Fresnel zones are elliptically shaped three-dimensional volumes, something like a rugby ball or american football, which surround the main direction of a line-of-sight radio path (as shown in Figure 8.5). The ®rst Fresnel zone (often lazily referred to as `the Fresnel zone') should be kept clear of obstacles so that destructive radio re¯ections from objects within this zone do not lead to serious interference of different re¯ected versions of the radio signal arriving at the receiver.
The surfaces of the various Fresnel zones (i.e the surfaces of the elliptical `footballs') correspond to points at which, if a re¯ected path into the receiving antenna were to be generated, it would have a very destructive interfering effect on the signal received via the direct-ray path. Figure 8.6a illustrates the re¯ection from an obstacle near the direct-ray (or
142 Radio Path and Radio Network Planning Considerations
Figure 8.2 A passive repeater used in a point-to-point link to overcome obstructed line-of-sight
line-of-sight path). Figure 8.6b shows the destructive effect of interference caused in the case that the re¯ected ray path is exactly half the wavelength (of the radio carrier signal) longer than the direct path. In this case, the two different signals (the direct one and the re¯ected one) arrive at the receiver in antiphase, summing to give a net signal of very little strength (i.e. causing high levels of attenuation or interference fading).
The Fresnel Zone 143
Figure 8.3 Taking advantage of line-of-sight obstacles to resolve interference and increase the potential for frequency re-use
Figure 8.4 There can be poor signal strength and thus coverage under very tall base stations!
The worst interference in Figure 8.6 results when the re¯ected signal arrives in exact antiphase from the direct path signal. This corresponds to a path difference of half the radio carrier signal wavelength (i.e. l/2). In other words, the path lengths a and b, when added, are a constant l/2 longer than the direct path, d. Anyone who remembers from his school days the trick of drawing an ellipse by using a length of string (of constant length, in this case equal to d l/2) looped around two posts (the positions of the transmitter and receiver) will recognise that there are a whole series of possible re¯ection points which could cause the destructive re¯ections, and that these lie on a series of ellipses.
Fresnel zones (Ellipsoids)
Eccentricity of ellipse e 2d/ 2d nl where n 1,2,3,4,5...
Length of ellipse d/e Height of ellipse d
ep 1 e2
The ®rst Fresnel zone corresponds to the volume within the ellipse with a path length difference of one half wavelength (i.e. n 1 in the formulae above). Re¯ections near the boundary of the ®rst Fresnel zone will cause serious signal interference. For this reason, it is usual to try to ensure (during link planning) that the ®rst Fresnel zone (sometimes simply called the Fresnel zone is free of obstacles. An obstacle intruding into the zone can be circumvented by using a taller mast, for example, or perhaps by locating the antenna at a different corner of the building. (Actually, re¯ections near the 3rd, 5th, 7th and other odd order Fresnel zones can be as disruptive as ®rst Fresnel zone re¯ections, but these are often ignored by planners in practice, due to the much greater complications in assessing them.
Signal delays of three, ®ve and seven wavelengths are less destructive than one half-wavelength delays due to the changing nature of the modulated signal Ð because the signal has changed slightly, the interfering signal is no longer a perfect negating match. In addition, re¯ections from even order Fresnel zones (2nd, 4th, 6th, etc.) tend to strengthen the signal by `positive' interference.)
For practical purposes, it is easiest for the planner (during his site survey visit) to take with him a pair of binoculars and try to determine whether a constant diameter `pipe' of clear space (free of obstacles) is available between the proposed transmitter and receiver antenna locations. The necessary diameter of the `pipe' depends upon the length of the link (d above) and the frequency of the radio channel to be used. We can calculate the diameter from the formulae below:
144 Radio Path and Radio Network Planning Considerations
Figure 8.5 Obstacles should be avoided in the ®rst Fresnel zone
Maximum diameter of (®rst) Fresnel zone (at midway point of link) 2p d nl) (all distances and wavelengths in metres)
Alternatively, maximum diameter 17.3p d n=f
Where d length of link (transmitter to receiver) in km, n whole number, characterizing the Fresnel zones, and f radio channel frequency in GHz.
Thus, at a frequency of 38 GHz over a link of length 8 km, the ®rst Fresnel zone has a diameter at the mid-point of the link of 17:3 p
8 1=38 8 metres. Meanwhile, a 7 GHz link of 70 km length has a Fresnel zone of maximum diameter 55 metres. This `free space pipe' should be checked for obstacles at the time of the link site survey (i.e. during the link planning stage prior to equipment installation).
The radius of the ®rst Fresnel zone at any point on the radio link path is given by F1 17:3 pf d1d2= f dg
Where d length of link in km, d1and d2 are distances in km from the end terminals to the point in question, f radio channel frequency in GHz.
The formula presented above is useful for determining whether an obstacle is intruding into the Fresnel zone (as in Figure 8.7).
Obstacles in the Fresnel Zone
In the case of unavoidable intrusion of an obstacle into the Fresnel zone of a particular radio link, it is advisable to estimate the resultant loss of received signal strength. The methodologies for calculating the diffraction losses caused by different types of obstacles are covered by ITU-R recommendation P.526. In Figure 11 of chapter 7 we presented the graph used in this recommendation for calculating diffraction losses caused by obstacles.
The Fresnel Zone 145
Figure 8.6 Interference caused by re¯ected ray paths arriving at the receiver out of phase