The Equivalence Among Three Approaches to Deriving Synthetic Array Patterns and Analyzing Processing Techniques

The equivalence of the vector addition, cross-correlation, and filtering approaches to deriving synthetic array patterns and analyzing processing techniques is demonstrated here. A mathematical model is defined which establishes a geometry, a transmitted and received signal, and a general synthetic array weighting function. A preliminary analysis of this model derives the signals received at the flight-path points where radar pulse transmission and reception occurred, and the effects at these flight-path points of the synthetic array weighting function. The weighted, received signal expression is then summed over the array, and the resultant shown to be a vector addition, a cross-correlation integral, or a filtering operation depending on the changes of variable and formal manipulations employed.