Beam spacing for angle diversity

In mobile communications, the multiple path propagation causes Rayleigh-like fading which limits the capacity of the channel. Antenna diversity is an established technique to mitigate the multipath. Design guidelines are rather limited, for example, the condition for space diversity in a uniform scenario is often quoted to be a half wavelength for omnidirectional antennas, although in practice a much closer spacing is possible, and desirable. By considering directional beams which are angularly spaced in an uncorrelated, directional scenario, the relations for the correlation coefficient between the fading signals received by the beams are derived. This allows the condition for angle diversity to be established. For medium to high directivity (>~6 dB), truncated (by the circular support) real Gaussian beams offer simple and accurate results, and for low directivity, real cosine beams are convenient. The real beams give pessimistic results in the sense that realistic, complex beams require a smaller angular spacing. Under the assumptions of the scenario being uncorrelated, simple relationships are established for angle diversity. These results have applications in the design of multiple beam antennas for mobile communications, optical beams for indoor communications, acoustic beamforming, and beams for the, classical multipath of scintillating atmospheres