Nakagami fading
Besides Rayleigh and Rician fading, refined models for the pdf of a signal amplitude exposed to mobile fading have been suggested.
Sometimes, the pdf of the amplitude of a mobile signal can be described by the Nakagami m-distribution.
Nakagami Facts
- If the envelope is Nakagami distributed, the corresponding instantaneous power is gamma distributed.
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The parameter m is called the 'shape factor' of the Nakagami or the gamma distribution.
- In the special case m = 1, Rayleigh fading is recovered,
with an exponentially distributed instantaneous power
- For m > 1, the fluctuations of the signal strength reduce compared to Rayleigh fading.
- Nakagami fading occurs for instance for multipath scattering with relatively large delay-time spreads, with different clusters of reflected waves. Within any one cluster, the phases of individual reflected waves are random, but the delay times are approximately equal for all waves. As a result the envelope of each cumulated cluster signal is Rayleigh distributed. The average time delay is assumed to differ significantly between clusters. If the delay times also significantly exceed the bit time of a digital link, the different clusters produce serious intersymbol interference, so the multipath self-interference then approximates the case of co-channel interference by multiple incoherent Rayleigh-fading signals.
- After k-branch maximum ratio combining (MRC) in a diversity system with Rayleigh-fading signals, the resulting signal is Nakagami with m = k. MRC combining of m-Nakagami fading signals in k branches gives a Nakagami signal with shape factor mk.
- The Nakagami model is also often used to describe the interference cumulated from the multiple independently Rayleigh-fading sources, particularly if these are identically distributed (same local-mean power).
- Sometimes the Nakagami model is used to approximate a Rician
distribution. While this may be accurate for the main body of the probability density, it becomes highly inaccurate for the tails. As bit errors or outages mainly occur during deep fades, these performance measures are mainly determined by the tail of the probability density function (for probability to receive a low power). This it is inaccurate to approximate the fading of wanted Rician signal
by a Nakagami model, if one is interested in error rates or outage rates.
Further study, printable document
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Mathematical model presented in postscript format. |
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Mathematical model presented in acrobat format. |
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