JPL's Wireless Communication Reference Website

Chapter: Wireless Propagation Channels
Section: Multipath Fading

Fade Duration

The mobile Rayleigh or Rician radio channel is characterized by rapidly changing channel characteristics. As the amplitude of a signal received over such a channel also fluctuates, the receiver will experience periods during which the signal can not be recovered reliably. If a certain minimum (threshold) signal level is needed for acceptable communication performance, the received signal will experience periods of This two-state simplification of the wireless channel behavior is called a Gilbert-Elliot model.

  Figure: fade and non-fade periods for a sample of a fading signal.

It is of critical importance to the performance of digital mobile networks that the block length or packet duration is chosen taking into account the expected duration of fades and non-fade intervals. One of two approaches can taken:

If the data block length is larger than the average non-fade period, almost all blocks will experience a signal fade and a corresponding burst of bit errors. This may result in an excessive packet dropping rate, unless powerful error correction codes are used. If the system supports a feedback signal with acknowledgments of received blocks, it is mostly advantageous to use only limited error correction coding, but to rely on retransmission of lost blocks. To minimize the number of retransmissions, one should choose the block length shorter than the average fade and non-fade period.

Average Fade Duration

We use:

Outage Probability = Average number of fades per second * Average fade duration

where the average number of fades per second is called the threshold crossing rate.

Expressions for Average (Non-) Fade Duration

In a Rayleigh fading channel with fade margin M, the average nonfade duration (ANFD) is
 
               Ö(M)
ANFD  =      _________
              Ö(2p)fD
 
where fD is the Doppler spread, M is the ratio of the local-mean signal power and the minimum (threshold) power needed for reliable communication.

  Average non-fade duration in Rayleigh-fading channel versus fade margin for n = 1, 2, 3, 4, 5 and 6 Rayleigh-fading interfering signals. Normalized by dividing by the Doppler Spread.  

The curve for n = 6 closely resembles the curve the ANFD in an interference-free but noise-limited channel.

Thus

Calculation of the distribution of non-fade periods is tedious, but has been elaborated by Rice. Because of the shape of the Doppler spectrum, fade durations that coincide with a motion of about half a wavelength are relatively frequent.

Exercise

A subscriber of an analog NMT cellular system (900 MHz) connects a 1200 bit/s modem to his cellular phone. He drives his car at 36 km/h. The signal experiences wide-sense stationary noise. Experiment with the Javascript embedded calculator to find the fade margin required to ensure an average nonfade duration enough to pass 600 bits uninterrupted.
Answer

The average fade duration (AFD) is

 
             Ö(M)
AFD   =   -------------- [ exp{ 1/M} -1]
           Ö(2p)  fD
 
Thus

  Average fade duration in Rayleigh-fading channel versus fade margin for n = 1, 2, 3, 4, 5 and 6 Rayleigh-fading interfering signals. Normalized by dividing by the Doppler Spread.  

Experiments revealed that at large fade margins, the fade durations are approximately exponentially distributed around their mean value.

For deep fades, Rice showed that for Rayleigh fading, the probability that a fade duration t lasts longer than T seconds tends to

                AFD       2 AFD2            2 AFD2
  P(t > T) =  2 ----  I1 [------]   exp[-  --------] 
                 T          pT2               pT2            
  
where I1 is the modified Bessel function of the first kind. For small z, I1(z) approximates z/2.

 

How do systems avoid long fades when the user is stationary?

  Analog  
  GSM
  DECT
  • Diversity at base station
  • Best channel selection by handset
  IS95 Cellular CDMA
  • Wide band transmission avoids most deep fades (at least in macro-cells with large delay spread)
  • Power control
  Wireless LANs



JPL's Wireless Communication Reference Website 1993, 1995.