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The general idea which can be drawn by reviewing wireless channel models says that the longer the range/distance, the more the delay spread, even in LOS microwave links. But I really wonder why it is true because by simple geometry, supposing a fixed environment like the following figure, the opposite seems true ($\tau_{2} / \tau_{1} \propto d_1 / d_2$) fig1 Is that because the more the range, the more the needed power, and therefore, a new environment which in this new environment, the more delay spread is more probable? Thanks!

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more delay spread is more probable?

exactly, if the shortest path is 2m, then you won't get a "detour" for a signal that's 200m long and still contributes significant power (measured to the total received power).

If your direct path is 2km, then, well, 200m detour will not relative make the signal much weaker and you'll have to account for the probability of such a path happening.

Now, LOS is a "bad" word: because it assumes ray physics. We know that obstacles / inhomogencies in the first Fresnel zone will cause your waves to be absorbed, reflected / scattered, diffracted, refracted… in short, you get effects that cause your received power to not be what you should be getting according to pure free space path loss.

If there's scattering, diffraction or refraction, you might well be introducing new paths in what you thought was "just" line of sight. Especially diffraction in long atmospheric paths will lead to multiple ways for your wave to reach the receiver, with different delays. That's a fun way to find out your system needs an equalizer late in design...

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