Chapter 8 Radio Wave Propagation Fresnel Zone Direct Path Indirect Receiver Fresnel Zone Transmitter Fig. 8.15 Fresnel zone. The profile of the topology between transmitting and receiving antennas can also be plotted. It is desirable to avoid any obstructions within the first Fresnel zone, which is defined as the surface of an ellipsoid of revolution with the transmitting and receiving antennas at the focal points in which the reflected wave has an indirect path half a wave- length longer than the direct paths. Figure 8.15 illustrates this, and the radius of the first Fresnel zone at any point (P) is given by equation 8.18, where R is the radius and d1 and d2 are the distances from point P to the ends of the path. (8.18) The height of the transmitting and receiving antennas above the intervening terrain and the roughness of the terrain have a marked effect on path attenuation and received field strength in the VHF and UHF bands. The Friis formula generally yields results that are too optimistic; that is, attenuation is too low and field strength is too high. Figure 8.16, repro- duced from ITU-R Recommendations, shows received field strength values at 10 meters above ground level for a radiated power of 1 kW for different transmit antenna heights. The field strengths are modified by correction factors for the terrain irregularity that is between the transmit and receive antennas, which can increase attenuation by up to 18 dB or reduce it by 7 dB depending on the topology. Average terrain irregularity is defined as the differences in height above and below 50 meters in only 10 percent of the path length. Figure 8.17 displays the attenuation correction factors for field strength for various terrain height differences. Frequencies at 900 MHz and 1800 MHz are used for comparatively short-distance "cel- lular" services, and communications are often limited by multipath interference caused by single or multiple reflections, particularly in urban environments. The only practical solu- tion is to try different positions f