We present compressed statistical testing (CST) with an illustrative application to radar target detection. We characterize an optimality condition for a compressed domain test to yield the same result as the corresponding test in the uncompressed domain. We demonstrate by simulation that under high SNR, a likelihood ratio test with compressed samples at 3.3x or even higher compression ratio can achieve detection performance comparable to that with uncompressed data. For example, our compressed domain Sample Matrix Inversion test for radar target detection can achieve constant false alarm rate (CFAR) performance similar to the corresponding test in the raw data domain. By exploiting signal sparsity in the target and interference returns, compressive sensing based CST can incur a much lower processing cost in statistical training and decision making, and can therefore enable a variety of distributed applications such as target detection on resource limited mobile devices.Engineering and Applied Science
