Theory of Radio Transmission by Tropospheric Scattering Using Very Narrow Beams

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Abstract
Calculations have been made for communication over a 300-km path between antennas, each consisting of a paraboloid of diameter 100 λ. It is assumed that, under normal atmospheric conditions, transmission over this distance is due to scattering by atmospheric irregularities and that the scattering phenomena are described by the formula used by Booker and Gordon. Over this path, the effect of spread in the direction of arrival of scattered power should become noticeable for beamwidths less than about 1.5 degrees. For the 0.73 degree-beams assumed, spread in the angle of arrival should show up quite markedly for synchronized beam swinging-that is, when the beams at both transmitter and receiver are swung imultaneously so that their axes continue to intersect. When the beams are swung 1 degree to one side of the great circle path, the reduction in power received should be about 7 db, as compared with more than 40 db that would occur for propagation purely in the vertical plane containing trsmitter and receiver. Narrowing the antenna beams to very small values is an important key to increasing circuit radio-frequency bandwidth capability, although at the expense of increasing antenna "aperture-medium coupling loss" (so-called "gain loss"). For the assumed circuit average bandwidth should be about 6 mcp, the loss being of the order of 10 db. For beams much larger than 1.5 degrees, the bandwidth should be limited by the medium to about 3 mcp, with negligible loss.