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Bivariate Complex α-μ Statistics
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DOI：10.1109/TVT.2022.3141232.png)
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Abstract
En 中文
In this correspondence, new fundamental statistics for the alpha-mu fading model are derived. Broadly speaking, these involve two correlated complex alpha-mu variates with identical clustering parameters, but arbitrary nonlinearity and power parameters and nonuniform phase distribution. More specifically, the following statistics are derived: (i) exact joint bivariate probability density function (PDF) of quadrature processes; (ii) exact joint bivariate phase-envelope PDF; (iii) approximate bivariate phase PDF; (iv) exact phase correlation coefficient; (v) exact phase autocorrelation coefficient as a function of the fading environment parameters; (vi) phase power spectrum density; (vii) exact phase difference PDF; and (viii) approximate phase difference PDF. As a by-product, a useful mathematical identity is obtained. Strikingly, the approximate phase difference PDF encompasses, as a particular case, the von Mises or Tikhonov PDF. An application example considers a signal transmission over a slow-flat alpha-mu fading channel, and the pilot symbol assisted modulation as the channel estimation technique, assuming imperfect channel estimation. It is clearly seen that a uniform phase assumption depicts a pessimistic scenario.
Keywords:
Fading channels
Probability density function
Autocorrelation
Nakagami distribution
Analytical models
Mathematical models
Telecommunications
Bivariate distribution
alpha-mu distribution
envelope distribution
phase distribution
quadrature processes
Journal
IF:
7.1
Papers:
1.8W
Citations:
6.6W