Application of Compressive Sensing to Atmospheric Observations with Imaging Radar

For conventional weather radar, the field of reflectivity and radial velocity are obtained by physically steering a pencil beam through the region of interest either mechanically with a dish antenna or electronically with a phased array antenna. As a result, the scan time is determined by the product of the number of beam positions and dwell time. On the other hand, an imaging radar can provide ultra-high temporal resolution using digital beam forming (DBF) technique, in which multiple receiving beams are formed simultaneously within the field of view (FOV) by exploiting the phase differences of signals from a number of spatially separated arrays of antennas. The FOV is defined by the transmitted beam width, which is typically wide enough to cover the region of interest. In other words, no physical beam-steering is needed for imaging radar. All the beams are formed in the digital domain after signals received from multiple antenna arrays. Therefore, the scan time is significantly reduced because it is only determined by the dwell time. Imaging radar also has the advantage of adaptive spatial clutter filtering, flexible update time at different beam positions and ranges, etc.

In this work, an emerging technology of compressive sensing (CS) is applied to imaging radar to measure the field of reflectivity within the FOV. CS was developed to recover a sparse signal or an image with much fewer measurements than those normally required. CS has been applied to many fields such as medical imaging, radar waveforms, etc. The imaging radar observation is first formulated as the retrieval of reflectivity field within FOV using signals from multiple receivers. Subsequently, CS is proposed to solve the underdetermined inverse problem. It has been shown theoretically that CS can provide optimal solution for an underdetermined inverse problem when the conditions of sparsity and incoherence are satisfied. The application of CS to weather observation is demonstrated using simulation, in which the radar configuration is based on the Atmospheric Imaging Radar (AIR) developed in the Advanced Radar Research Center (ARRC) of the University of Oklahoma. AIR transmits a fan beam width 20 degree in elevation and one degree in azimuth and consists of 36 spatially separated receivers. In other words, RHI scan can be obtained in ultra-high temporal resolution. In simulation, a number of model reflectivity fields is generated to statistically evaluate the performance of CS for various amounts of measurement errors and different receiver configuration. The performance of CS is further compared to the conventional DBF using Fourier and Capon methods. Our preliminary results have shown that CS can provide relatively robust and high quality estimates of reflectivity field for most cases.