Pattern translation and rotation in uncorrelated source distributions for multiple beam antenna design

In the uncorrelated scenario model, a continuous source distribution illuminates a receiver with waves bearing signals that are uncorrelated with respect to their angle of arrival. This model is used for multipath situations such as scintillating atmospheres, but also can be applied to optical beams for indoor communications, acoustic beamforming, and, of particular interest here, mobile communications. For diversity antennas operating in such a scenario, patterns that produce uncorrelated signals are required. An angular separation of directive beams in multipath scenarios acts to decorrelate the received signals. It is of interest to quantify the minimum angular spacing required of beams in order to provide a framework for the design and configuration of the antennas. The approach is to consider only the main lobe of the antenna pattern and to take it as a real function. This is reasonable as long as most of the energy is conveyed via the main beam. In practice, the sidelobe structure and nonuniformity in the phase of an actual pattern act to improve the situation in the sense that the decorrelation angles become smaller. The conditions for angular diversity result in a simple rule-of-thumb for the minimum beam separation requirement, which is essentially independent of the directivity. Finally, both scalar and vector elliptic beams rotated about their boresight axes are analyzed for the decorrelation rotation angle as a function of the ratio of the ellipticity. The resulting design curves offer a guideline to beam configuration for multipath scenarios.