transmission Concepts and
Terminology
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Transmission Terminology

• data transmission occurs between a transmitter
  receiver via some medium
• guided medium
• eg. twisted pair, coaxial cable, optical fiber
• unguided / wireless medium
• eg. air, water, vacuum

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Transmission Terminology

• 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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Transmission Terminology

• Simplex transmission
• one direction
• eg. television
• Half-duplex transmission
• either direction, but only one way at a time
• eg. police radio (walkie-talkie push-to-talk and
  release-to-listen)
• Full-duplex transmission
• both directions at the same time
• eg. telephone

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Time domain concepts of signals

• time domain concepts
• analog signal
• various 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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Analog and digital signals
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Periodic signals

• The signal period T is the inverse of signal
  frequency f
• The signal s(t) is periodic if
• The signal amplitude is denoted by A

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Sine wave

• Mathematically, the sine wave is given by
• Three parameters
• Peak amplitude (A)
• maximum strength of signal
• usually measured in volts
• Frequency ( f )
• rate of change of signal
• measured in Hertz (Hz) or cycles per second
• period time for one repetition ( T )
• T 1/f
• Phase ( ? )
• relative position in time

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Varying Sine Waves
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Wavelength (?)

• is the distance occupied by one cycle
• assuming signal velocity v, then ? vT
• or equivalently ?f v, since T1/f
• for the special case when vc
• c 3108 m/s (speed of light in free space)
• c?f

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Frequency Domain Concepts

• signal are made up of many frequencies
• components are sine waves
• Fourier analysis can shown that any signal is
  made up of component sine waves
• Fourier series of a square wave with
  amplitudes A and A

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Fourier Transform

• Mathematical tool that relates the
  frequency-domain description of the signal to its
  time-domain description

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Time-domain vs frequency-domain
Figure 3.5a frequency domain function for the
signal of Figure 3.4c.
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Time-domain vs frequency-domain
Time-domain
Frequency- domain
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Spectrum and bandwidth

• Spectrum
• range of frequencies contained in signal
• Absolute bandwidth
• width of spectrum
• effective bandwidth
• often just bandwidth
• narrow band of frequencies containing most
  energy
• DC Component
• component of zero frequency

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Acoustic Spectrum
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Analog and digital data transmission

• data
• entities that convey meaning
• signals signalling
• electric or electromagnetic representations of
  data, physically propagates along medium
• transmission
• communication of data by propagation and
  processing of signals

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Audio Signals

• freq range 20Hz-20kHz (speech 100Hz-7kHz)
• easily converted into electromagnetic signals
• varying volume converted to varying voltage
• can limit frequency range for voice channel to
  300-3400Hz

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Digital Data

• as generated by computers etc.
• has two dc components
• bandwidth depends on data rate

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Analog Signals
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Digital signals
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Advantages and disadvantages of digital signals

• cheaper
• less susceptible to noise
• but greater attenuation
• digital now preferred choice

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Transmission Impairments

• signal received may differ from signal
  transmitted causing
• analog - degradation of signal quality
• digital - bit errors
• most significant impairments are
• attenuation and attenuation distortion
• delay distortion
• noise

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Attenuation

• where signal strength falls off with distance
• depends on medium
• received signal strength must be
• strong enough to be detected
• sufficiently higher than noise to receive without
  error
• so increase strength using amplifiers/repeaters
• is also an increasing function of frequency
• so equalize attenuation across band of
  frequencies used

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Delay distortion

• propagation velocity varies with frequency
• hence various frequency components arrive at
  different times
• particularly critical for digital data
• since parts of one bit spill over into others
• causing intersymbol interference

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Noise

• Additional unwanted signals inserted between
  transmitter and receiver
• Thermal
• due to thermal agitation of electrons
• uniformly distributed
• white noise
• Interference from other users in a multi-user
  environment (e.g., mobile environment)

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Noise

• crosstalk
• a signal from one line is picked up by another
• impulse
• irregular pulses or spikes
• eg. external electromagnetic interference
• short duration
• high amplitude
• a minor annoyance for analog signals
• but a major source of error in digital data
• a noise spike could corrupt many bits

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Noise example
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Data-rate

• Data rate is the rate, in bits per second (bps),
  at which data can be communicated

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Spectrum, bandwidth and Data-rate

• Spectrum of a signal is the range of frequencies
  that it contains
• Absolute bandwidth is the width of the spectrum
• Effective bandwidth is a relatively narrow band
  that contains most signal energy
• Any transmission system has a limited bandwidth
• Square wave have infinite components and hence
  infinite bandwidth, but most energy in first few
  components
• Limited bandwidth increases distortion
• Limited bandwidth also limit the data rate that
  can be carried

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Bandwidth
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Data-rate and bandwidth
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Channel Capacity

• Channel Capacity max possible rate at which
  data can be transmitted over a given
  communication path, under given conditions
• Channel capacity is a function of
• data rate - in bits per second bps
• bandwidth - in Hertz Hz
• noise - on communication link
• error rate - the rate at which errors occur,
  reception of 1 when 0 is transmitted, and visa
  versa

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Nyquist Bandwidth

• Consider noise free channels
• If rate of signal transmission is 2B then we can
  carry signal with frequencies no greater than B
  
• i.e., given bandwidth B, highest signal rate is
  2B
• For binary signals (0,1), 2B bps need bandwidth
  B Hz
• Can increase rate by using M signal levels or M
  symbols (e.g. M4, Quaternary 00, 01, 10,11)
• Nyquist formula is
• So increase rate by increasing signal levels
• at cost of receiver complexity
• limited by noise other impairments

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Shannon Capacity Formula

• Consider relation of data rate, noise error
  rate
• faster data rate shortens each bit so bursts of
  noise affects more bits
• given noise level, higher rates means higher
  errors
• Signal-to-Noise Ratio (SNR)
• SNR in decibles (dB)
• Shannons channel capacity (C) in bits/s is
  related to the channel bandwidth (B) in Hertz and
  SNR by
• theoretical maximum capacity
• get lower in practise

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Nyquit bandwidth and Shannon Capacity

• Example Suppose that the spectrum of a channel
  is between 3MHz and 4MHz and the SNRdB24dB.
  Find
• 1. The channel bandwidth (B)
• 2. The channel capacity (C)
• 3. Based on Nyquist formula, how many signalling
  levels are required to achieve the max capacity
• Solution
• 1. B 4MHz - 3MHz 1MHz
• 2.
• 3.

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Decibels and signal strength

• It is customary to express gain or loss
  (attenuation) in decibels
• Logarithmic unit (compressed scale)
• Multiplication and division reduce to addition
  and subtraction
• The decibel power gain (GdB)
• The decibel power loss (LdB)
• The decibel voltage loss

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Decibels and signal strength

• Example 1 if a signal with a power level of 10mW
  is inserted onto a transmission line and the
  measured power some distance away is 5mW, then
  the loss can be expressed as
• Example 2 Consider a series of transmission
  elements in which the input is at a power level
  of 4mW, the first element is a transmission line
  with 12dB loss, the second element is an
  amplifier with 35dB gain, and the third element
  is a transmission line with 10dB loss.
• 1. The net gain is -12 35 10 13dB
• 2. The output power (Pout)

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Decibels and signal strength

• The dBW (decibel-Watt)
• Example a power of 1W is 0dBW,
• a power of 1000W is 30dBW,
• a power of 1mW is 30dBW
• The dBm (decibel-milliWatt)
• Example a power of 1mW is 0dBm,
• a power of 30dBm is 0dBW

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Example

• Given a receiver with an effective noise
  temperature of 294K and a 10 MHz bandwidth. Find
  the thermal noise level (N0) at the receivers
  output in units of dBW?

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The expression Eb/N0

• The expression Eb/N0 is the ratio of signal
  energy per bit (Eb) to noise power density per Hz
  (N0)

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Example

• For Binary Phase Shift Keying (BPSK) modulation,
  Eb/N0 8.4 dB is required for a bit error rate
  of 10-4 (one bit error out of every 10000 bits).
  If the effective noise temperature is 290 K (room
  temperature) and the data rate is 2400 bps, what
  received signal power level is required?

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Eb/N0 versus SNR

• We can relate Eb/N0 to the Signal-to-Noise Ratio
  (SNR)

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Example

• Suppose we want to find the minimum Eb/N0
  required to achieve a spectral efficiency C/B of
  6bps/Hz

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