In this work, a novel theoretical framework is presented for using recent advances in frequency diversity arrays (FDAs). Unlike a conventional array, the FDA simultaneously transmits a unique frequency from each element in the array. As a result, special time and space properties of the radiation pattern are exploited to improve cross-range resolution. The idealized FDA radiation pattern is compared with and validated against a full-wave electromagnetic solver, and it is shown that the conventional array is a special case of the FDA. A new signal model, based on the FDA, is used to simulate SAR imagery of ideal point mass targets and the new model is used to derive the impulse response function of the SAR system, which is rarely achievable with other analytic methods. This work also presents an innovative solution for using the convolution back-projection algorithm, the gold standard in SAR image processing, and is a significant advantage of the proposed FDA model. The new FDA model and novel SAR system concept of operation are shown to reduce collection time by 33 percent while achieving a 4.5 dB improvement in cross-range resolution as compared to traditional imaging systems
