Statistics of the Product of Two α-ℱ Variates With Applications

In this letter, we consider the product of two independent and not identically distributed \alpha - \cal {F} variates. Specifically, novel closed-form expressions for the probability density function, the cumulative distribution function, and the n -th moments for the envelope as well as the inst...

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Bibliographic Details
Published in:IEEE communications letters 2021-06, Vol.25 (6), p.1761-1765
Main Author: Badarneh, Osamah S.
Format: Article
Language:English
Subjects:
Asymptotic properties
Bit error rate
cascaded fading channels
Channel capacity
Closed form solutions
Codes
Distribution functions
Exact solutions
Fading channels
Mathematical analysis
Measurement
Monte Carlo simulation
Power system reliability
Probability density function
Probability density functions
product distribution
Signal to noise ratio
α-ℱ fading
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Summary:In this letter, we consider the product of two independent and not identically distributed \alpha - \cal {F} variates. Specifically, novel closed-form expressions for the probability density function, the cumulative distribution function, and the n -th moments for the envelope as well as the instantaneous signal-to-noise ratio (SNR) are derived. Subsequently, closed-form expressions for the outage probability, the average bit error rate, and the ergodic channel capacity are derived alongside their asymptotic ones. The analytical expressions are validated through numerical and Monte-Carlo simulations, where excellent agreements are observed over a wide range of SNR values. Furthermore, the asymptotic curves follow the slope of the exact curves at high SNR values.
ISSN:1089-7798
1558-2558
DOI:10.1109/LCOMM.2021.3062598