It is the distance ratio rather than the actual distance change that determines the space attenuation. A given distance change has a greater effect at points close to a source than it has far from the source.
Space attenuation is important for antennas that use a reflector or a lens.
Parabolic reflectors have different parts of the reflector at different distances from the feed. The edge of the reflector is usually further from the feed than the centre of the reflector is. Parts of the reflector that are 1/2 the distance to the feed, compared to the edge, for instance the centre of a f/D=0.25 reflector, have 4 times the power density. This means that for parabolic reflector antenna four focal lengths across, fed at its focus, the power density hitting the reflector at the edge is 1/4 the power density close to the centre. The reflection from the reflector gives the same power density at the projected aperture that hit that part of the reflector. This power density ratio then appears in the projected aperture of the reflector, so that aperture has a 4:1 power density ratio across it. This means that the gain is less than could be had from an antenna of this area, because the maximum gain is when the power is spread equally over the projected aperture. However, most antennas need a power taper anyway because sidelobe levels are more important than peak gain, and an edge taper reduces sidelobe levels. The feed also will have its own power taper across its beam, and the feed taper and the space attenuation are combined to give the required 10 dB or 20 dB (just examples) edge illumination to give the required sidelobe level. Antenna design books give tables relating edge taper to sidelobe levels, and also the space attenuation (edge relative to centre) for different F/D parabolic reflectors.
A similar reasoning applies to lenses, or reflect-arrays.
Just remember that the term " free space "attenuation (which is widely used) assumes a lossless "space"; this is no the case when e.g. microwaves penetrate through the atmosphere and we all know that the receiver field strength for geostationary satellites goes down in (heavy) rain..and due to the losses in the atmosphere the noise temperature goes up in parallel which may leas to insufficient signal to noise ratio at the LNB module.
If by space attenuation you mean free-space attenuation, it is important in all propagation problems, because whatever else is happening this 1/r^2 attenuation happens and needs to be there in the calculation whatever else is there too, such as atmospheric attenuation, rain, fog, trees, reflections etc. etc etc.
It is the basis of the Frijs equation and give a starting point you can add to.
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