Path loss vs fading; time dispersion fading

Path loss vs fading

Path loss is the average drop in signal power as the distance from the transmitter grows. Fading is the quick change of the received signal around that average, caused by multipath and motion.

Time dispersion fading

Time dispersion happens because multipath copies of a symbol arrive at different delays, so the received pulse is spread out in time. It is described by the rms delay spread σ_τ in time, or the coherence bandwidth B_c ≈ 1/(5σ_τ) in frequency. Depending on how the signal compares with these, there are two types.

1. Flat fading

• Condition: B_s ≪ B_c and T_s ≫ σ_τ.
• The channel has constant gain and linear phase over the full signal bandwidth, so all spectral parts of the signal fade together.
• The shape of the spectrum is kept but the received amplitude goes up and down (deep fades). Little or no ISI.
• Amplitude usually follows a Rayleigh distribution. Called a narrowband channel.
• Example: AMPS 30 kHz channel in a typical urban area.

2. Frequency selective fading

• Condition: B_s > B_c and T_s < σ_τ (a common rule is T_s < 10σ_τ).
• Different frequency components of the signal get different gains and phases.
• Received signal contains several delayed, attenuated versions of the symbol, so the pulse is spread in time and causes inter-symbol interference (ISI).
• Called a wideband channel; needs equalizers, RAKE receivers or OFDM.

 Flat fading           Freq. selective fading
 |H(f)|                |H(f)|
 |~~~~~~~~~~~~~        | /\    /\    /\
 |  [signal]           |/  \/\/ [signal]\
 +------------- f      +------------------ f
  B_s << B_c             B_s > B_c