Theory and Evaluation of Gain Patterns of Synthetic Arrays

The results of an analysis of synthetic array gain patterns, including sidelobe response, are summarized. Both focused and unfocused arrays are examined. The phase time history of echos from reflectors on the ground as a function of position is used to modify the equations for the broadside synthetic array for application to forward-looking antenna arrays. The dependence of the ``optimal´´ length and resolution of an unfocused array on the look angle is derived. The gain patterns of unfocused synthetic arrays are presented for arrays of various lengths with both rectangular and exponential amplitude weighting. Calculations are made showing that the physical antenna gain pattern acts as amplitude weighting with resultant sidelobe suppression and illustrating that the final gain pattern cannot be expressed as the product of the space factor of the array times the real antenna gain pattern. However, unless the length of the synthetic array is about equal to or greater than the real antenna beamwidth times the range, the product approximation error is negligible in the region near the main lobe and amounts to a reduction in gain. The results of this analysis are then put in the form of design curves from which such parameters as the maximum resolution of an unfocused array and the length of array necessary for a given resolution at a given frequency can be obtained.