On the limits of simple array antennas for uncorrelated patterns

For analysis, the simplest array comprises two isotropic antenna elements with same amplitude and same phase. A phase shifter in one branch provides the degree of freedom for basic pattern adjustment. We seek orthogonal patterns with respect to the element spacing, d, and the phase shift, δ. Approximate orthogonality (finite, but small correlation coefficient between patterns) is still useful in adaptive antennas in multipath scenarios. We consider the two-dimensional full/half plane space, i.e., θ = π, 2π, for which there is a closed form solution. We also look for approximate pattern orthogonality for partial coverage. To treat the integrals of the latter case, we use accurate numerical integration methods with the aid of commercial software. The results for different angle and angular spread of coverage, show that for partial coverage, the broadside direction is more effective (lower pattern correlation) than the same coverage in the endfire direction. Deploying the single degree of freedom (phase shift) in a three (or more) element array allows more complex patterns but brings no extra pattern orthogonality capability.