Generalised MGF of the  extreme distribution and its applications to performance analysis

Gong, Jintaek; Lee, Hoojin; Park, Min‐Ho; Choi, Jeung-Won; Kang, Joonhyuk

doi:10.1049/el.2018.7020

Cited by 4 publications

(4 citation statements)

References 8 publications

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“…The G‐MGF of a random variable

X

is defined as [5–8]

{scriptM}_{X}^{(n)} false(s false) ≜ E false{X^{n} e^{X s} false} = \int_{0}^{\infty} x^{n} {normale}^{x s} f_{X} false(x false) d x,

where

f_{X} false(x false)

is the PDF of

X

and

E {\cdot}

denotes the expectation operator. Then, if

n \in {double-struckZ}^{+}

, the G‐MGF equals the

n

th order derivative of the MGF

{scriptM}_{X} false(s false) ≜ E false{e^{X s} false} = {scriptM}_{X}^{(0)}

, and the

n

th order moment of

X

can be obtained as

E false{X^{n} false} = {scriptM}_{X}^{(n)} false(0 false)

.…”

Section: G‐mgf Based Analysismentioning

confidence: 99%

“…We here illustrate the applicability of the G‐MGF for the SNR

γ

of coherent FSO systems in the different scenarios: (1) AoF and (2) EC. Additionally, it is noticeable that the G‐MGF can be further applicable to the various performance evaluations, for example, error probability analysis, outage probability with interference, energy detection, and physical layer security [5–8].…”

Section: Applications To Performance Analysismentioning

confidence: 99%

“…It has been well acknowledged that the generalised momentgenerating function (G-MGF) can be adopted to effectively calculate the achievable performance metrics of interest [5][6][7][8]. Thus, in this letter, we analyse the performance of coherent FSO systems with multiple receivers based on the G-MGF, where the channel model and system model [1][2][3][4] are adopted.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

G‐MGF based performance analysis of coherent FSO systems with multiple receivers

Jeong

Kang

Lee

2021

Electronics Letters

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This letter investigates the performance of coherent free-space optical systems with multiple receivers especially through the generalised moment-generating function based approach. Specifically, we first derive a closed-form expression of the generalised moment-generating function of the signal-to-noise ratio for the coherent free-space optical systems. The derived generalised moment-generating function formula is further utilised to effectively analyse the several performance metrics such as amount of fading and ergodic capacity. The accuracy of our theoretical analyses are corroborated via some numerical results.

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“…The G‐MGF of a random variable

X

is defined as [5–8]

{scriptM}_{X}^{(n)} false(s false) ≜ E false{X^{n} e^{X s} false} = \int_{0}^{\infty} x^{n} {normale}^{x s} f_{X} false(x false) d x,

where

f_{X} false(x false)

is the PDF of

X

and

E {\cdot}

denotes the expectation operator. Then, if

n \in {double-struckZ}^{+}

, the G‐MGF equals the

n

th order derivative of the MGF

{scriptM}_{X} false(s false) ≜ E false{e^{X s} false} = {scriptM}_{X}^{(0)}

, and the

n

th order moment of

X

can be obtained as

E false{X^{n} false} = {scriptM}_{X}^{(n)} false(0 false)

.…”

Section: G‐mgf Based Analysismentioning

confidence: 99%

“…We here illustrate the applicability of the G‐MGF for the SNR

γ

Section: Applications To Performance Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

G‐MGF based performance analysis of coherent FSO systems with multiple receivers

Jeong

Kang

Lee

2021

Electronics Letters

Self Cite

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show abstract

“…Recently, in [8] the performance of energy detection over

\kappa

‐

\mu

Extreme fading was analysed in the context of spectrum sensing in cognitive radio networks. Also, some closed‐form expressions of the generalized moment generating function were derived in [9]. The

\kappa

‐

\mu

Extreme model has shown to be an excellent fit with real field measurements.…”

Section: Introductionmentioning

confidence: 99%

Performance of MPSK modulation with imperfect phase‐recovery under severe fading conditions

Silva

Souza

Nardelli

et al. 2022

Electronics Letters

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The authors study the performance of M‐ary phase‐shift keying (MPSK) modulation with imperfect carrier phase recovery in scenarios experiencing severe fading conditions. Specifically, MPSK is analysed over κ$\kappa$‐μ$\mu$ Extreme fading channels assuming a Gaussian‐distributed noisy phase. For the theoretical framework, they derive the analytical expressions for the upper bound on the average symbol error probability, as well as their corresponding asymptotic behaviour in the high signal‐to‐noise ratio (SNR) regime. The derived expressions are valid for arbitrary values of the fading parameter m$m$, and Monte Carlo simulations are provided to verify the accuracy of the proposed mathematical analysis. Furthermore, the authors discuss how the channel parameter and phase variance affect the system performance for a wide range of SNR values.

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New Results on the Second Order Scattering Fading Model: Amount of Fading and Energy Detection

López-Fernández

López‐Martínez

2020

IEEE Trans. Veh. Technol.

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We present a generalization of the notoriously unwieldy second-order scattering fading model, which is helpful to alleviate its mathematical complexity while providing an additional degree of freedom. This is accomplished by allowing its dominant specular component associated to line-of-sight propagation to randomly fluctuate. The statistical characterization of the newly proposed model is carried out, providing closedform expressions for its probability and cumulative distribution functions, as well as for its generalized Laplace-domain statistics and raw moments. We exemplify how performance analysis can be done in this scenario, and discuss the role of the fading model parameters on system performance.

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Generalised MGF of the extreme distribution and its applications to performance analysis

Cited by 4 publications

References 8 publications

G‐MGF based performance analysis of coherent FSO systems with multiple receivers

G‐MGF based performance analysis of coherent FSO systems with multiple receivers

Performance of MPSK modulation with imperfect phase‐recovery under severe fading conditions

New Results on the Second Order Scattering Fading Model: Amount of Fading and Energy Detection

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