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AuthorTempone, Raul (4)Bagci, Hakan (3)Ulku, Huseyin Arda (3)Alouini, Mohamed-Slim (2)Haji Ali, Abdul Lateef (2)View MoreDepartment

Applied Mathematics and Computational Science Program (5)

Computer, Electrical and Mathematical Sciences & Engineering (CEMSE) (5)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division (5)

Electrical Engineering Program (5)

Computer Science Program (1)View MoreSubjectCEM (1)Wireless (1)View MoreType
Poster (5)

Year (Issue Date)2016 (2)2015 (2)2014 (1)Item Availability
Open Access (5)

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An Efficient Simulation Method for Rare Events

Rached, Nadhir B.; Benkhelifa, Fatma; Kammoun, Abla; Alouini, Mohamed-Slim; Tempone, Raul (2015-01-07) [Poster]

Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a well-known challenging problem. Closed-form expressions for the sum distribution do not generally exist, which has led to an increasing interest in simulation approaches. A crude Monte Carlo (MC) simulation is the standard technique for the estimation of this type of probability. However, this approach is computationally expensive, especially when dealing with rare events. Variance reduction techniques are alternative approaches that can improve the computational efficiency of naive MC simulations. We propose an Importance Sampling (IS) simulation technique based on the well-known hazard rate twisting approach, that presents the advantage of being asymptotically optimal for any arbitrary RVs. The wide scope of applicability of the proposed method is mainly due to our particular way of selecting the twisting parameter. It is worth observing that this interesting feature is rarely satisfied by variance reduction algorithms whose performances were only proven under some restrictive assumptions. It comes along with a good efficiency, illustrated by some selected simulation results comparing the performance of our method with that of an algorithm based on a conditional MC technique.

Computation of Electromagnetic Fields Scattered From Dielectric Objects of Uncertain Shapes Using MLMC

Litvinenko, Alexander; Haji Ali, Abdul Lateef; Uysal, Ismail Enes; Ulku, Huseyin Arda; Oppelstrup, Jesper; Tempone, Raul; Bagci, Hakan (2016-01-06) [Poster]

Simulators capable of computing scattered fields from objects of uncertain shapes are highly useful in electromagnetics and photonics, where device designs are typically subject to fabrication tolerances. Knowledge of statistical variations in scattered fields is useful in ensuring error-free functioning of devices. Oftentimes such simulators use a Monte Carlo (MC) scheme to sample the random domain, where the variables parameterize the uncertainties in the geometry. At each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver is executed to compute the scattered fields. However, to obtain accurate statistics of the scattered fields, the number of MC samples has to be large. This significantly increases the total execution time.
In this work, to address this challenge, the Multilevel MC (MLMC [1]) scheme is used together with a (deterministic) surface integral equation solver. The MLMC achieves a higher efficiency by balancing the statistical errors due to sampling of the random domain and the numerical errors due to discretization of the geometry at each of these samples. Error balancing results in a smaller number of samples requiring coarser discretizations. Consequently, total execution time is significantly shortened.

Litvinenko, Alexander; Haji Ali, Abdul Lateef; Uysal, Ismail Enes; Ulku, Huseyin Arda; Tempone, Raul; Bagci, Hakan; Oppelstrup, Jesper (2015-01-07) [Poster]

Simulators capable of computing scattered fields from objects of uncertain shapes are highly useful in electromagnetics and photonics, where device designs are typically subject to fabrication tolerances. Knowledge of statistical variations in scattered fields is useful in ensuring error-free functioning of devices. Oftentimes such simulators use a Monte Carlo (MC) scheme to sample the random domain, where the variables parameterize the uncertainties in the geometry. At each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver is executed to compute the scattered fields. However, to obtain accurate statistics of the scattered fields, the number of MC samples has to be large.
This significantly increases the total execution time. In this work, to address this challenge, the Multilevel MC (MLMC [1]) scheme is used together with a (deterministic) surface integral equation solver. The MLMC achieves a higher efficiency by “balancing” the statistical errors due to sampling of the random domain and the numerical errors due to discretization of the geometry at each of these samples. Error balancing results in a smaller number of samples requiring coarser discretizations. Consequently, total execution time is significantly shortened.

Nyström-discretized Magnetic Field Integral Equation for 2D Electromagnetic Scattering

Al-Harthi, Noha A.; Ulku, Huseyin Arda; Yokota, Rio; Keyes, David E.; Bagci, Hakan (2014-05-04) [Poster]

A Unified Simulation Approach for the Fast Outage Capacity Evaluation over Generalized Fading Channels

Rached, Nadhir B.; Kammoun, Abla; Alouini, Mohamed-Slim; Tempone, Raul (2016-01-06) [Poster]

The outage capacity (OC) is among the most important performance metrics of communication systems over fading channels. The evaluation of the OC, when equal gain combining (EGC) or maximum ratio combining (MRC) diversity techniques are employed, boils down to computing the cumulative distribution function (CDF) of the sum of channel envelopes (equivalently amplitudes) for EGC or channel gains (equivalently squared enveloped/ amplitudes) for MRC. Closed-form expressions of the CDF of the sum of many generalized fading variates are generally unknown and constitute open problems. We develop a unified hazard rate twisting Importance Sampling (IS) based approach to efficiently estimate the CDF of the sum of independent arbitrary variates. The proposed IS estimator is shown to achieve an asymptotic optimality criterion, which clearly guarantees its efficiency. Some selected simulation results are also shown to illustrate the substantial computational gain achieved by the proposed IS scheme over crude Monte Carlo simulations.

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