I. ANALYTICAL DERIVATION OF 3-D TOA/2-D-AOA DISTRIBUTIONSA signal, transmitted from a mobile user in a landmobile radiowave wireless cellular communication system, arrives at the cellular base station through multiple propagation multipaths. Each multipath carries its own propagation history of electromagnetic reflections and diffractions and corruption by multiplicative noise-a history reflected in that multipath's amplitude, Doppler, arrival angle, and arrival time delay at the receiving antenna(s). The values of these amplitudes, Doppler frequency shifts, arrival angles, and arrival time delays depend on the electromagnetic properties of and the spatial geometry among the mobile transmitter, the scatterers, and the receiving antennas. Each receiving antenna's data measurement sums these individually unobservable multipaths.The time of arrival (TOA) 1 distribution function characterizes the channel's temporal delay spread and frequency incoher- ence, which in turn determines the obtainable temporal diversity and the extent of intersymbol interference. The two-dimensional (2-D) azimuth-elevation angle of arrival (AOA) determines the angular spread and spatial decorrelation across the spatial aperture of an receiving antenna. The multipaths' nonzero elevation AOAs are most common in urban areas or over hilly terrains or with low-lying receiving antennas, where the propagating wave reflects off vertical structures like buildings or hills. The nonzero elevation AOA is critical for the use of a vertical or planar receiving antenna array, a fact recognized by the European Union's COST Action 259 [19]."Geometric modeling" idealizes the aforementioned wireless propagation environment via a geometric abstraction of the spatial relationships among the transmitter, the scatterers, and the base station. Geometric models thus attempt to embed measurable fading metrics integrally into the propagation channel's idealized geometry, such that the geometric parameters would affect these various fading metrics in an interconnected manner to reveal conceptually the channel's underlying fading dynamics. This work will maximally embed all derived statistics intrinsically within the propagation channel's geometry and to avoid a priori ad hoc statistical assumptions of the received signal's measurable statistics. See [27] for additional discussion on the nature of geometric modeling of wireless propagation.Geometric modeling contrasts with site-specific/terrain-specific/building-specific empirical measurements or ray-shooting/ ray-tracing computer simulations, which are applicable only to the one particular propagation setting under investigation but cannot be easily generalized to wider scenarios. One geometric model can apply for a wide class of propagation settings, producing the received signal's measurable fading metrics (e.g., the uplink and downlink probability density functions of the multipaths' arrival delay and 2-D arrival angle as in this paper) applicable generally within that class of channels.Geometric modeling contras...

For radiowave landmobile cellular wireless communication in ‘bad urban’ environments dominated by high rises, this paper analytically derives closed‐form expressions for the trivariate and bivariate joint distributions of the time‐of‐arrival and two‐dimensional azimuth‐elevation direction‐of‐arrival of the uplink multipaths. These expressions are explicitly in terms of the parameters of a ‘geometrical’ model of the three‐dimensional spatial relationships among the mobile station, the scatterers and the base station. This present ‘geometric model’ idealises the scatterers as uniformly located within the volume of a three‐dimensional vertical above‐ground cylinder whose flat bottom circular base centres at the mobile. Copyright © 2012 John Wiley & Sons, Ltd.

1 This work is first in the open literature to characterize the probability distribution (not merely the mean and variance) of the carrier-to-interference ratio (CIR) of an ad hoc CSMA/CA wireless communication network, via Monte Carlo simulations. This paper is also first in the open literature to model an ad hoc network accounting for all following factors: (1) more realistically modeling of the network nodes' spatial distribution via a two-dimensional Poisson process whereby network nodes are randomly placed at arbitrary two-dimensional plane (instead of nodes locating deterministically at only regular grid points), (2) suppression of nodes within the carrier sensing range of a transmitting node to micmac the CSMA/CA Medium Access Control (MAC) protocol (i.e. nodes self-restrain from transmission when neighboring a transmitting node), (3) microscopic Rayleigh fading, (4) propagation-distance-dependent path-loss and (5) more than one service class. Monte Carlo simulations of a CSMA/CA ad hoc network generate CIR data, whose probability distribution function and parameters are identified via leastsquares curve-fitting. The Inverse Normal distribution is the most well-rounded distribution, in the sense of providing a good fit (if not the best fit) to all nine Monte-Carlo simulation scenarios. The Rayleigh is the best univariate pdf. It can fit all scenarios very well, except the case without micro-fading and low pathloss.

This paper presents a new bivariate joint distributions of uplink multipaths' two-dimensional (2D) azimuthelevation direction-of-arrival (DOA) for a landmobile cellular wireless communication system. These distributions are based on a "geometrical" model of the three-dimensional (3D) spatial relationships among the mobile-station (MS), the scatterers, and the base-station (BS). This "geometric model" has the scatterers spatially distributed inside an above-ground 3D vertical cylinder whose flat bottom circular base centers at the mobile, and whose density tapers off as height increases. These distributions are rigorously derived via thorough mathematics, and expressed in closed form explicitly in terms of the DOA variables.R 2 + [r sin(θ) sin(φ)]

1 This paper presents a new trivariate joint and bivariate distributions of a landmobile cellular wireless communication system's uplink multipaths' time-of-arrival (TOA) and two-dimensional (2D) azimuth-elevation direction-ofarrival (DOA). These distributions are rigorously derived via thorough mathematics, based on a "geometrical" model of the three-dimensional (3D) spatial relationships among the mobile-station (MS), the scatterers, and the base-station (BS). Unlike earlier "geometric models" that assume the scatterers to have only a 2D spatial density (for example, uniform density within a disc around the mobile), this present "geometric model" have the scatterer spatial density as uniform within a 3D vertical aboveground cylinder whose flat bottom circular base centers at the mobile.