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.