The analogy between the Butler matrix and the neural-network direction-finding array

The Butler matrix and the neural network have been compared to provide insights about the neural-network behavior for a direction-finding array. The goal of the paper has been tutorial, since the two systems are only really comparable in the very limited case considered: an ideal array with equal element spacings, no failures, and using the orthogonal beam locations as training points. Within the constraints of this specialized case, the comparison illustrates the role of pre- and post-processing, the function of the Gaussian radial basis function, and the considerations in determining the weights applied to the Gaussian or modified sine function node outputs. In addition, the comparison points out the basic similarity of the two procedures, and reveals some insights about the operation of a neural network from the perspective of antenna engineering.