Modeling Uncertainty in Phased Arrays Through the Interval Analysis

The Interval Analysis (IA) is presented as a powerful mathematical tool for the robust and efficient analysis of the power pattern tolerances in phased arrays with errors on the control points (amplitude and phase weights). It is shown that the analytical expression of the power pattern can be extended as interval function by exploiting the rules of IA. The close-form relationship of the "interval" power pattern, identifying an upper bound function and a lower bound one, is expressed as a function of the expected maximum deviation of the excitation weights from their nominal/ideal values. Thanks to the IA Inclusion Property, it is guaranteed that the power pattern bounds are not violated by whatever pattern generated by the actual array with control point errors not exceeding the expected deviations.