دعوى رد الإمام مالك خبر الآحاد الصحيح: دراسة تطبيقية

The importance of this study is to reveal the truth of the case of the response of Imam Malik (179 e) - the leader of the School of Archeology - the story of the atheists by violating the work of the people of the city; The study resulted in the results of the most important response of this lawsuit for several reasons, the first of which is that the work of the people of the city is a frequent occurrence, Rather, the imam has an approach based on the introduction of the frequent on the individual, and that many of the issues of work are supported by the correct hadeeth, and the one that is contrary to it is apparent, and it is permissible to combine or say the copies when proven.

Modeling and Characterization of Cellular Mobile Channels for 3-D Radio Propagation Environments

In order to meet the increasing demands of capacity in land mobile radio cellular communication systems, the use of directional antennas has become an integral part of future communication systems. With purpose to gauge the capabilities of systems with directional antennas, it is essential to have a precise knowledge of angular and temporal representation of the dispersion of multipath waves in 3-D propagation environments. Such representation of propagating waves can only be achieved with the use of spatial channel models. Therefore, this thesis focuses on modeling and characterization of cellular mobile channels for 3-D radio propagation environments. The research work in this thesis consists of three parts. Part-I aims at the physical modeling of cellular mobile channels in 3-D radio propagation environments. Part- II characterizes the impact of mobility on the Doppler spectrum; while, part-III provides a geometrically based performance analysis of handovers in land mobile radio cellular systems. The thesis begins with an overview of the basics of spatial channel models in different cellular environments and then proceeds towards a detailed and compre- hensive survey of spatial channel models. Further, a generalized 3-D scattering model is proposed for macro-cellular land mobile radio cellular systems with a Mobile Station (MS) located at the center of a 3-D scattering semi-spheroid and a Base Station (BS) employing a directional antenna located outside of the semi- spheroid. The effect of directional antenna is thoroughly observed on spatial and temporal characteristics of the proposed model. Closed-form expressions for joint and marginal Probability Density Functions (PDFs) of Angle of Arrival (AoA) seen at MS and BS in correspondence with azimuth and elevation angles are derived. Furthermore, closed-form expressions for propagation path delays and trivariate joint PDFs of Time of Arrival (ToA) seen at MS and BS in correspondence with azimuth and elevation angles are derived. Moreover, the theoretical results along with observations illustrate the effect of directional antenna on the spatio-temporal statistics of the proposed 3-D spatial model. All the statistics are derived for both uniform and Gaussian scatter densities. The proposed 3-D scattering model for the case of uniform scatter density, is shown to deduce all previously-proposed 2-D and 3-D models that assume uniform distri- bution of scatters with directional or omnidirectional antennas, found in literature for macro-cell environment. The theoretical results obtained are compared with some notable 2-D and 3-D scattering models to validate the generalization of the proposed model. Obtained theoretical results (for the case of Gaussian scatter density) for spatial statistics at BS are compared with an empirical set of mea- sured data (found in literature), which also demonstrates the validity of proposed model. vi In the second part of thesis, the effect of mobile motion on the statistical character- istics of Doppler spectrum is presented. An analytical model to quantify the effect of directivity of the radiated waves from the BS antenna on the Doppler spectrum in 3-D radio propagation environment is proposed. Closed-form expressions for trivariate PDFs of propagation path distance, power, and Doppler shift are de- rived. Furthermore, general expressions for joint and marginal PDFs of elevation AoA, power, and Doppler shift are established. The obtained theoretical results along with the observations are presented that illustrate the effect of directivity of the antenna beam-width and the direction of MS’s motion on the distribution characteristics of power Doppler spectrum. It is established that for motion of the MS in all directions, the spread in distribution of the Doppler shift observed is reduced significantly due to the use of directional antenna at the BS with a nar- row beam directed towards the desired user. It is also observed that, for a sharp azimuthal beam of directional antenna, the multipath components corresponding to the scatterers in elevation plane result in the reduction of Doppler shift with an increase in their vertical distance from MS. In part-III, an analysis for the impact of various channel parameters on the per- formance of handover in mobile radio cellular systems is presented. Using the proposed analytical model, a mathematical relation for the handover margin with velocity of MS, direction of mobile motion, and propagation environment is derived on the basis of path loss propagation model. Relationship for the ratio between the radius of coverage area and the length of overlapped region between adjacent cells is derived, which guarantees to satisfy the required handover margin. The impact of velocity and direction of MS’s motion on the handover margin is com- prehensively analyzed. The impact of propagation environment on the handover margin is also analyzed, where it has been observed that, the handover margin decreases significantly with an increase in the path loss exponent. For dense urban areas with higher propagation path loss exponent, the time margin available to perform the handover is less; therefore, quicker decision of handover is required to be made.