With regard to small scale fading of a received signal in a mobile/wireless environment, I wonder if some kind of statistics are available which may tell us about the relative importance of different types of small-scale fading. In other words, in a given geographical area of certain type (let us say), what are the (approximate) respective percentages of (i) signals which are Rayleigh-distributed, (ii) signals which are Rice-distributed, (iii) signals which are Nakagami-distributed?
Practical channel does not have any of these distributions, but what is usually done is to measure channel and then fit a random distribution to it.
Nakagami has more degrees of freedom than Rayleigh, thus Nakagami will always provide a better fit to measurement data than Rayleigh. But many people ignore this fact for analytical simplicity and to avoid over-modeling. Both these models are for non-line-of-sight channels where there is zero mean.
Ricean fading is used when you have line-of-sight propagation, with a non-zero mean. So you need to figure out how often users are in line-of-sight. I think I've seen some 3GPP document saying that the probability of that is 1-distance/200 for distances smaller than 200 meters and then it is zero. At least it was something like that... At the end of the day, it depends on the actual scenario you are interested in simulating.
if u say that u want to know which data comes from i,ii,iii is better to use EM-methods with the model Data ~ (p-1)*p*Rayleight+(p-2)*p*Rice+(p-2)*(p-1)*Nakagami
estimating P(Zi=0), P(Zi=1),P(Zi=2) from the mixture (something common in literature) it will tell me exactly if Data is a signal from i, ii, or iii
Practical channel does not have any of these distributions, but what is usually done is to measure channel and then fit a random distribution to it.
Nakagami has more degrees of freedom than Rayleigh, thus Nakagami will always provide a better fit to measurement data than Rayleigh. But many people ignore this fact for analytical simplicity and to avoid over-modeling. Both these models are for non-line-of-sight channels where there is zero mean.
Ricean fading is used when you have line-of-sight propagation, with a non-zero mean. So you need to figure out how often users are in line-of-sight. I think I've seen some 3GPP document saying that the probability of that is 1-distance/200 for distances smaller than 200 meters and then it is zero. At least it was something like that... At the end of the day, it depends on the actual scenario you are interested in simulating.
All these distributions are interconnected. I believe that Rice distribution can also fit measured received signal in each scenario. However, the difference could be in the Rice K-factor. If Rice factor converges to zero we get a Rayleigh distributed received signal. Note that Rayleigh distribution is a subclass of Rice fading distribution. If one substitutes m-factor of Nakagami-m distribution by m=(K+1)^2/(2K+1), where K- is Rice factor, the resulting distribution is a Rice Fading distribution.
Additionally, it is not only the scenario that defines that fading envelop of a received signal. Systems aspects (e.g. bandwidth and beamforming gain) also play a crucial role in defining fading envelop of a Rx signal. Therefore, i recommend to study fading distributions with the system aspects. For details, i would recommend to study our contributions
-->" Influence of System Aspects on Fading at mm-Waves "
-->" On the Stochastic and Deterministic Behavior of mmWave Channels "
-->" Investigations on Fading Scaling with Bandwidth and Directivity at 60 GHz "
Dear Sir,
I suppose an attempt to answer will start by evaluating empirical channel measurements and evaluate the divergence from each distribution based on sampling environment or other parameter(s). Then you might have 'an insight' on how 'far' you are from classic models.
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