On a Ratio of Functions of Exponential Random Variables and Some Applications

Annavajjala, Ramesh; Chockalingam, A.; Mohammed, Saif Khan

doi:10.1109/tcomm.2010.091710.100038

Cited by 20 publications

(12 citation statements)

References 10 publications

(19 reference statements)

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“…With the aid of the definition of Meijer's G-function [31, eq. (1.112)], ( 14) can be expressed in exact closed-form as shown in (10) and the proof is accomplished.…”

Section: B Ratio Of Products Of Inid Mg Variatesmentioning

confidence: 99%

“…On the other hand, different distributions of ratio of products of RVs have been analysed by the previous works. For example, the performances of the maximal ratio combining (MRC) diversity reception and multi-carrier code-division multiple access (MC-CDMA) system affected by an interference were studied in [10] by using the statistics of independent and identically distributed (i.i.d.) exponential variates.…”

Section: Introductionmentioning

confidence: 99%

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Ratio of Products of Mixture Gamma Variates with Applications to Wireless Communications

Al‐Hmood¹,

Abbas²,

Al-Raweshidy³

2020

Preprint

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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.

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“…With the aid of the definition of Meijer's G-function [31, eq. (1.112)], ( 14) can be expressed in exact closed-form as shown in (10) and the proof is accomplished.…”

Section: B Ratio Of Products Of Inid Mg Variatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ratio of Products of Mixture Gamma Variates with Applications to Wireless Communications

Al‐Hmood¹,

Abbas²,

Al-Raweshidy³

2020

Preprint

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“…The N instantaneous SNR are exponential random variables however the M instantaneous SNRs don't have exponential distribution since they are defined as ratio of two exponential random variables [13]. Based on equation (7), finding closed form expression of γ * SC is not evident as we are dealing with two sets of random variables with different averages and different distributions.…”

Section: B the Power Adjustment Sub-channel Selection Scheme (Pascs)mentioning

confidence: 99%

Sub-channels selection schemes with interference management for underlay cognitive networks

Chamkhia

Hasna

2013

2013 IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC)

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Cognitive Radio is a promising concept that offers solution to spectral crowding problem by introducing opportunistic usage of the unoccupied licensed frequency bands. Improving the network capacity and reliability of the communication has been recently studied and this through the introduction of cooperative technology in the CR networks. Furthermore, OFDM system is considered to be a good candidate to enhance the flexibility of the CR network, where individual carriers can be switched off for occupied frequencies by the primary user (PU) or for interfering Sub-channels. In this paper, an underlay cognitive network based on OFDM technique is proposed where secondary users (SUs) coexisting with a PU are adhering to stringent interference threshold constraint. Cooperative technology will help improving the CR network performances under PU limitation. This paper proposes new Sub-channel selection schemes which adapt either the transmission power or the sequential order of selection to enhance the system performances. We first provide the exact probability density function (PDF) of the received SNR at the secondary destination. Then, the PDFs are used to derive closed form expressions of the outage probability, the average BER and the ergodic capacity. Analytic results are validated by simulation for the proposed Sub-channels selection schemes.

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“…On the other hand, several distributions of the ratio of products of RVs have been analysed by the previous works. For example, the performances of the maximal ratio combining (MRC) diversity reception and multi-carrier code-division multiple access (MC-CDMA) system in the presence of an interference were studied in [14] by using the statistics of independent and identically distributed (i.i.d.) exponential variates.…”

Section: Introductionmentioning

confidence: 99%

Ratio of products of mixture gamma variates with applications to wireless communications systems

Al‐Hmood

Al-Raweshid

2021

IET Communications

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The fading scenario of many realistic wireless communication transmission systems, such as, multi‐hop communications and spectrum sharing in cognitive radio networks (CRNs), can be modelled by the product and the ratio of the product of the random variables (RVs) of the channel distribution. However, there is no work has been investigated in the literature to provide unified statistics of the product and the ratio of the products that can be used for a wide range of non‐composite and composite fading conditions. Accordingly, in this paper, the statistical properties, namely, probability density function (PDF), cumulative distribution function (CDF), and moment generating function (MGF) of the product and the ratio of the product of independent and non‐identically distributed (i.n.d.) mixture Gamma (MG) RVs are derived. A MG distribution has been widely employed to approximate with high accuracy most of the conventional fading models, for example, Rayleigh, Nakagami‐m, Nakagami‐q (Hoyt), and Nakagami‐n (Rician) as well as the generalised composite fading channels, such as, generalised‐K(KG),α−μ/gamma, κ−μ/gamma, and η−μ/gamma. Hence, the derived PDF, CDF, and MGF are utilized for the Beaulieu–Xie and α−λ−η−μ shadowed fading channels that have not been yet presented by the previous works due to mathematical intractability of their statistics. Thus, the equivalent parameters of a MG distribution for these channels are given. To this end, simple closed‐form mathematically tractable expressions of the performance metrics are obtained. The derived statistics are applied to analyse the outage probability (OP), the average error probability for different modulation schemes, the effective rate (ER) of wireless communication systems and the average area under the receiver operating characteristics (AUC) curve of energy detection over cascaded fading channels. Moreover, the OP of the multi‐hop communications systems with co‐channel interference (CCI), both the lower bound of secure OP (SOPL) and probability of non‐zero secrecy capacity (PNSC) of the physical layer security (PLS), and the outage and delay‐limited capacities of CRNs are studied via using the statistics of the ratio of the product of MG variates. A comparison between the numerical results and the Monte Carlo simulations is presented to verify the validation of our analysis.

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On a Ratio of Functions of Exponential Random Variables and Some Applications

Cited by 20 publications

References 10 publications

Ratio of Products of Mixture Gamma Variates with Applications to Wireless Communications

Ratio of Products of Mixture Gamma Variates with Applications to Wireless Communications

Sub-channels selection schemes with interference management for underlay cognitive networks

Ratio of products of mixture gamma variates with applications to wireless communications systems

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