JPL's Wireless Communication Reference Website

Chapter: Wireless Channels
Section: Multipath fading, Rayleigh fading

Multiple Rayleigh-fading signals

In wireless system, typically interference from multiple transmitters is experienced. Each signal may experience multipath fading and shadowing. Cumulation of multiple Rayleigh-fading signals requires investigation of the nature of the signals contributing to the interference. We consider the signal behaviour during an observation interval of duration T which is short compared to the rate of channel fading This implies that the fading does not affect the amplitudes and phases of the signals. However, modulation can affect amplitudes and phases during T. Two extreme cases are distinguished: With coherent addition, the joint interference signal may exhibit deep fades, caused by mutual cancelling of phasors from the signals. This cannot continue for a sustained period due to the phase variations caused by angle modulation of each signal or by slightly different carrier frequencies due to Doppler shifts and free-running oscillators.

With incoherent cumulation, the joint interference signal behaves as a band-limited Gaussian noise source if the number of components is sufficiently large. Moreover, any fade of one of the signals is likely to be hidden by the other interfering signals. Hence, the joint interference signal tends to exhibit less multipath fluctuations per unit of time than the signal from one individual interferer.

Multiple incoherent Rayleigh-fading signals with equal mean-power

If the interference is caused by the power sum of n Rayleigh-fading signals, with identical local-mean power , the pdf of the joint interference power is the n-th convolution of the exponential distribution of the power of an individual interfering signal. The pdf of the joint interference power is found to have a gamma distribution. It may not be fully appropriate to speak of the envelope of such a joint interference signal, but if one defines the amplitude to be proportional to the square root of the power, then one finds that the amplitude has a Nakagami distribution.

The pdf of the joint interference power caused by interfering signals with different local-mean powers can be approximated by a gamma distribution.

JPL's Wireless Communication Reference Website Jean-Paul M.G. Linnartz, 1993, 1995.