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The electromagnetic field in front of an infinite flat array of antennas can be subdivided into wave channels, each including one of the antennas. Each channel behaves like a hypothetical waveguide similar to a transmission line made of two conductors in the form of parallel strips. A simple derivation then leads to the radiation resistance of each antenna and to some limitations on the antenna spacing. In the usual flat array of half-wave dipoles, each allotted a half-wave-square area, and backed by a plane reflector at a quarter-wave distance, the radiation resistance of each dipole is 480/π = 153 ohms. In a finite array, this derivation is a fair approximation for all antennas except those too close to the edge. This derivation also verifies the known formula for the directive gain of a large flat array in terms of its area. The same viewpoint leads to the radiation resistance of an antenna in a rectangular waveguide, which has previously been derived by more complicated methods.
H.A. Wheeler (1948) studied this question.