Chapter: Wireless Channels
where G(m) is the gamma function, with G(m + 1) = m! for integer shape factors m. The mean value is . In the special case that m = 1, Rayleigh fading is recovered, while for larger m the spread of the signal strength is less, and the pdf converges to a delta function for increasing m.
Here denotes the probability that pi < pth. Note that outage events vanish with the m-th power of the thresholds. This explains that (MRC) diversity effectively improves the performance of a radio link.
We define the fade margin h of a radio link as the ratio of the average received power over the threshold (i.e., the minimum required power for reliable communication), thus . The outage probability in a Nakagami fading channel can be expressed as