In this paper, the statistical properties of the product of independent and non-identically distributed mixture Gamma (MG) random variables (RVs) are provided first. Specifically, simple exact closed-form expressions for the probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) are derived in terms of univariate Meijer's G-function. The statistical characterisations of the distribution of the ratio of products of MG variates are then derived. These statistics are used to analyse the outage probability (OP), the average error probability for different modulation schemes, the effective rate (ER) of communications systems and the average area under the receiver operating characteristics (AUC) curve of energy detection over cascaded fading channels. Additionally, the lower bound of secure outage probability (SOP L ) and probability of non-zero secrecy capacity (PNSC) of the physical layer and the OP of the multihop communications systems with decode-and-forward (DF) relaying protocol and cochannel interference (CCI) are studied by utilising the statistics of the ratio of the products. The derived performance metrics are applied for the Beaulieu-Xie and α − λ − η − µ shadowed fading channels that have not been yet investigated in the literature. Accordingly, the equivalent parameters of a MG distribution for the aforementioned channels are given. A comparison between the numerical results and the Monte Carlo simulations is presented to verify the validation of our analysis.
In this paper, the performance of the selection combining (SC) scheme over Fisher-Snedecor F fading channels with independent and non-identically distributed (i.n.i.d.) branches is analysed. The probability density function (PDF) and the moment generating function (MGF) of the maximum i.n.i.d. Fisher-Snedecor F variates are derived first in terms of the multivariate Fox's H-function that has been efficiently implemented in the technical literature by various software codes. Based on this, the average bit error probability (ABEP) and the average channel capacity (ACC) of SC diversity with i.n.i.d. receivers are investigated. Moreover, we analyse the performance of the energy detection that are widely employed to perform the spectrum sensing in cognitive radio networks via deriving the average detection probability (ADP) and the average area under the receiver operating characteristics curve (AUC). To validate our analysis, the numerical results are affirmed by the Monte Carlo simulations.
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