Gwon, YoungjuneKung, H.Vlah, Dario2016-01-212011Gwon, Youngjune, H. T. Kung, and Dario Vlah. 2011. Compressive Sensing with Directly Recoverable Optimal Basis and Applications in Spectrum Sensing. Harvard Computer Science Technical Group TR-08-11.http://nrs.harvard.edu/urn-3:HUL.InstRepos:24829617We describe a method of integrating Karhunen-Loeve Transform (KLT) into compressive sensing, which can as a result leverage KLT’s optimality in revealing the sparsity of a signal. We present two complementary results: (1) by using the KLT to find the optimal basis for decoding we can drastically reduce the number of measurements for compressive sensing used in applications such as spectrum sensing; (2) by using compressive sensing we can compute the KLT basis directly from measurements of the input signal, with substantially fewer samples than the Nyquist rate. For a non-stationary signal, we suggest strategies in addressing the trade-off of incurring additional measurements for updating a KLT basis or compensating an obsolete KLT basis in signal recovery. We validate our results with field experiments to detect multiple radio transmitters and sense the UHF spectrums using software-defined radios.en-USResearch Paper or Report2016-01-21