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Mobile and wireless communications physical layer development and implementation Part 2

Tham khảo tài liệu 'mobile and wireless communications physical layer development and implementation part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Wireless Transmission in Tunnels 11 We can infer from the above discussion that the attenuation caused by the walls which are perpendicular to the major electric field is much higher than that contributed by the walls parallel to the electric field. Fig. 5. Attenuation rates in dB 100m of VP and HP modes with m n 1 in a rectangular tunnel of dimensions 4.3x2.15 m. sr 10. The approximate attenuation rates given by 27-28 for the horizontally and vertically polarized HP and VP modes with m n 1 are plotted versus the frequency in Figure 5. Here the tunnel dimensions are chosen as w h 4.3m 2.15m and sr 10. It is clear that the VP mode has considerably higher attenuation than its HP counterpart. The attenuation rates obtained by exact solution of equations 22 and 25 are also plotted for comparison. It is clear that both solutions coincide at the higher frequencies. Ray theory When it is required to estimate the field at distances close to the source the mode series becomes slowly convergent since it is necessary to include many higher order modes. As clear from the above argument higher order modes are hard to analyze in a rectangular tunnel. In this case the ray series can be adopted for its fast convergence at short distances say of tens to few hundred meters from the source. At such distances the rays are somewhat steeply incident on the walls hence their reflection coefficients decrease quickly with ray order. Therefore a small number of rays are needed for convergence. A geometrical ray approach has been presented by Mahmoud and Wait 1974a where the field of a small linear dipole in a rectangular tunnel is obtained as a ray sum over a twodimensional array of images. It is verified that small number of rays converges to the total field at sufficiently short range from the source. Conversely the number of rays required for convergence increase considerably in the far ranges where only one or two modes give an accurate account of the field. The reader is referred to .