An application of universal polynomial chaos expansion to numerical stochastic simulations of an UWB EM wave propagation

Górniak, Piotr

doi:10.23919/eucap.2017.7928835

Cited by 2 publications

(3 citation statements)

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“…In the wireless communications, the literature presents hypotheses that the propagation behavior is closer to the deterministic chaotic. Alternative models to the Monte Carlo were proposed, such as the Monte Carlo hybrid system with chaotic polynomial, with aim of achieve a fast convergence [8] and the chaotic polynomial system, to derive mean and variance of an electromagnetic distribution, useful in cases of numerical simulations where a transfer function of a channel or the radius is not provided analytically [9]. Initiatives based on deterministic chaotic equations have been proposed to adjust statistical errors in the propagation model and represent the resulting waveform closer to that found in Nature [10].…”

Section: Introductionmentioning

confidence: 99%

Deterministic Chaotic Propagation Model

Botelho,

Akamine,

Lopes

2023

IEEE Access

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Coverage prediction is an essential method of planning broadcast and long-range wireless communication systems, minimizing the need for field measurements to adjust the coverage area and consequently reducing the time and cost of implementation. Coverage prediction methods use statistical simplifications in conjunction to uncertainty quantification algorithms to assist in modeling multipath effects and impulsive noise, notably hard to be statistically considered. This paper presents a new approach to represent electromagnetic wave propagation uncertainties based on chaotic dynamical systems to model the behavior of multipath effect and impulsive noise. A novel Deterministic Chaotic Propagation Model (DCPM) is presented and used to predict coverage area in a DVB-T2 broadcast system in diverse transmission environments. The results indicate that the predicted area of bad reception is smaller in comparison to the one obtained using traditional methods. Therefore, fewer signal repeaters can be used to provide good TV reception in this area, causing a significant cost reduction in the set-up of a broadcast system. Another parameter used to evaluate the quality of reception is the carrier to noise power ratio (C/N) threshold for a bit error rate (BER) of 10-7 . The DCPM indicate a C/N threshold equal to 13.7 dB in dense urban environment and 13.4 dB in rural environment using a moderately less robust modulation configuration. Employing a more robust configuration, the C/N threshold is equal to 0.9 dB in all environments. These numbers match the obtained by the traditional propagation models.

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Section: Introductionmentioning

confidence: 99%

Deterministic Chaotic Propagation Model

Botelho,

Akamine,

Lopes

2023

IEEE Access

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“…The main idea of the proposed approach is to notice that stochastic polynomials associated with the most common probability density functions in such pairs as normal distribution -Hermite polynomials, Beta distribution -Jacobi polynomials [12,19], etc. can be expanded in series relative to each other, and the coefficients of these expansions can be calculated by means of analytical integration resulting in known analytical relationships [20][21][22]. Thanks to the use of this property, we can calculate the coefficients in the PCE method only once, regardless of changes in the types of probability density function and/or variation of ranges of random parameters, what significantly shortens the simulation times in the case described above.…”

Section: Introductionmentioning

confidence: 99%

“…In our approach, changing the values of random variables (e.g., an average and a standard deviation) or changing the range of a random variable (e.g., a random variable range for a Beta distribution) does not require, as it was already noted above, recalculation of the expansion coefficients through direct numerical integration or linear regression, which must be done for each frequency. The introduced UECs can be recalculated, as it was mentioned, using explicit analytical formulas [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Pce-Based Approach to Worst-Case Scenario Analysis in Wireless Telecommunication Systems

Górniak¹,

Bandurski²

2019

PIER B

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In the paper, we present a novel PCE-based approach for the effective analysis of worstcase scenario in a wireless telecommunication system. Usually, in such analysis derivation of polynomial chaos expansion (PCE meta-model) of a considered EM field function for one precise set of probability densities of random variables does not provide enough information. Consequently, a number of PCE meta-models of the EM field function should be derived, each for the different joint probability density of a vector of random variables, e.g., associated with different mean (nominal) values of random variables. The general polynomial chaos (gPC) approach requires numerical calculations for each PCE meta-model derivation. In order to significantly decrease the time required to derive all of the PCE meta-models, the novel approach has been introduced. It utilizes the novel so-called primary approximation and the novel analytical formulas. They significantly decrease the number of numerical calculations required to derive all of the PCE meta-models compared with the gPC approach. In the paper, we analyze the stochastic EM fields distributions in a telecommunication system in a spatial domain. For this purpose, analysis of uncertainties associated with a propagation channel as well as with transmitting and receiving antennas was introduced. We take advantage of a ray theory in our analysis. This allows us to provide the novel method for rapid calculation of a PCE meta-model of a telecommunication system transfer function by using the separate PCE meta-models associated with antennas and a propagation channel.

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An application of universal polynomial chaos expansion to numerical stochastic simulations of an UWB EM wave propagation

Cited by 2 publications

References 4 publications

Deterministic Chaotic Propagation Model

Deterministic Chaotic Propagation Model

Pce-Based Approach to Worst-Case Scenario Analysis in Wireless Telecommunication Systems

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