Properties of the Mobile Radio Propagation Channel

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Properties of the Mobile Radio Propagation Channel

• Jean-Paul M.G. Linnartz
• Nat.Lab., Philips Research

2
Statistical Description of Multipath Fading

• The basic Rayleigh / Ricean model gives the PDF
  of envelope
• But how fast does the signal fade?
• How wide in bandwidth are fades?

• Typical system engineering questions
• What is an appropriate packet duration, to avoid
  fades?
• How much ISI will occur?
• For frequency diversity, how far should one
  separate carriers?
• How far should one separate antennas for
  diversity?
• What is good a interleaving depth?
• What bit rates work well?
• Why can't I connect an ordinary modem to a
  cellular phone?
• The models discussed in the following sheets
• will provide insight in these issues

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The Mobile Radio Propagation Channel
A wireless channel exhibits severe fluctuations
for small displacements of the antenna or small
carrier frequency offsets.
Amplitude
Frequency
Time
Channel Amplitude in dB versus location (
timevelocity) and frequency
4
Some buzz words about Time Dispersion and
Frequency Dispersion
Time Dispersion Frequency Dispersion
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Fading is characterised by two distinct mechanisms

• 1. Time dispersion
• Time variations of the channel are caused by
  motion of the antenna
• Channel changes every half a wavelength
• Moving antenna gives Doppler spread
• Fast fading requires short packet durations, thus
  high bit rates
• Time dispersion poses requirements on
  synchronization and rate of convergence of
  channel estimation
• Interleaving may help to avoid burst errors
• 2. Frequency dispersion
• Delayed reflections cause intersymbol
  interference
• Channel Equalization may be needed.
• Frequency selective fading
• Multipath delay spreads require long symbol times
• Frequency diversity or spread spectrum may help

6
Time dispersion of narrowband signal (single
frequency)
Transmit cos(2p fc t) Receive I(t) cos(2p fc
t) Q(t) sin(2p fc t) R(t) cos(2p fc t f)

• I-Q phase trajectory
• As a function of time, I(t) and Q(t) follow a
  random trajectory through the complex plane
• Intuitive conclusion
• Deep amplitude fades coincide with large phase
  rotations

7
Doppler shift

• All reflected waves arrive from a different
  angle
• All waves have a different Doppler shift

The Doppler shift of a particular wave is
Maximum Doppler shift fD fc v / c

• Joint Signal Model
• Infinite number of waves
• Uniform distribution of angle of arrival f
  fF(f) 1/2p
• First find distribution of angle of arrival the
  compute distribution of Doppler shifts
• Line spectrum goes into continuous spectrum

8
Doppler Spectrum
If one transmits a sinusoid, what are the
frequency components in the received signal?

• Power density spectrum versus received frequency
• Probability density of Doppler shift versus
  received frequency
• The Doppler spectrum has a characteristic
  U-shape.
• Note the similarity with sampling a
  randomly-phased sinusoid
• No components fall outside interval fc- fD,
  fc fD
• Components of fD or -fD appear relatively
  often
• Fades are not entirely memory-less

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Autocorrelation of the signal
We now know the Doppler spectrum. But how fast
does the channel change?

• Wiener-Kinchine Theorem
• Power density spectrum of a random signal is the
  Fourier Transform of its autocorrelation
• Inverse Fourier Transform of Doppler spectrum
  gives autocorrelation of I(t) and Q(t)

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Autocovariance of amplitude
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How to handle fast multipath fading?
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Frequency Dispersion

• Frequency dispersion is caused by the delay
  spread of the channel
• Frequency dispersion has no relation to the
  velocity of the antenna

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Frequency Dispersion Delay Profile
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Typical Delay Spreads
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Channel Parameters at 1800 MHz

• Environment Delay Spread Angle spread Max.
  Doppler shift
• Macrocellular Rural flat 0.5 ms 1 degree 200
  Hz
• Macrocellular Urban 5 ms 20 degrees 120 Hz
• Macrocellular Hilly 20 ms 30 degrees 200 Hz
• Microcellular Factory, Mall 0.3 ms 120
  degrees 10 Hz
• Microcellular Indoors, Office 0.1 ms 360
  degrees 2..6 Hz

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Typical Delay Profiles
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How do systems handle delay spreads?
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Frequency and Time Dispersion
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Scatter Function of a Multipath Mobile Channel
Gives power as function of

f

Doppler Shift (derived from angle )
Excess Delay


Example of a scatter plot
Horizontal axes


x-axis
Excess delay time


y-axis
Doppler shift
Vertical axis


z-axis
received power
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Scatter Function of a Multipath Mobile Channel
Example of a scatter plot
Excess Delay
Doppler Shift derived from angle f
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Correlation of Fading vs. Frequency Separation
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Coherence Bandwidth
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Effects of fading on modulated radio signals
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Effects of Multipath (I)
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Effects of Multipath (II)
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Time Dispersion Revisited

• The duration of fades and
• the optimum packet length

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Time Dispersion Revisited Duration of Fades
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Two-State Model
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Average Fade / Nonfade Duration
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Level Crossings per Second
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Average nonfade duration
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How to handle long fades when the user is
stationary?
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Optimal Packet length
35
Optimal Packet length
fc 900 MHz 72 km/h (v20 m/s) fade margin 10 dB
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Derivation of Optimal Packet length
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Average fade duration
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Conclusion

• The multipath channel is characterized by two
  effects
• Time and Frequency Dispersion
• Time Dispersion effects are proportional to speed
  and carrier frequency
• System designer needs to anticipate for channel
  anomalies