Exact Power Pattern Bounds for Arrays Affected by Calibration Errors and Mutual Coupling

Interval methods have become popular for finding reliable bounds on power patterns for arrays affected by bounded errors. Such bounds can be used in the evaluation and design of antenna and transducer arrays, such as, to determine the worst-case sidelobe level and identify detrimental error configurations. The uncertainty of the element responses can be represented as regions in the complex plane. Previous interval arithmetic methods either wrap these complex intervals into simple shapes before summing, or approximate the power pattern bounds directly. The bounds given by these methods are relaxed, which makes the evaluation pessimistic. Tenuti et al. addressed this by introducing the polygon arithmetic that can approximate bounds with arbitrary tightness at the cost of significantly increased computational complexity. In the current work, we show how the exact bounds can be achieved, and how the complexity can be reduced. We introduce a generalization of the polygon by “inflating” the vertices. This generalization is named polyarc and can exactly represent complex intervals bounded by arcs and edges. Compared to the polygon, polyarc offers simultaneously tighter bounds and reduced complexity; thereby increasing the utility of the interval arithmetic tolerance analysis in the fields of communication, sensing, and imaging.