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					  Wireless and Mobile
Communication Systems




  Lecture Slide Part 1 Version 2011-2012
  Mohd Nazri Mahmud
                   Fading
• Large-scale fading (shadowing)
  – Long term variation in the mean signal level
    caused by the mobile unit moving into the
    shadow of surrounding objects
• Small-scale fading (multipath)
  – Short term fluctuation in the signal amplitude
    caused by the local multipath

  Reference for Fading: Mobile Wireless
   Communications by Mischa Schwartz
             Shadow fading
• Long term shadow fading due to variations in
  radio signal power due to encounters with terrain
  obstructions such as hills or manmade
  structures such as buildings
• The measured signal power differ substantially
  at different locations even though at the same
  radial distance from a transmitter
• Represents the medium scale fluctuations of the
  radio signal strength over distances from tens to
  hundreds of meters
           Shadow Fading
• Many empirical studies demonstrate that
  the received mean power fluctuates about
  the average power with a log-normal
  distribution
• Can be modelled by a gaussian random
  variable with standard deviation, δ
                  Shadow fading
Consider the signal power equation in dB.

  PR,dB  10 log10  2  x  10 log10 g (d )  PT ,dB  10 log10 GT G R

The shadow-fading random variable x, measured
  in dB is taken to be a zero-mean gaussian
  random variable with variance δ2

                                            x2
                                        
                                    e       2 2
                         f ( x) 
                                    2 2
                     Shadow fading
    PR,dB  10 log10  2  x  10 log10 g (d )  PT ,dB  10 log10 GT G R

    PR,dB  10 log10  2  pdB

• Ignoring the multipath effect, α
          P R,dB  10 log10 g (d )  PT ,dB  10 log10 GT G R
• The term pdB is the local-mean power
  modelled as a gaussian random variable
  with average value P R ,dB
• The pdf for pdB is            
                                 pdB  P
                                                 2
                                                 
                                                                    
                                          R , dB

                                                 e         2 2
                                   f ( pdB ) 
                                                          2     2
             Shadow fading




• Typical value of δ range from 6 to 10dB
• Shadowing complicates cellular planning
• To fully predict shadowing effect, up-to-date and
  highly detailed terrain data bases are needed
               Multipath fading
• A small scale fading that describes short-term, rapid
  amplitude fluctuations of the received signal during a
  short period of time
• The actual power received over a much smaller distance
  vary considerably due to the destructive/constructive
  interference of multiple signals that follow multiple paths
  to the receiver
• The direct ray is actually made up of many rays due to
  scattering multiple times by obstructions along its path,
  all travelling about the same distance
• Each of these rays appearing at the receiver will differ
  randomly in amplitude and phase due to the scattering
Multipath fading
              Multipath fading
• Small-scale fading can be further classified into
  flat(or non-selective) fading and frequency
  selective fading
• Flat fading
  – small-scale fading is defined as being flat if the
    received multipath components of a symbol do not
    extend beyond the symbol’s time duration
  – If the delay of the multipath components with respect
    to the main component is smaller than the symbol’s
    duration time, a channel is said to be subject to flat
    fading
               Multipath fading
– In a flat fading channel inter-symbol interference (ISI) is absent
– The channel has a constant gain and a linear phase response
  over a bandwidth that is greater than the bandwidth of the
  transmitted signal.




– The spectral characteristics of the transmitted signal are
  preserved at the receiver
– The channel does not cause any non-linear distortion due to time
  dispersion
– However, the strength of the received signal generally changes
  slowly in time due to fluctuations caused by multipath
              Multipath fading
– In a flat-fading channel, the bandwidth of the transmitted signal,
  Bs is much less than the Coherence bandwidth, Bc of the
  channel
– The symbol period of the transmitted signal is much greater than
  the delay spread
– The delay spread, is the variation in the propagation delays of
  multiple scattered rays
– Typical values of delay spread are 0.2µs (rural area), 0.5µs
  (suburban area), 3-8µs (urban area), <2 µs (urban microcell) and
  50-300ns (indoor picocell)
   Frequency selective fading
• Frequency selective fading
  – small-scale fading is defined as being frequency
    selective if the received multipath components of a
    symbol extend beyond the symbol’s time duration
  – The effect of multipath fading on the reception of
    signals depends on the signal bandwidth
  – For relatively large bandwidth, different parts of the
    transmitted signal spectrum are attenuated differently,
  – This is manifested in the inter-symbol interference
    (ISI)
    Frequency selective fading
• Frequency selective fading
  – If the delay of the multipath components with respect
    to the main component is larger than the symbol’s
    duration time, a channel is said to be subject to
    frequency selective fading
  – The received signal includes multiple versions of the
    same symbol, each one attenuated (faded) and
    delayed.
  – The received signal is distorted producing ISI
    Frequency selective fading
• Frequency selective fading
  – The channel has a constant gain and a linear phase
    response over a bandwidth that is much smaller than
    the bandwidth of the transmitted signal.




  – The spectral characteristics of the transmitted signal
    are not preserved at the receiver
  – Certain frequency components have larger gains than
    others
    Frequency selective fading
• Frequency selective fading
  – the bandwidth of the transmitted signal, Bs is much
    greater than the Coherence bandwidth of the channel
  – The symbol period of the transmitted signal is much
    smaller than the delay spread
  – Digital symbol intervals, Ts smaller than 5 or 6 times
    the delay spread,ds give rise to frequency selective
    fading (Ts <2πds)
  – Typical values of delay spread are 0.2µs (rural area),
    0.5µs (suburban area), 3-8µs (urban area), <2 µs
    (urban microcell) and 50-300ns (indoor picocell)
            Multipath fading
• For flat fading, it is found that the multipath
  can be modelled by using the
  Rayleigh/Ricean statistics
• With Rayleigh statistics, the pdf of the
  random variable α is given by
                                     2
                                 
                                       2
                                     2 r
                 f ( )  2 e
                          r
Multipath fading
      Multipath fading-Rayleigh
• Rayleigh fading is viewed as a reasonable model for
  urban environments where there are many objects in the
  environment that scatter the radio signal before it arrives
  at the receiver
• there is no dominant propagation along a LOS between
  the transmitter and receiver.
• The central limit theorem holds that, if there is sufficiently
  much scatter, the channel impulse response will be well-
  modelled as a Gaussian process irrespective of the
  distribution of the individual components
• such a process will have zero mean and phase evenly
  distributted between 0 and 2π radians.
• The envelope of the channel response will therefore be
  Rayleigh distributed
Multipath fading
      Multipath fading-Rician
• If the environment is such that, in addition
  to the scattering, there is a strongly
  dominant signal seen at the receiver,
  usually caused by a LOS, then the mean
  of the random process will no longer be
  zero, varying instead around the power-
  level of the dominant path.
• Such a situation may be better modelled
  as Rician fading.
Multipath fading
    Small-scale fading due to
    movements: Doppler shift
• How rapidly the channel fades will be
  affected by how fast the receiver and/or
  transmitter are moving
• Motion causes Doppler shift in the
  received signal components
• the change in frequency of a wave for a
  receiver moving relative to the transmitter
                     Doppler shift
• Say a mobile phone moving at velocity v km/hr in the x direction and
  the radio wave impinging on the receiver at an angle βk
• The motion introduces a Doppler frequency shift,
               fk = vcos βk/λ




• If the ray is directed opposite to the mobile’s motion (β=0), then
  fk=v/λ
• The frequency of the signal has increased by the Doppler spread, fk
         Fast and Slow Fading
• Slow or fast fading depends on the coherence time, Tc
• Coherence time is the measure of period over which the
  fading process is correlated
• Tc is related to the delay spread, Tc=1/ds
• The fading is said to be slow if the symbol duration, Ts is
  smaller than the coherence time (or the bandwidth of the
  signal is greater than the Doppler spread.
            Time selective fading
• Occurs when the channel changes its characteristics during signal
  transmission
• This is due to the relative mobility of the transmitter and the receiver
  or some other time-varying behaviour in the propagation
  environment
• This causes the overall radio channel to be time-variant with time-
  varying delays and attenuations for the individual multipath
  components
• Receiver mobility causes the signal to change in comparison with
  the coherence time, Tc=0.18/fm where fm=the maximum Doppler
  frequency.
• The Doppler effect leads to time selective fading if Ts>Tc
• However, if the signal itself changes rapidly enough with respect to
  the reciprocal of the Doppler maximum frequency spread, fm ,
  distortion will not happen
• There is a minimum bandwidth beyond which the time selective
  fading can be eliminated
                  Assignments

A wireless LAN system operates at a data rate of
  54 Mbps. Determine whether or not this signal
  will encounter a frequency selective fading in the
  following areas
     •   Rural area
     •   Urban area
     •   Indoor area

				
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posted:9/5/2012
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