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An Introduction to Wireless Fading Channels Name of the author: Nitin Jain Date Created   : 8 th  Jan 2010
Contents ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Wireless Channel ,[object Object],[object Object],[object Object],[object Object],Distance x Amplitude
Physical Phenomena
Physical Phenomena ,[object Object],[object Object],[object Object]
Path Loss Model ,[object Object],[object Object],[object Object],[object Object]
Wireless Propagation ,[object Object],[object Object],[object Object]
Path Loss Model ,[object Object],[object Object],[object Object],[object Object],[object Object]
Free Space Path Loss log (distance) Rx signal power(dBm)
Shadow Fading ,[object Object],[object Object],[object Object],[object Object],[object Object]
With Shadow Fading log (distance) Rx signal power(dBm) Shadow Fading Path loss
Large, medium and small scale fading ,[object Object],[object Object],[object Object]
Cause of Multipath Fading ,[object Object],[object Object],[object Object],[object Object]
Causes of Multipath fading Cont.. ,[object Object],[object Object]
Practical examples of small scale multipath fading ,[object Object],[object Object],[object Object]
Multipath Fading- Most difficult ,[object Object],[object Object]
Rayleigh Fading Mechanism ,[object Object],[object Object],[object Object],[object Object]
Rayleigh Fading  ,[object Object]
With Rayleigh Fading
Rayleigh Fading waveform envelope
Time Dispersion phenomenon time h(t) Freq Freq transform Different frequencies suffer different attenuation
Delay Spread –Time Domain interpretation
Delay Spread ,[object Object],[object Object],[object Object],[object Object],is the second moment ,[object Object],time h(t) Excess delay spread time h(t) Excess delay spread
Delay Spread- Freq. Domain Interpretation
Time spreading : Coherence Bandwidth ,[object Object],Freq Channel frequency   response W Freq W Channel frequency response f 0
More on flat fading Condition f0 > W does not guarantee flat fading. As shown above, frequency nulls (frequency selective fading) may be there occasionally  even though f0 > W.  Similarly, frequency selective fading channel may also show flat fading sometimes. ,[object Object],Freq Channel frequency   response W
Bit Rate Limitations by Delay Spread
Coherence Bandwidth and delay spread ,[object Object],[object Object],[object Object],Where  is r.m.s. delay spread
Effects of Flat & frequency selective fading ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Summary of Time dispersion ,[object Object],[object Object],Flat Fading BW of signal < BW of channel  Or  Delay Spread < Symbol period Frequency selective  Fading BW of signal > BW of channel  Or  Delay Spread > Symbol period
Time variant behavior of the channel ,[object Object],time h(t) Excess delay spread time h(t) Excess delay spread Impulse response Impulse response
Time Variance ,[object Object],[object Object]
Basic Doppler effect t) Propagation time is a function of time due to mobile car.  c is the light velocity and v m  is the car speed
Doppler spread in Multipath freq |X(f)| f c f c  + f d1  f c  + f d2  f c  + f d  |Y(f)| freq Due to multipaths, a single sinusoid by base station is perceived as summation of 3 sinusioids f c +f d1 , f c +f d2  and f c +f d  , where f d  is maximum doppler frequency = f c *(v m /d). Due to different arrivals of angle due to multipaths, perceived velocity is different for multipaths. After passing through multipath channel v m v m  cos ( θ 1 )   v m  cos ( θ 2 )   θ 1 θ 2
Doppler Spectrum This is called classical Doppler spectrum & shows how a single sinusoid ends up  having a broad spectrum due to multipath & relative motion between Tx and Rx. A popular model assumes that distribution of angle of arrival is distributed uniformly between 0 & 2 π  which leads to following spectrum Imagine now multiple paths with different angles of arrival causing amagamalation of various frequencies between f c  +f d  & f c -f d .
Time variant Channel: Coherence Time ,[object Object],[object Object],[object Object]
Frequency Dual Fourier Transform T 0 Function  denotes space time correlation  for the channel response to a sinusoid . So this indicates the amount of correlation between two sinusoids sent at different times t 1  & t 2  .
Waveform of Rayleigh Fading Signal
Time Variance : Fast Fading ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Time variance: Slow Fading ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Summary of Overall Fading
Summary of Multipath Fading characterization
References ,[object Object]

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Introduction To Wireless Fading Channels

  • 1. An Introduction to Wireless Fading Channels Name of the author: Nitin Jain Date Created : 8 th Jan 2010
  • 2.
  • 3.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9. Free Space Path Loss log (distance) Rx signal power(dBm)
  • 10.
  • 11. With Shadow Fading log (distance) Rx signal power(dBm) Shadow Fading Path loss
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 21. Time Dispersion phenomenon time h(t) Freq Freq transform Different frequencies suffer different attenuation
  • 22. Delay Spread –Time Domain interpretation
  • 23.
  • 24. Delay Spread- Freq. Domain Interpretation
  • 25.
  • 26.
  • 27. Bit Rate Limitations by Delay Spread
  • 28.
  • 29.
  • 30.
  • 31.
  • 32.
  • 33. Basic Doppler effect t) Propagation time is a function of time due to mobile car. c is the light velocity and v m is the car speed
  • 34. Doppler spread in Multipath freq |X(f)| f c f c + f d1 f c + f d2 f c + f d |Y(f)| freq Due to multipaths, a single sinusoid by base station is perceived as summation of 3 sinusioids f c +f d1 , f c +f d2 and f c +f d , where f d is maximum doppler frequency = f c *(v m /d). Due to different arrivals of angle due to multipaths, perceived velocity is different for multipaths. After passing through multipath channel v m v m cos ( θ 1 ) v m cos ( θ 2 ) θ 1 θ 2
  • 35. Doppler Spectrum This is called classical Doppler spectrum & shows how a single sinusoid ends up having a broad spectrum due to multipath & relative motion between Tx and Rx. A popular model assumes that distribution of angle of arrival is distributed uniformly between 0 & 2 π which leads to following spectrum Imagine now multiple paths with different angles of arrival causing amagamalation of various frequencies between f c +f d & f c -f d .
  • 36.
  • 37. Frequency Dual Fourier Transform T 0 Function denotes space time correlation for the channel response to a sinusoid . So this indicates the amount of correlation between two sinusoids sent at different times t 1 & t 2 .
  • 38. Waveform of Rayleigh Fading Signal
  • 39.
  • 40.
  • 42. Summary of Multipath Fading characterization
  • 43.

Notes de l'éditeur

  1. Think wireless channel as a FIR filter with a practically finite impulse response. The response of the filter keeps on changing due to time varying coefficients. The taps of the filter are corresponding to multipaths’s amplitude.
  2. Coherence bandwidth f0 is a statistical measure of the range of frequencies over which all the signal spectral components are affected in a similar way by the channel i.e. exhibiting fading or no fading. Coherence bandwidth is inversely proportional to excess delay spread. Same channel can show flat fading behaviour depending upon
  3. This just illustrates how delay spread puts a limit on maximum achievable data rate without needing an eqaulizer. Of course, various communication standards use various techniques to overcome this limits.
  4. Doppler shift will be positive or negative depending upon whether mobile is moving to or going away from base station.
  5. Here the effect of time dispersion &amp; time variant behaviour of the model can be seen easily. When Doppler spread is larger, time between two consecutive fades is shortened accordingly.