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

Abstract

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.

Modeling of the 5G-Band Patch Antennas Using ANNs under the Uncertainty of the Geometrical Design Parameters Associated with the Manufacturing Process

“…However, the variations of them both have an overall influence on |S11|, which corresponds to less than 3% of the whole variance of |S11|. This observation is reflected in the details of the presentation of the novel application of the method from [15] to the FDTD-PCE computations in the following paragraphs. The author takes advantage of the fact that each nominal value of g0 corresponds to a nominal resonance frequency (f0) of the antenna.…”

“…This section presents an application of the author's method from [15] to the FDTD-PCE computations of data for training and testing of ANNs that are used to model the stochastic behavior of |S 11 | of an ordinary patch antenna. The following notation is used in the paper.…”

“…Before the presentation of the novel application of the method from [15] to the FDTD-PCE computations of training and testing data for the ANNs, let us remind the design parameters of an ordinary patch antenna, whose arrays are shown in Figures 1 and 2. These parameters are denoted by g 0 , w 0 , and y 0 and recalled in Figure 10.…”

“…It is based on the author's analytical transformations and proper segmentation of the support of those design random variables. The aforementioned method was introduced in [15] where it was used with the uniform theory of diffraction (UTD) for worst-case analysis in a wireless telecommunication channel. In this paper, the method is applied and adjusted for the first time to FDTD-PCE computations.…”

“…In the second section, the author presents the measurement results of two series of patch antenna arrays and gives the extracted uncertainty of the geometrical design random variables. The third section of the paper presents a novel application of the method from [15] to FDTD-PCE computations, which enables a reduction of the number of required FDTD simulation runs for the computation of the mean and standard deviation of |S 11 | for a predefined set of nominal values of design parameters. The novel results of modeling the stochastic behavior of |S 11 | of ordinary patch antennas by ANNs for the 24.5-28.7 GHz frequency band are presented in Section 4 of the paper.…”