What will be the equation to get large scale fading coefficients if I consider Nakagami-m fading with lognormal shadowing considered in a MIMO channel? Like the following equation in case of Rayleigh fading how to get beta for nakagami fading?
beta(db)= -148.1-37.6log(d in km)+z
where z is the shadow fading.
Will the above equation be same for all types of fading distribution(rayleigh, rician, nakagami etc.) or it will vary?
If it doesn't vary then how can I model for nakagami-m fading?
Generally speaking, the large-scale fading coefficient beta(dB) is disconnected from the type of small-scale fading distribution. So you could use one way to selecting beta and then pick any distribution (Rayleigh, Rician, Nakagami) to model the small-scale fading variations around it.
However, the formula for beta(dB) that you describe is not universal. The numbers have probably been selected by making measurements in a particular type of propagation environment. In that environment, a certain small-scale fading distribution might be closer to reality than another one. What I say is that, if you change the small-scale fading distribution, then you are changing the type of propagation environment that you are generating and then one might have to change the large-scale fading as well...
Thanks Emil sir for your response. I just wanted to be clear that if I want to use this formula and also use nakagami fading distribution then will this beta(db) formula change or it will only effect overall subchannel coefficient? And also how to get that small scale coefficient for nakagami fading?
Please reply Emil Björnson sir.
Yes, you can consider the large scale model and the small scale mode independently. The small scale model determines the statistical distribution (e.g., Nakagami, Rayleigh, Rician, etc) of the overall channel gain random variable while the large scale model determines the variance of the distribution.
For example, you can consider the Nakagami or Rayleigh or Rician distributions with variance=1 for the small scale fading component. Any distribution considered for the small scale fading component also applies to the overall channel gain random variable but the variance is determined according to the model chosen for the large scale fading component. For example, if unite variance Nakagami distribution is chosen for the small scale component of the channel gain then the overall channel gain would also have Nakagami distribution but with the variance that is given by the large scale formula for example you specified in your question. The formula, however is not universal as professor Bjornson also mentioned and is based on the path loss + shadowing model with path loss exponent = 3.7 and the path loss gain measured at 1Km reference distance value.
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