Integrals and Series

Prudnikov, A. P.; Brychkov, Yu. A.; Marichev, O. I.

doi:10.1201/9780203750643

Cited by 327 publications

(496 citation statements)

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“…The integral in the brackets is evaluated in (3) using ∞ 0 x a−1 e −P x dx = (a) P −a given in [11]. Thus, the moment expression of (2) becomes…”

Section: Derivation Of the Proposed Estimatormentioning

confidence: 99%

“…However, because it is difficult to obtain the closed forms for the shape parameter estimators given by (11) and (12), numerical routines are compulsory. To this end, we have optimized the squared errors of the proposed estimators given by (11) and (12) via the fminsearch function of the Matlab routine.…”

Section: Derivation Of the Proposed Estimatormentioning

confidence: 99%

“…To this end, we have optimized the squared errors of the proposed estimators given by (11) and (12) via the fminsearch function of the Matlab routine. Note that the optimized function is given byν…”

Section: Derivation Of the Proposed Estimatormentioning

confidence: 99%

“…In the next section, we compare the estimation performances of the proposed FPNOME given by (12), (15), and (16) to the methods given in [5,8,10] and (11).…”

Section: Derivation Of the Proposed Estimatormentioning

confidence: 99%

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K-clutter plus noise parameter estimation using fractional positive and negative moments

Mezache¹,

Chalabi

Laroussi

et al. 2016

IEEE Trans. Aerosp. Electron. Syst.

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In this correspondence, fractional negative-order moments are used to estimate the K-clutter plus noise parameters. Combining the fractional positive and negative moments, we aim to improve the accuracy of the estimation outcomes. This is achieved through the reduction of the effect of the two first intensity moments involved in the equation of the unknown parameters. For instance, the proposed fractional positive-and negative-order moments' estimator, given in terms of two confluent hypergeometric functions, is solved numerically to yield the shape parameter. Using single pulse and multiple pulses in various clutter plus noise scenarios, we show, via both simulated and IPIX real data, a comparison of the new estimator with the estimators based on the higher-order moments, the fractional positive-order moments, the [zlog(z)], and the constrained maximum likelihood.

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“…The integral in the brackets is evaluated in (3) using ∞ 0 x a−1 e −P x dx = (a) P −a given in [11]. Thus, the moment expression of (2) becomes…”

Section: Derivation Of the Proposed Estimatormentioning

confidence: 99%

Section: Derivation Of the Proposed Estimatormentioning

confidence: 99%

Section: Derivation Of the Proposed Estimatormentioning

confidence: 99%

“…In the next section, we compare the estimation performances of the proposed FPNOME given by (12), (15), and (16) to the methods given in [5,8,10] and (11).…”

Section: Derivation Of the Proposed Estimatormentioning

confidence: 99%

See 2 more Smart Citations

K-clutter plus noise parameter estimation using fractional positive and negative moments

Mezache¹,

Chalabi

Laroussi

et al. 2016

IEEE Trans. Aerosp. Electron. Syst.

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show abstract

“…The moment generating function of the received SINR γ is expressed as First, it is assumed that the dominant components of the κ - μ shadowed random variables, i.e., are mutually independent, and the PDF of can be given by [28] where β 0 = min{ μ l κ l / m }, Γ(⋅) is the Gamma function, and δ k can be derived by the following formula where δ 0 = 1. Define , , then the conditional PDF of γ in Eq (9) can be expressed as Averaged upon Z , we obtain the unconditional PDF of γ where , , and By using [29], the integral in Eq (17) can be solved, and substituting it into Eq (16) yields where , and 1 F 1 ( a ; b ; z ) is the confluent Hypergeometric function [30]. From Eqs (12) and (18), the moment generating function of γ is given by Using the properties of the linearity and frequency shifting of the Laplace transform, it follows that The Laplace transform in Eq (20) can be identified with [31], so the moment generating function of γ can be expressed as where .…”

Section: Incomplete Generalized Mgf Of the κ-μ Shadowed Variatesmentioning

confidence: 99%

Outage Probability of MRC for κ-μ Shadowed Fading Channels under Co-Channel Interference

et al. 2016

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In this paper, exact closed-form expressions are derived for the outage probability (OP) of the maximal ratio combining (MRC) scheme in the κ-μ shadowed fading channels, in which both the independent and correlated shadowing components are considered. The scenario assumes the received desired signals are corrupted by the independent Rayleigh-faded co-channel interference (CCI) and background white Gaussian noise. To this end, first, the probability density function (PDF) of the κ-μ shadowed fading distribution is obtained in the form of a power series. Then the incomplete generalized moment-generating function (IG-MGF) of the received signal-to-interference-plus-noise ratio (SINR) is derived in the closed form. By using the IG-MGF results, closed-form expressions for the OP of MRC scheme are obtained over the κ-μ shadowed fading channels. Simulation results are included to validate the correctness of the analytical derivations. These new statistical results can be applied to the modeling and analysis of several wireless communication systems, such as body centric communications.

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Nonstationary Casimir Effect and Analytical Solutions for Quantum Fields in Cavities with Moving Boundaries

Dodonov

Advances in Chemical Physics

106

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Integrals and Series

Cited by 327 publications

References 0 publications

K-clutter plus noise parameter estimation using fractional positive and negative moments

K-clutter plus noise parameter estimation using fractional positive and negative moments

Outage Probability of MRC for κ-μ Shadowed Fading Channels under Co-Channel Interference

Nonstationary Casimir Effect and Analytical Solutions for Quantum Fields in Cavities with Moving Boundaries

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