Rayleigh Fading
Understanding Rayleigh Fading
Rayleigh fading is the defining characteristic of non-line-of-sight wireless channels. In urban environments, buildings, vehicles, and terrain scatter the transmitted signal into dozens of paths. When these paths combine at the receiver, they interfere constructively (signal enhancement) and destructively (deep fades), creating rapid signal variations.
Rayleigh Fading Statistics
- Amplitude: Follows Rayleigh distribution. Probability of deep fade decreases exponentially.
- Phase: Uniformly distributed from 0 to 2 pi.
- Fade depth: 10 dB fades occur about 0.5% of the time. 20 dB fades occur about 0.05%.
- Fade rate: At carrier frequency f_c and velocity v, the maximum Doppler frequency f_d = v x f_c / c determines the fade rate.
Mitigating Rayleigh Fading
- Diversity: Multiple antennas, frequencies, or time slots. The probability that all branches fade simultaneously is very low.
- OFDM: Divides the channel into many narrow subcarriers, each experiencing flat fading.
- MIMO: Uses multipath constructively to create parallel data channels.
Frequently Asked Questions
What is Rayleigh fading?
Rayleigh fading describes the rapid signal strength fluctuations in a non-line-of-sight wireless channel caused by multipath. The signal envelope follows a Rayleigh distribution, with frequent deep fades of 20-40 dB. It is the standard model for urban and indoor channels.
How deep are Rayleigh fades?
The Rayleigh distribution predicts that fades of 10 dB below the mean occur about 0.5% of the time, 20 dB fades about 0.05%, and 30 dB fades about 0.005%. These deep fades cause burst errors in digital communications.
How do you combat Rayleigh fading?
The primary techniques are diversity (spatial, frequency, or time), OFDM (which converts frequency-selective fading to many flat-fading subchannels), and MIMO (which exploits multipath for capacity gain). Link margins of 10-30 dB are also used.