Asymptotically Exact Approximations for the Symmetric Difference of Generalized Marcum &lt;inline-formula&gt; &lt;tex-math notation="TeX"&gt;$Q$&lt;/tex-math&gt;&lt;/inline-formula&gt;-Functions

López‐Martínez, F. Javier; Romero-Jerez, Juan M.

doi:10.1109/tvt.2014.2337263

Cited by 14 publications

(5 citation statements)

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“…(37) Finally, by bringing (35) and ( 37) into (33a), the critical point of P out in θ s can be found in the following implicit equation In this case, although f 4 = α us is a decreasing function of θ s , the decrement rate of f 4 is much smaller than 1 as the denominator of f 4 is larger than 1, f 1 and f 2 increase from a relatively small value to ∞ as θ s increases within [0, π 2 ], so the decrement rate of f 4 is much slower than the increment rates of f 1 and f 2 . As a result, the left side of ( 38) is an increasing function of θ s .…”

Section: Appendix B the Proof Of Lemmamentioning

confidence: 99%

“…)x can be neglected, and then we havey info ≈ ( A+2 A 2 +2 )x + c. (57)In order to determine c, one can find that x → ∞ results iny info = ( A+2 A 2 +2 )x + c → ∞, and y ≫ y − ( A+2 A 2 +2 )x.By using the asymptotic relationship between the generalized Marcum Q-function and the Gaussian Q-function[35], one can have that Q 1 (x, y) ≈ Q(y − ( A+2 A 2 +2 )x) ≈ Q(c), then we have1 + 2Q(c) log(Q(c))K 1 (−2 log(Q(c))) = P th . (58)…”

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UAV-Aided Wireless Power Transfer and Data Collection in Rician Fading

Liu

Xiong

et al. 2021

IEEE J. Select. Areas Commun.

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A UAV-aided wireless power transfer and data collection network is studied, where it is assumed that when the harvested energy at the sensor node (SN) cannot surpass its circuit activation threshold or the received data rate at UAV falls below a minimal required rate threshold, the information outage occurs. The closed-form expressions of energy outage probability and rate outage probability are derived at first, and then the overall outage probability and coverage performance of the system are analyzed. Based on which, an optimization problem is formulated to minimize the overall outage probability by optimizing UAV's elevation angle and the time splitting (TS) factor. Since the problem is non-convex and has no known solution, an alternating optimization (AO)-based algorithm with Golden-section (GS) based linear search method is designed to find the global optimal solution. In order to explore the maximum coverage area of the UAV for a given tolerable outage probability, another optimization problem is also formulated to maximize the coverage range by optimizing UAV's elevation angle. By using Karush-Kuhn-Tucker (KKT) conditions, the closed-form solution of the optimal elevation angle for maximizing the coverage area is derived. Monte Carlo simulations verify the accuracy of the derived closed-form expression of the overall outage probability and the semi-closed-form expressions of the optimum UAV's elevation angle and TS factor. It shows that there exist a unique optimum elevation angle and the TS factor to achieve the minimum overall outage probability, and significant performance gain can be obtained by using our proposed optimization scheme. The developed theoretical results can be useful to the design of UAV-aided wireless communication systems with wireless power transfer.

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Section: Appendix B the Proof Of Lemmamentioning

confidence: 99%

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confidence: 99%

UAV-Aided Wireless Power Transfer and Data Collection in Rician Fading

Liu

Xiong

et al. 2021

IEEE J. Select. Areas Commun.

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“…Corollary 4: For high SNRs, i.e., for large values of arguments a and b, (31) can be simplified as [37] lim γ→∞ P out = lim…”

Section: Corollarymentioning

confidence: 99%

Statistical Modeling of the FSO Fronthaul Channel for UAV-Based Communications

Najafi

Ajam

Jamali

et al. 2020

IEEE Trans. Commun.

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In this paper, we investigate the statistics of the free space optics (FSO) communication channel between a hovering unmanned aerial vehicle (UAV) and a central unit. Two unique characteristics make UAV-based FSO systems significantly different from conventional FSO systems with static transceivers. First, for UAV-based FSO systems, the incident laser beam is not always orthogonal to the receiver lens plane. Second, both position and orientation of the UAV fluctuate over time due to dynamic wind load, inherent random air fluctuations in the atmosphere around the UAV, and internal vibrations of the UAV. On the contrary, for conventional FSO systems, the laser beam is always perpendicular to the receiver lens plane and the relative movement of the transceivers is limited. In this paper, we develop a novel channel model for UAV-based FSO systems by quantifying the corresponding geometric and misalignment losses (GML), while taking into account the non-orthogonality of the laser beam and the random fluctuations of the position and orientation of the UAV. In particular, for diverse weather conditions, we propose different fluctuation models for the position and orientation of the UAV and derive corresponding statistical models for the GML. We further analyze the performance of a UAV-based FSO link in terms of outage probability and ergodic rate and simplify the resulting analytical expressions for the high signal-to-noise ratio (SNR) regime. Finally, simulations validate the accuracy of the presented analysis and provide important insights for system design. For instance, we show that for a given variance of the fluctuations, the beam width should be properly adjusted to minimize the outage probability. introduce the following new challenges: i) For conventional FSO links, it is typically assumed that the laser beam is orthogonal with respect to (w.r.t.) the receiver lens plane, as orthogonality maximizes the amount of laser power collected by the photo-detector (PD) located behind the lens [12]. However, orthogonality may not hold for UAV-based FSO communication systems. For example, the position of a UAV may depend on the locations and traffic needs of the users, while the CU may not be able to adjust the orientation of the receiver lens due to limited mechanical capabilities. In addition, using one receiver lens and multiple PDs [15], [16], the CU may receive data from several UAVs having different positions. Hence, it is not possible to orthogonally align the laser beams of all UAVs with the receiver lens plane. ii) Unlike 1 The receiver can only capture the fraction of power that falls on its lens. This phenomenon is known as geometric loss. Moreover, misalignment of the center of the optical beam and the center of the receiver lens further increases the geometric loss. This phenomenon is known as misalignment loss [12].

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“…In [1] the authors approximated the symmetric difference (2) for ν ∈ N and large values of a > b ≥ 0 by…”

Section: Introductionmentioning

confidence: 99%

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Bounds for the symmetric difference of generalized Marcum Q-functions

Baricz

Meszaros

2015

2015 IEEE 10th Jubilee International Symposium on Applied Computational Intelligence and Informatics

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Abstract-Recently, an approximation for large values of a and b for the symmetric difference of Marcum Q-functions Qν (a, b) was given in [1] in the case of integer order, i.e. when ν = n ∈ N. Motivated by this result, in this note we study the symmetric difference of Marcum Q-functions Qν (a, b) of real order ν ≥ 1 for the parameters a > b > 0. Our aim is to use some of the lower and upper bounds of the Marcum Q-function that appear in the literature to obtain some tight bounds for the symmetric difference. Another approach, presented in this note, is to investigate the difference via closed forms of the Marcum Q-function.Index Terms-Symmetric difference of Marcum Q-functions; lower and upper bounds; approximations.

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Asymptotically Exact Approximations for the Symmetric Difference of Generalized Marcum <inline-formula> <tex-math notation="TeX">$Q$</tex-math></inline-formula>-Functions

Cited by 14 publications

References 24 publications

UAV-Aided Wireless Power Transfer and Data Collection in Rician Fading

UAV-Aided Wireless Power Transfer and Data Collection in Rician Fading

Statistical Modeling of the FSO Fronthaul Channel for UAV-Based Communications

Bounds for the symmetric difference of generalized Marcum Q-functions

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