Distribution of the Product of Squared Correlated Shadowed Rician Random Variables

Hazra, Soumita; Arti, M K

doi:10.1109/spin48934.2020.9070891

Cited by 3 publications

(4 citation statements)

References 17 publications

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“…The cumulative distribution function of the dual‐hop satellite–terrene link employing SR fading with correlated LOS constituents is given by [18, Eq. (17)]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \begin{array}{rcl} F_{N} false(n false) & = Q_{1} Q_{2} \sum_{a_{1} = 0}^{\infty} \sum_{d_{1} = 0}^{\infty} \sum_{a_{2} = 0}^{\infty} \sum_{d_{2} = 0}^{\infty} C_{1} false(a_{1} false) K_{1} false(a_{1}, d_{1} false) C_{2} false(a_{2} false) \\ \times K_{2} false(a_{2}, d_{2} false) 2.047em2.047em(\frac{b_{1}}{b_{2}} 2.047em2.047em)^{u_{1} false(P_{1}, d_{1}, P_{2}, d_{2} false)} n^{scriptx false(P_{1}, d_{1}, P_{2}, d_{2} false)} \\ \times G_{13}^{21} 2.047em2.047em[(n / 4 b_{1} b_{2}) 2.047em2.047em| \begin{matrix} center center1em4pt \\ 1 - x (P_{1}, d_{1}, P_{2}, d_{2}) \\ u_{1}, u_{2}, - x (P_{1}, d_{1}, P_{2}, d_{2}) \end{matrix} 2.047em2.047em] . \end{array} \end{matrix}

where

scriptx false(P_{1}, d_{1}, P_{2}, d_{2} false) = false(P

…”

Section: System Modelmentioning

confidence: 99%

“…The moment generating function of the dual‐hop satellite–terrene link employing SR fading with correlated LOS constituents is given by [18, Eq. (23)]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ M_{N} (s) & = {scriptQ}_{1} {scriptQ}_{2} \sum_{a_{1} = 0}^{normal∞} \sum_{d_{1} = 0}^{normal∞} \sum_{a_{2} = 0}^{normal∞} \sum_{d_{2} = 0}^{normal∞} {scriptC}_{1} (a_{1}) {scriptK}_{1} (a_{1}, d_{1}) {scriptC}_{2} (a_{2}) \\ \times {scriptK}_{2} (a_{2}, d_{2}) \frac{l^{x (P_{1}, d_{1}, P_{2}, d_{2}) - (1 / 2)} s^{- x (P_{1}, d_{1}, P_{2}, d_{2})}}{(π + 1) (l - 1)} \\ \times [G_{l, 2 l}^{2 l, l} (2.047em2.047em(\frac{1}{4 b_{1} b_{2}} 2.047em2.047em)^{l} false(s l false)^{- l} | z (l, u_{1}, u_{2}))] (\frac{b_{1}}{b_{2}})^{u_{1}} \end{matrix}

where

z false(

…”

Section: System Modelmentioning

confidence: 99%

“…In [17], the authors propounded the application of the sum of SR random variables (RVs) with correlated LOS components in satellite complexes. The statistical characterisation of the product distribution of squared SR RVs with correlated LOS components is propounded in [18]. Space station–relay–ES linkage employing SR fading for the instances, where uninterrupted dissemination is non‐viable, is meditated in [19].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of binate hop cascaded satellite terrene link with correlated LOS constituents

Hazra

Arti

2020

IET Communications

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“…The cumulative distribution function of the dual‐hop satellite–terrene link employing SR fading with correlated LOS constituents is given by [18, Eq. (17)]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ \begin{array}{rcl} F_{N} false(n false) & = Q_{1} Q_{2} \sum_{a_{1} = 0}^{\infty} \sum_{d_{1} = 0}^{\infty} \sum_{a_{2} = 0}^{\infty} \sum_{d_{2} = 0}^{\infty} C_{1} false(a_{1} false) K_{1} false(a_{1}, d_{1} false) C_{2} false(a_{2} false) \\ \times K_{2} false(a_{2}, d_{2} false) 2.047em2.047em(\frac{b_{1}}{b_{2}} 2.047em2.047em)^{u_{1} false(P_{1}, d_{1}, P_{2}, d_{2} false)} n^{scriptx false(P_{1}, d_{1}, P_{2}, d_{2} false)} \\ \times G_{13}^{21} 2.047em2.047em[(n / 4 b_{1} b_{2}) 2.047em2.047em| \begin{matrix} center center1em4pt \\ 1 - x (P_{1}, d_{1}, P_{2}, d_{2}) \\ u_{1}, u_{2}, - x (P_{1}, d_{1}, P_{2}, d_{2}) \end{matrix} 2.047em2.047em] . \end{array} \end{matrix}

where

scriptx false(P_{1}, d_{1}, P_{2}, d_{2} false) = false(P

…”

Section: System Modelmentioning

confidence: 99%

“…The moment generating function of the dual‐hop satellite–terrene link employing SR fading with correlated LOS constituents is given by [18, Eq. (23)]

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ M_{N} (s) & = {scriptQ}_{1} {scriptQ}_{2} \sum_{a_{1} = 0}^{normal∞} \sum_{d_{1} = 0}^{normal∞} \sum_{a_{2} = 0}^{normal∞} \sum_{d_{2} = 0}^{normal∞} {scriptC}_{1} (a_{1}) {scriptK}_{1} (a_{1}, d_{1}) {scriptC}_{2} (a_{2}) \\ \times {scriptK}_{2} (a_{2}, d_{2}) \frac{l^{x (P_{1}, d_{1}, P_{2}, d_{2}) - (1 / 2)} s^{- x (P_{1}, d_{1}, P_{2}, d_{2})}}{(π + 1) (l - 1)} \\ \times [G_{l, 2 l}^{2 l, l} (2.047em2.047em(\frac{1}{4 b_{1} b_{2}} 2.047em2.047em)^{l} false(s l false)^{- l} | z (l, u_{1}, u_{2}))] (\frac{b_{1}}{b_{2}})^{u_{1}} \end{matrix}

where

z false(

…”

Section: System Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of binate hop cascaded satellite terrene link with correlated LOS constituents

Hazra

Arti

2020

IET Communications

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“…On the other hand, other works such as [6], [7] dealt with the distribution of the product of shadowed-Rician RVs.…”

Section: Introductionmentioning

confidence: 99%

On the Distribution of the Sum of Málaga-$\mathcal{M}$ Random Variables and Applications

Illi,

Bouanani,

Ayoub

2020

Preprint

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In this paper, a very accurate approximation method for the statistics of the sum of Málaga-M random variates with pointing error (MRVs) is proposed. In particular, the probability density function of MRV is approximated by a Fox's Hfunction through the moment-based approach. Then, the respective moment-generating function of the sum of N MRVs is provided, based on which the average symbol error rate is evaluated for an N -branch maximal-ratio combining (MRC) receiver. The retrieved results show that the proposed approximate results match accurately with the exact simulated ones. Additionally, the results show that the achievable diversity order increases as a function of the number of MRC diversity branches.

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Distribution of squared sum of products of independent Nakagami- m random variables

Samuh

Salhab

2023

Communications in Statistics - Simulation and Computation

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Distribution of the Product of Squared Correlated Shadowed Rician Random Variables

Cited by 3 publications

References 17 publications

Analysis of binate hop cascaded satellite terrene link with correlated LOS constituents

Analysis of binate hop cascaded satellite terrene link with correlated LOS constituents

On the Distribution of the Sum of Málaga-$\mathcal{M}$ Random Variables and Applications

Distribution of squared sum of products of independent Nakagami- m random variables

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