The information content of multiple receive aperture SAR systems

For SAR to perform correctly, the number of unique measurements obtained by the radar (i.e., the rank of the received signal´s covariance matrix) must be greater than the number of pixels illuminated. For a single aperture SAR, the coherent processing interval (CPI) and bandwidth determine the number of independent measurements collected; therefore, the received time-bandwidth product limits the maximum unambiguous illumination area, or swathwidth. For a multiple aperture SAR (MSAR), however, the rank of the received signal is not as easy to determine. When the array is large, its beamwidth determines resolution rather than the radar´s bandwidth and CPI length. Furthermore, redundant lags in the space-time-frequency co-array reduce the amount of unique information collected. This paper generalizes the theory behind determining the rank of a signal received from stationary targets. Resolution is determined by all radar parameters including CPI length, bandwidth, and array extent. The co-array concept for antenna arrays, which is a measure of the lags sampled in the array´s spatial covariance matrix, is extended and applied. A hybrid coarray is derived that indicates lags sampled in the hybrid spacetime-frequency space. The hybrid co-array is then applied to signals received by MSAR to show that the number of unique lags in the hybrid co-array limits the number of unique samples collected. The results provide important analysis tools for MSAR systems that are likely in the future, especially sparse, constellation-flying satellite systems