Empirical Models of the Azimuthal Reception Angle—Part I: Comparative Analysis of Empirical Models for Different Propagation Environments

Abstract

Statistical properties of the reception angle have a significant impact on the choice of the antenna system patterns and decide on the received signal-processing methods. For angle of arrival in azimuth plane, comparative analysis of the empirical models and the approximation error evaluation are the purpose of this paper. Here, the presented analysis is focused on models such as the von Mises, modified Gaussian, modified Laplacian, and modified logistic. For each model, the approximation accuracy is determined with respect to measurement data for seven different propagation scenarios. The measures such as the least-squares error, difference of standard deviations, Kolmogorov-Smirnov statistic, and Cramer-von Mises statistic are used for evaluation of the approximation errors. Comparative analysis for four empirical models, differentiation of propagation environments, multi-criterial evaluation of approximation errors in significant degree fill a gap in the previous analysis presented in the literature. The obtained results show that the empirical models provide a better fit to the measurement data than the geometrical models, and the smallest errors of approximation are for the modified Laplacian and logistic distributions.

Empirical Models of the Azimuthal Reception Angle—Part II: Adaptation of the Empirical Models in Analytical and Simulation Studies

“…where N = 7 is the number of scenarios described in Part I [1], r E [n] and r s [n] are the estimated AS and DS for the nth scenario, while r E ¼ 7:328 and r s ¼ 0:7203 ls are the sample means of the estimated ASs and DSs, respectively. For empirical data included in Table 1, the correlation coefficient is computed to be q = 0.8537.…”

“…In Part I of this paper [1], the measure for the parameter selection and evaluation of the approximation error is the least-squares error (LSE). The optimal parameters of the models and corresponding LSEs are shown in [1, Table 4] and [1, Table 5], respectively.…”

“…Part I of this paper [1] is focused on a comparative analysis of empirical and geometrical (theoretical) models of the probability density function (PDF) of azimuth AOA (AAOA) for different environmental conditions. Empirical models are based on standard distributions such as Gaussian [2][3][4][5], Laplacian [2,3,[6][7][8][9][10][11][12], logistic [13][14][15][16], and von Mises [3,[17][18][19][20][21], which are being modified due to limited support of PDF of AAOA.…”

“…The theoretical models are defined by the geometrical structures that describe the spatial position of scattering elements. In [1], the comparative analysis of PDF models also takes into account the results from [22], which relate to the best geometrical models such as uniform elliptical (receiver (Rx) outside) [23], Gaussian [6,24,25], and Rayleigh circular (Rx outside) [26]. A comparison shows that the smallest approximation errors of the measured data are provided by modified Laplacian and uniform elliptical (Rx outside) PDF for empirical and geometrical models, respectively.…”

“…In Part I of this paper [1], the accuracy of AAOA measurement mapping results by empirical and geometrical PDF models is shown. Part II is focused on the adaptation method of the empirical models to the different types of propagation environments.…”