Doppler%20shifts:%20Effect%20on%20Communication%20systems

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Doppler shifts Effect on Communication systems

• Kartik Natarajan

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Doppler Overview/Review

• Apparent shifts in frequency of transmitted
  signal due to motion of transmitter/receiver or
  both.
• Shift depend on the relative velocity of the
  transmitter and receiver.
• Non-relativistic motion Relativistic motion
• Cellular communication hampered by multipath
  fading effects and receiver movement
  (non-relativistic Doppler).

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Small Scale Fading

• Rapid fluctuations in receiving conditions due to
  small movement of the receiver.
• Fading is caused by phase differences between
  waves reaching the receiver.
• Some causes
• Multipath Fading (Rayleigh and Rician)
• Frequency shift due to movement Doppler

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Doppler Fading (1/3)

• For a vehicle moving in a straight line at
  constant velocity v , the Doppler frequency
  shift, fd is given by
• Typical frequency range
• Most Cellular - 800 to 1500MHz
• UHF 300 to 3000MHz (used by TV, PCS etc.)
• Typical Doppler shifts
• 5Hz to 300 Hz
• For example, at for a carrier frequency of 2GHz
  and a mobile speed of 68 mph, max fd 200Hz

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Doppler Fading (2/3)

• Doppler Spread (BD) The difference between the
  maximum and minimum values of fd.
• Coherence Time (TC)
• Statistical measure of the time duration over
  which the channel is invariant.
• Defined as 1/ BD.
• Doppler spread and Coherence time characterizes
  fading speed and its frequency selectiveness.

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Doppler Fading (3/3)

• Characterization of fading channels
• Fast fading TS gt TC, and BS lt BD
• Higher the fading speed, more the distortion
• Slow fading TS ltlt TC, and BS gtgt BD
• Flat fading BS ltlt BD
• Non-Flat of Frequency selective fading
• BS gt BD

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Received Power Spectrum with Doppler (1/3)

• Assumptions
• Isotropic antenna with unity gain and receiving
  average power p (without Doppler).
• PDF of the direction of waves reaching the
  receiver is uniformly distributed between 0 and
  2?.
• Waves coming in from different directions add up
  to give a PSD S(f).
• Received signal frequency, f f0 fd
• The PSD for signals in the range f to fdf
  corresponds to the waves coming in the direction
  given by /- (? d?).
• gt S(f)df 2 d?(p/2?) d?p/?

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Received Power Spectrum with Doppler (2/3)

• Also, df -fmsin? where fd fmcos?
• But sin? sqrt(1 cos2(?))
• sqrt(fm2 (f- f0)2)/ fm
• So, df - sqrt(fm2 (f- f0)2)
• Substituting back, we get
• S(f) p/(?sqrt(fm2 (f- f0)2))

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Received Power Spectrum with Doppler (3/3)
Doppler Power Spectrum