The angular correlation interval for static and dynamic patterns in phased array antennas

Static and dynamic radiation patterns are investigated, and the differences are brought out by a statistical analysis. The two types of patterns can be separately identified because the static pattern represents the case in which the beam is stationary as the target moves, and the dynamic pattern represents the case in which the beam is electronically scanned through the target. In each type of pattern, the spatial angle for which high correlation occurs is computed from an approximate analysis. That information, when combined with the error fields resulting from randomized phase shifter quantization, is used to predict the detailed differences between the two types of patterns. A knowledge of the difference is important in selecting the least expensive method of phased array pattern testing, particularly for large antennas. The radiation pattern ensemble statistics in the presence of elemental amplitude and phase errors were found to be the same for either type of pattern. Therefore, uncorrelated samples of either pattern will establish the array radiation characteristics. However, it is shown both in an approximate analysis and experimentally that quite a difference can exist between individual static and dynamic patterns. The exact amount of difference depends on many factors, but primarily on the aperture size and the number of phase-shifter bits. In the effort described here, the various errors throughout the antenna are characterized by their mean and standard deviation in a probability distribution function. As a result, their effect on radiation patterns is described in terms of probabilities. The general analytical approach of Ruze (Ref.1) and Adams (Ref. 2) is used as a background. The analysis is divided into several sections. The ensemble statistics of the errored radiation pattern are first described and examined for sensitivity to the type of pattern. Next, the differences between static and dynamic patterns are indicated by reference to spatial autocorrelation functions and heuristic aperture analysis. The analysis, though approximate, appears to provide useful results, as illustrated by the good comparison between theoretical and experimental patterns for a 48-element linear array.