Abrar Ahmed

A 3-D Propagation Model for Emerging Land Mobile Radio Cellular Environments.

A tunable stochastic geometry based Three-Dimensional (3-D) scattering model for emerging land mobile radio cellular systems is proposed. Uniformly distributed scattering objects are assumed around the Mobile Station (MS) bounded within an ellipsoidal shaped Scattering Region (SR) hollowed with an elliptically-cylindric scattering free region in immediate vicinity of MS. To ensure the degree of expected accuracy, the proposed model is designed to be tunable (as required) with nine degrees of freedom, unlike its counterparts in the existing literature. The outer and inner boundaries of SR are designed as independently scalable along all the axes and rotatable in horizontal plane around their origin centered at MS. The elevated Base Station (BS) is considered outside the SR at a certain adjustable distance and height w.r.t. position of MS. Closed-form analytical expressions for joint and marginal Probability Density Functions (PDFs) of Angle-of-Arrival (AoA) and Time-of-Arrival (ToA) are derived for both up- and down-links. The obtained analytical results for angular and temporal statistics of the channel are presented along with a thorough analysis. The impact of various physical model parameters on angular and temporal characteristics of the channel is presented, which reveals the comprehensive insight on the proposed results. To evaluate the robustness of the proposed analytical model, a comparison with experimental datasets and simulation results is also presented. The obtained analytical results for PDF of AoA observed at BS are seen to fit a vast range of empirical datasets in the literature taken for various outdoor propagation environments. In order to establish the validity of the obtained analytical results for spatial and temporal characteristics of the channel, a comparison of the proposed analytical results with the simulation results is shown, which illustrates a good fit for 107 scattering points. Moreover, the proposed model is shown to degenerate to various notable geometric models in the literature by an appropriate choice of a few parameters.

Angular characteristics of a unified 3-D scattering model for emerging cellular networks

A stochastic geometry-based unified three-dimensional (3-D) channel model for emerging land mobile radio cellular systems is proposed. Uniformly distributed scattering objects are assumed bounded within an ellipsoidal shaped scattering region (SR) hollowed with an elliptical-cylindric scattering free region. To ensure the degree of expected accuracy of the proposed model, the outer bounding ellipsoid and inner bounding elliptical-cylinder are designed to be tuneable as required, unlike its counterparts in the existing literature, independently along all the axes and rotatable in horizontal plane around their origin centered at the mobile station (MS). Closed-form analytical expressions for joint and marginal probability density functions (PDFs) of angle-of-arrival (AoA) in azimuth and elevation planes observed at the base station (BS) are derived. The obtained analytical results for angular statistics of the channel are presented along with a thorough analysis. Moreover, the impact of various physical model parameters on angular statistics of the channel is presented. To evaluate the robustness of the proposed generalized model and analytical method, a comparison with experimental datasets is also presented. The obtained analytical results are seen to fit a vast range of empirical datasets obtained for different outdoor propagation environments available in the literature.

Small-Scale Fading Statistics of Emerging 3-D Mobile Radio Cellular Propagation Channels

In delivering fifth generation (5G) communication networks, the fundamental advancements in the scale of antenna arrays, density of networks, mobility of communicating nodes, size of cells, and range of frequencies necessitate the derivation of an appropriate and reliable channel model. A tunable three dimensional (3-D) geometric channel model comprehending the mobility of user terminal together with high degree of flexibility in modelling the shape, orientation, and scale of the scattering region is proposed. Characterization of Doppler spectrum, quantization of multipath dispersion in angular domain, and second order fading statistics of the radio propagation channel is presented. Mathematical expressions for joint and marginal probability density function of Doppler shift and multipath power are derived for this advanced 3-D hollow geometric scattering model. Next, an analysis on the Doppler spectrum is presented, where the impact of various physical channel parameters on its statistical characteristics is analyzed. Since, the quantification of multipath dispersion in 3-D angular domain is of vital importance for designing large scale planner antenna arrays with very high directional resolution for emerging 5G communications, therefore, a thorough analysis on the multipath shape factors (SFs) of the proposed analytical 3-D channel model is conducted. Finally, the analysis on SFs is extended for characterization of second order fading statistics of multipath channels.

3-D Spatial Modeling of Network Interference in Two-Tier Heterogeneous Networks

The multi-tier heterogeneous network (HetNet) architecture can potentially address the massive connectivity and high throughput demands of the emerging fifth generation (5G) of wireless networks. However, the inter-tier interference in HetNets is considered to be a major performance bottleneck. This paper proposes a geometry-based three-dimensional (3-D) stochastic channel model for the spatial characterization of the sum interference in a two-tier HetNet with small cells in tier-1 overlaid with massive multiple-input-multiple-output equipped macro-cell base stations in tier-2. The angular spreads of the interference and the desired signals are analyzed by using the theory of 3-D multipath shape-factors and analytical expressions are derived for their second-order fading statistics, viz: level-crossing-rate (LCR), average-fade-duration (AFD), spatial autocovariance, and the coherence distance. Further, analytical expressions to investigate the second-order fading statistics against signal-to-interference ratio are also derived. The validation of the derived analytical expressions is established through a comparison with computer-based simulations. To provide insights into the network sum interference mechanism, the LCR and AFD expressions are derived for the special case when the rate of fluctuation of the desired signal is much higher than that of the interference signal and vice versa. Furthermore, the impact of the model’s physical parameters, such as the link distance and the receiver’s direction of motion as well as the fading distribution parameters such as its intensity and shape factors on the fading statistics of the interference are evaluated. These results demonstrate that the elevation angle has a significant impact on the interference characterization in HetNet architectures such that it cannot be ignored in modeling emerging 5G communication scenarios.

Analysis on multipath shape factors of air-to-ground radio communication channels

This paper first presents an extension of a notable three dimensional (3D) channel model for air-to-ground (A2G) radio propagation environments, from the plain distribution of angular energy to the quantization of multipath shape factors (SFs). Next, the paper presents a comprehensive analysis on the characteristics of multipath SFs for A2G radio propagation environments observed at both ends of the link. The analysis include the impact of various physical channel parameters on angular spread, true standard deviation, angular constriction, and direction of maximum fading. These SFs are obtained by exploiting the analytical and empirical results available in the literature for the distribution of energy in 3D angular space. Finally, a mechanism for classification of A2G propagation environments into taxiing, en-route, and take-off scenarios on the basis of SFs is presented.

Angle and time of arrival characteristics of 3D air-to-ground radio propagation environments

A three dimensional (3D) geometric channel model is proposed for ground-to-air (G2A) and air-to-ground (A2G) communication links. A low-elevated ground station (GS) and a high-elevated air station (AS) are taken at foci points of a virtual bounding ellipsoid corresponded from known knowledge of delay of longest propagation path. The effective region of scatterers around the GS is designed on the basis of this ellipsoid truncated by the average rooftop level (or average height of sea waves) and ground plane. Closed-form expressions for joint and marginal probability density functions (PDFs) of angle of arrival (AoA) observed at AS and GS in correspondence with azimuth and elevation angles are derived. Furthermore, closed-form expressions for density of energy with respect to the delay of arriving multipath waves corresponded from both the elevation and azimuth AoA are derived independently when observed from either end of the communication link. Moreover, effect of different physical parameters of the channel on distribution of energy in angular and temporal domains is presented. The comparison of analytical results with results of a notable model is also presented. In order to verify the derived analytical expressions, a comparison of analytical results with the performed simulation results is presented, which shows a good match.