Directivity estimates reveal tradeoffs in source tolerance design
Directivity Estimates and Tolerance Tradeoffs in the Presence of Random Perturbations
Information Theory
Summary
Making devices that send signals strongly in one direction can be tricky because small changes or errors can reduce their focus. The authors provide a new way to predict how much signal focus is lost when these changes happen, even in complicated device setups. Their method helps designers understand tradeoffs between how focused a signal is and how much error can be tolerated. This approach works fast and can use simple data from simulations or measurements.
What this means in practice
- •For antenna engineers: Design antenna arrays with well-understood tradeoffs between signal focus and component tolerance using this predictive method.
- •For acoustic system designers: Optimize directional sound sources by estimating how physical variations affect directivity and tolerance tradeoffs.
Authors
Kurt Schab, Lukas Jelinek, Miloslav Capek, Mats Gustafsson
Abstract
The practicality of realizing high-directivity sources is studied using a generalized sensitivity metrics. These measures are based on the error model adopted in previous studies on array tolerance, but account for heterogeneous array characteristics in an arbitrary source-expansion basis, making it applicable to the study of continuous sources, ideal uncoupled arrays, and heterogeneous arrays with mutual coupling. The formulation provides the ensemble average of realized directivity under the selected error model, making it a fast predictor of anticipated directivity reduction due to source perturbation. The data required to compute these predictions are straightforward to obtain via simulation or measurement, with a significant simplification when the system can be approximated as lossless. The directivity and the proposed tolerance measures allow for the formulation of optimization problems illustrating the tradeoff between these measures. Several examples demonstrate these tradeoffs, special cases, comparison to previous estimates of maximum directivity, and the accuracy of sensitivity as a predictor of statistical performance over large ensembles of design realizations.