On the independent amplitude, level reduction of a broadside linear array by the orthogonal method

Summary form only given. The design problem of a linear antenna array has been in focus for many years. Several design techniques have been proposed which are described in standard textbooks. Among them is the orthogonal method that was initially proposed by Unz (1966) and subsequently applied by Sahalos (1974) to several design problems. The method is, general and guarantees an minimum mean square error approximation of the desired pattern. One of the problems related to linear array design is the quantization of amplitudes. Quantization is appropriate in arrays of solid-state modules with saturated output amplifiers. The main problem is to devise a method that is able to reduce the number of the independent amplitude levels while approximating the desired pattern in an optimal sense. We model the problem as a set partitioning combinatorial problem, in which each possible configuration is evaluated by the orthogonal method and a configuration is chosen that best approximates the desired pattern minimizing the mean square error. The total number of different configurations is given by a Striling number of the second kind. This means that even for a moderate number of elements the problem becomes computer intensive and it is appropriate to utilize possible symmetries that are known a priori to reduce the computation time. We present the formulation and several examples, demonstrating the applicability of the method.