Random removal of radiators from large linear arrays

The effects on the radiation pattern whenNpairs of symmetrically located radiators are removed at random from a large(2N_{0}+1)-element linear array are studied as a statistical problem. It has been possible to determine the limiting bounds of the radiation pattern the probability that the main-lobe beamwidth is not widened by more than a given percentage, the probability that a certain sidelobe does not deteriorate by a specified amount and the probability that all sidelobes are below a specified level. The general analysis is valid for arrays with an arbitrary amplitude distribution which is symmetrical with respect to the center element and with an arbitrary progressive phase shift. Curves showing computed statistical data for a 201-element array with both the uniform and a cosine-squared amplitude distribution are presented.