Synthetic Aperture Processing with Limited Storage and Presumming

The number of transmitted pulses associated with the Doppler histories of a side-looking radar may greatly exceed the desired azimuth compression ratio of the system. This discrepancy is taxing if the storage required for the azimuth processing is provided by cores, magnetic drums, and the like. Thus, as a practical matter, one considers presumming of the data prior to correlation in an attempt to achieve the desired performance with a minimum amount of digital storage. In this paper, the optimum (in terms of resolution) presummer is derived, along with the optimum apportionment of the available storage capacity between the presumming and correlation operations. Under the condition (or generally pessimistic approximation) that the illumination pattern of the antenna uniformly illuminates a Doppler bandwidth equal to the PRF of the radar, the optimum presumming coefficients are the first Np Fourier coefficients of a function which is one of the Doppler bandwidth to be correlated and zero on the remainder of the PRF bandwidth, where Np is the number of transmitted radar pulses over which presumming is provided. Increasing Np reduces the degradation due to presumming, but may leave inadequate storage for correlation. Hence, we optimize the apportionment between the two operations and present the obtainable resolution as a function of total storage and the number of transmitted pulses in the received Doppler history.