This paper describes the application of the optimization technique known a s dynamic programming' to the design of "thinnedyy array antennas with unequal element spacings. Dynamic programming is a systematic procedure for efficientlyutilizingthe capabilities of modernhigh speeddigital computing machines to find optimum solutions to problems not computationally feasible by conventional means.It is used here to determine the optimum configuration of element spacings to achieve a desired radiation pattern.One possible method for designing an unequally spaced array is to simply try all possible combipations of element positions and select the best. However, the number of combinations that must be examined increases exponentially with the number of elements and it is generally not practical to employ this brute-force procedure except in the simplest of cases. The advantage of dynamic programming is that it reduces the number of combinations that must be examined. It accomplishes this saving by converting a single N-dimensional optimization problem to a sequence of N one-dimensional optimization problems. The smaller number of combinations with dynamic programming results from the judicious programmed elimination of configurations which are determined by the computer to offer no advantage. That is, the application of dynamic programming allows for many alternatives to be discarded before they are evaluated completely.A program was written for the IBM 7094 digital computer to determine the optimum .spacings of linear arrays consisting of up to 25 pairs of elements (51 elements total, including the one in the center). The criterion for selecting the optimum radiation pattern was that the highest sidelobe peak, within a specified angular region, should be less than the highest peak of any other pattern. This is a special case of the general criterion of minimizing maximum deviations. It is found to result in radiation patterns with relatively uniform sidelobes over the region of optimization. Dynamic programming produces significantly better designs than achieved with purely random selection, space-taper designs, or empirical designs.This technique not only permits the selection of the optimum configuration of elements in a thinned array but its inherent flexibility also permits the effect of variation in the design parameters tobedetermined. The peak sidelobe level as a
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