Antenna pattern synthesis based on optimization in a probabilistic sense

Antenna optimization theory is usually formulated on the premise that all parameters could be adjusted with unlimited accuracy. Since no practical antenna can be built with absolute precision, only optimization in some probabilistic sense of a random performance index appears to be meaningful. The method also generalizes and gives meaning to the concept of regularization used by others. An approximate solution to the probability distribution of the random performance index is obtained. From this several possible senses of optimization may be defined. Several examples in the synthesis of a two-dimensional secant pattern are studied in detail. In general, it may be impractical to build an array with deterministically optimum currents but also next to impossible to even compute the currents accurately. A detailed numerical analysis is given to show possible sources of errors.