Analytically derived TOA-DOA distributions of uplink/downlink wireless-cellular multipaths arisen from scatterers with an inverted-parabolic spatial distribution around the mobile

Abstract

This letter presents the joint/marginal distributions of the uplink (downlink) multipaths' azimuth angles of arrival and times of arrival at the cellular base station (mobile). These closedform explicit densities are rigorously derived based on a new "geometrical model" wherein omnidirectional scatterers are modeled as spatially distributed at an inverted parabolic spatial distribution on a two-dimensional disc centered at the mobile. This "inverted parabolic" density, in contrast to the uniform disc density or the rim density, indirectly accounts for scattering power loss. This new model better least-squares-fit some empirical data than its competing models can.

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

“…Distribution of scatterers in propagation environment is an additional characteristic that defines each geometrical model. For these models, the following distributions are used: uniform [2,4,5,8,14], Gaussian [15,16], Raleigh and exponential [2], hyperbolic [1], conical [17], parabolic [3,18], and inverted parabolic [19]. The choice of the geometrical structure (shape, position, size) and scattering distribution determines the accuracy of the mapping of the actual propagation conditions.…”

Angle and Time of Arrival Statistics for a 3-D Pie-Cellular-Cut Scattering Channel Model

“…Thus, it is necessary to have reliable understanding of radio-propagation characteristics of the transmission path between the BS and the MS, which leads to the design of effective signal processing techniques. Therefore, a number of different types of 2-D geometrical models are proposed in [1][2][3][4][5][6][7][8][9][10][11][12][13][14], that are currently available such as circular scattering model, ellipse scattering model [1,2], and hollow-disc scattering model [3,4]. In these models, distributions of the scatterers are assumed to be uniform or non-uniform spatial distributions.…”

“…In these models, distributions of the scatterers are assumed to be uniform or non-uniform spatial distributions. The non-uniform spatial distributions are the inverted par-abolic [5], Gaussian [6][7][8], exponential, Rayleigh [9] and hyperbolic [10]. Furthermore, a 2-D geometrically based single-bounce model with a directional antenna at the BS is presented in [11][12][13][14].…”

Angle and Time of Arrival Statistics of a Three Dimensional Geometrical Scattering Channel Model for Indoor and Outdoor Propagation Environments

“…Geometrical scattering channel models have been developed to describe the angle of arrival (AOA) and time of arrival (TOA) probability density functions (pdfs) of the received multipath signals. In the current literature, several two dimensional (2D) [1][2][3][4][5][6][7][8][9][10][11][12][13] and three dimensional (3D) [14][15][16][17] geometrical scattering channel models have been suggested for various types of wireless communication environments. For example, in macrocellular wireless environments, where the base station (BS) antennas are elevated and the scatterers are assumed to be located around only the mobile station (MS) antenna, many 2D and 3D geometric channel models have been developed [3-8, 11, 15, 17].…”