Analytically Derived Uplink/Downlink TOA and 2-D-DOA Distributions With Scatterers in a 3-D Hemispheroid Surrounding the Mobile

Abstract

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...

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

“…Therefore, it is very essential to consider the spreading of multipath signals in 3-D space (i.e. simultaneously both in azimuth and elevation planes) [15][16][17][18][19][20][21][22]. In [16,17], power spectral density and PDFs of AOA for a nonzero elevation plane using a 3-D scattering model are theoretically derived, and in these models authors do not consider spreading of multipath waves in the azimuth and elevation planes.…”

“…simultaneously both in azimuth and elevation planes) [15][16][17][18][19][20][21][22]. In [16,17], power spectral density and PDFs of AOA for a nonzero elevation plane using a 3-D scattering model are theoretically derived, and in these models authors do not consider spreading of multipath waves in the azimuth and elevation planes. However, Janaswamy [18] proposed a 3-D semispheroid model with a low MS antenna and an elevated BS antenna, the model presented here is useful in macrocell environments where significant multipath components can arrive both from horizontal and vertical directions at the BS and the MS. A similar model is presented in [19,20], where uniform distributed scattering objects are assumed in 3-D semispheroid and MS is considered non-elevated located in scattering region.…”

On the Geometric Modeling of the Up link Channel in a Cellular System

“…In any case, the outcome of a model should be interpreted taking into account the required accuracy. This is the main reason why models such the ones presented in [23][24][25][26][27][28][29] have been proposed. In [23] a 3-D deterministic simulation model that takes into account both temporal and spatial channel characteristics is presented.…”

“…However the computational cost of ray tracing techniques still remains their major drawback. Proposals in [25][26] approach the problem of spatial AoA pdf derivation differently. The mobile is assumed to be surrounded by scatterers forming a spheroid, [25], and a half-spheroid, [26], surface allowing the derivation of closed-form pdf expressions.…”

“…Proposals in [25][26] approach the problem of spatial AoA pdf derivation differently. The mobile is assumed to be surrounded by scatterers forming a spheroid, [25], and a half-spheroid, [26], surface allowing the derivation of closed-form pdf expressions. Their simplicity makes them very useful for the performance evaluation of a wireless communication system in a macrocellular environment.…”