Simple general formula for PDF of angle of arrivalinlarge cell operational environments

Piechocki, Robert J.; Tsoulos, George V.; McGeehan, JP

doi:10.1049/el:19981264

Cited by 47 publications

(23 citation statements)

References 2 publications

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Ziółkowski

Kelner

2016

Wireless Pers Commun

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This paper focuses on modeling of the statistical reception angle properties that are the result of the environmental influence on transmitted signals. Numerous measurements have shown that the statistical properties of angle of arrival (AOA) significantly depend on the type of propagation environment. In practice, this means that in the analytical and simulation studies, the use of statistical models of AOA required their adaptation to propagation conditions in research scenario. Despite the large number of papers that are devoted to the AOA modeling, the method of fitting models to the environment is not presented in any of the publications. This paper fills this gap. For the assessment of the propagation properties and environment type classification, the basis is the rms delay spread (DS). Therefore, the presented method of the model adaptation to the environment type consists of determining the relationship between the model parameter and DS of environment. Here, the probability density function (PDF) of models such as the modified Gaussian, modified Laplacian, modified logistic, and von Mises distribution are considered as the statistical models of azimuth AOA. For seven different propagation environments, the measurement results are used as a reference data. A comparative analysis shows that the modified Laplacian PDF provides the smallest error fit to measurement data. However, in theoretical analysis and simulation studies, other empirical models can be used due to relatively low approximation errors. The presented results are the basis for the adaptation error assessment of the empirical model for any of the research scenario.

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Section: Introductionmentioning

confidence: 99%

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

Ziółkowski

Kelner

2016

Wireless Pers Commun

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“…One-dimensional azimuth-AOA marginal distributions (without considering TOA or elevation), likewise analytically derived using thorough mathematics based on various geometric models of the scatterers' 2-D spatial locations, have scatterers modeled as: 1) uniformly distributed only on a uniform circular disc around the mobile in [7], [8], [10], [11], [20]; 2) uniformly distributed only on a uniform hollow-disc around the mobile in [24]; 3) uniformly distributed only on a uniform elliptical disc with foci at the mobile and the base station in [5], [10], [14], [18]; 4) circularly Gaussian distributed centered at the mobile in [16]; and 5) distributed according to an inverted parabola at the mobile in [28].…”

Section: Literature Review On Geometric Modeling Formentioning

confidence: 99%

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

Olenko

Wong

Qasmi³

et al. 2006

IEEE Trans. Antennas Propagat.

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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...

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“…The angular spread of the channel can be described by the pdf of the angle of arrival, which was calculated for such a model in [11] and shown to be for elsewhere (8) where , i.e., the cluster radius over the distance between the MS and the BS. The formula given in (8) is a special case of the elliptical case derived in [11].…”

Section: B Geometrical Relationsmentioning

confidence: 99%

“…The formula given in (8) is a special case of the elliptical case derived in [11]. The elliptical cluster model is more flexible as a static GBSR model.…”

Section: B Geometrical Relationsmentioning

confidence: 99%

See 1 more Smart Citation

A new stochastic spatio-temporal propagation model (SSTPM) for mobile communications with antenna arrays

Piechocki

McGeehan

Tsoulos³

2001

IEEE Trans. Commun.

Self Cite

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Abstract-In order to evaluate the performance of third-generation mobile communication systems, radio channel models are required. The models should be capable of handling nonstationary scenarios with dynamic evolution of multipaths. In this context and due to the introduction of advanced antenna systems to exploit the spatial domain, a further expansion is needed in order to include the nonstationary characteristics of the channel. In an attempt to solve these problems, this paper presents a new stochastic spatiotemporal propagation model. The model is a combination of the geometrically-based single reflection and the Gaussian wide-sense stationary uncorrelated scattering models, and is further enhanced in order to be able to handle nonstationary scenarios. The probability density functions of the number of the multipath components, the scatterers' lifetime, and the angle of arrival are calculated to support these features. The input parameters of the model are based on results from measurement campaigns published in the open literature.

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Simple general formula for PDF of angle of arrivalinlarge cell operational environments

Cited by 47 publications

References 2 publications

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

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

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

A new stochastic spatio-temporal propagation model (SSTPM) for mobile communications with antenna arrays

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