Thinned, unequally spaced arrays designed by dynamic programming

Abstract

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

Unequally Spaced Arrays Based on the Poisson Sum Formula

“…For large , the radiation pattern for uniform amplitude with unequal spacing is approximated by (7). (13) This is identical to the radiation from a continuous source distribution with amplitude variation of ( ). We can then equate ( ) to well known distribution such as Taylor distribution [21].…”

“…Matrix method was employed by Unz [1]- [3] and Baklanor et al [4] Perturbation method was proposed by Harrington [5], and several approximate integral techniques were proposed by Lo [6] and others [7]- [9]. General discussions were presented by King [10], Andreason [11], Sandler [12], and Skolnik [13]. Probabilistic approach was taken by Lo [14], [15], and Maher and Cheng [16].…”

Planar Thinned Arrays: Optimization and Subarray Based Adaptive Processing

“…In this manner, the number of elements in the array is fixed and it is deterministically set by the thinning factor. This is different from thinning using dynamic programming [4,5], where a deterministic approach is used to test all the possible insertions of an active element, including a pruning strategy to reduce the number of trials.…”

“…Starting from [2], in [3] 2 International Journal of Antennas and Propagation Mailloux and Cohen studied a regular grid based thinning approach with the joint use of stepped amplitude tapering to further reduce the SLL. In [4,5] Skolnik et al proposed a trialand-error technique called "Dynamic Programming, " which has been devised to reduce the number of total trials with respect to the brute approach. As for the previous thinning approaches, "Dynamic Programming" is not supposed to reach the optimal array configuration.…”

Array optimization and adaptive processing for sub-array based thinned arrays

“…Another technique introduced by Skolnik for this problem is the Dynamic Programming [3] [4], which aims at reducing the computational cost of the statistical techniques to obtain a thinned array with desired characteristics. In the 90's Haupt applied genetic algorithms to the design of thinned arrays [5] [6], while more recently also the use of simulated annealing was attempted to the same purpose [7].…”