Fast Evaluation of the Radiation Patterns of True Time Delay Arrays With Beam Steering

A multilevel algorithm for the computation of the transient radiation patterns of true time delay (TTD) conformal arrays over a range of observation and beam steering directions is presented. The multilevel algorithm is based on hierarchical decomposition of the array into smaller sub-arrays of elements. At the finest level of decomposition, the angular-temporal radiation patterns of single-element sub-arrays are obtained over a sparse angular grid of directions and short temporal duration, by either measurement or calculation. Subsequent steps of the algorithm comprise multilevel aggregation of delayed sub-array contributions. This process continues until the transient radiation pattern of the whole array is obtained. At each level, the radiation pattern is interpolated to a finer angular grid of observations and steering directions followed by temporal delay compensation. The multilevel array decomposition algorithm attains a computational complexity substantially lower than that of the direct evaluation. Furthermore, the algorithm is particularly efficient for large arrays with large numbers of elements.