فقہی قاعدہ

The experts from various fields have maintained some rules and regulations in understanding and acquiring skills in this field of knowledge. This is due to their efforts which make very simple to understand it similarly the experts of ʽilm-ul-Fiqah i.e. Mujtahedyn and respected Fuqahāʼ have formulated some rules and regulations in the light of Qurʼan, Sunnah and decision act of companions of Muhammad (SAW) which also made it not only simple but it furnish skills and strategies in solving problems in field of Fiqah.

Geometric Modeling and Characterization of 3-D Land Mobile Radio Cellular Propagation Channels

Accurate knowledge of radio channel characteristics is of immense importance to meet the dynamic requirements of the emerging fifth generation (5G) communication networks. The existing widely used radio channel models are not adequate for the 5G potential candidate technologies because of numerous strong and obvious reasons including very large antenna arrays with high directional resolution (massive MIMO), direct machine-to-machine (M2M) communication links, small sized cells with high users’ density, and less elevated base stations (BS), etc. Among the various channel modelling approaches, the geometrically based channel modelling is a notable method for establishing the probabilistic relationships between spatial locations of transmitter, receiver, and scattering objects. In various indoor and outdoor radio propagation environments, the local vicinity of mobile user terminals is usually a scattering free region. This aspect has been incorporated in various two dimensional (2-D) scattering models available in the literature; however, no three dimensional (3-D) model exists in the literature which is flexible enough to adapt such propagation scenarios. In this thesis, a geometry based 3-D stochastic channel model for land mobile radio cellular propagation environments is proposed, which offers high degree of flexibility in the geometry of scattering volumes to accurately adapt the targeted propagation scenario. The research contributions of this thesis are divided into two main parts, viz: spatial channel model for macro-cellular and M2M (and pico-cellular) radio propagation environments. In the first part, a geometrically based tunable spatial channel model for macrocellular propagation environments is presented. 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 the MS. To ensure the degree of expected accuracy, the proposed model is designed to be tunable (as required) with nine degrees of freedom, which is 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 origins centered at MS. The elevated 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 (PDF) of angle-of-arrival (AoA) and time-of-arrival (ToA) are derived for both up- and down-links. Performance of antenna array systems and signal processing techniques implemented at the BS strongly depend on the available knowledge of the radio channel’s characteristics regarding the dispersion of multipath waves in horizontal and vertical planes. 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 (SF) of the proposed analytical 3-D channel model is conducted. Mobility of user terminal imposes time variability in radio channel’s characteristics. In order to comprehend the mobility of user terminal into the proposed channel model, characterization of Doppler spectrum and second order fading statistics of the radio propagation channel is also presented. Mathematical expressions for joint and marginal PDF of Doppler shift and multipath power are derived. An analysis on the spatial, temporal, Doppler spectrum, and second order fading statistics of the radio channel is presented, where the impact of various physical channel parameters on its statistical characteristics is analyzed. In the second part of the thesis, the proposed channel model for macrocellular environments is extended for small cells and machine to machine (M2M) communication scenarios by considering the effective scattering objects around both ends of the communication link. Using the proposed model, closed-form expressions for the joint PDF of AoA and ToA are derived in azimuth and elevation planes. Similar to the analysis conducted for macrocellular environment in first part of the thesis, a comprehensive analysis on the impact of various input geometric parameters on the spatial and temporal statistics of the channel is presented. In order to evaluate the robustness and establish the validity of the proposed analytical model, a comparison of the proposed analytical results with experimental datasets (available in the open literature) and performed computer simulation results is presented. The proposed analytical results are seen to fit a vast range of empirical datasets taken for various outdoor radio propagation environments. This good agreement in analytical, experimental, and simulation results establishes validity of the proposed model. Moreover, the proposed model is shown to degenerate to various notable geometric channel models in the literature by an appropriate choice of a few parameters.