Gwon, YoungjuneKung, H.Vlah, Dario2012-12-062012Gwon, Youngjune, H.T. Kung, and Dario Vlah. 2012. Compressive sensing with optimal sparsifying basis and applications in spectrum sensing. Paper presented at IEEE 2012 Global Telecommunications Conference (GLOBECOM 2012), Annaheim, CA, December 3-7, 2012.http://nrs.harvard.edu/urn-3:HUL.InstRepos:10000991We describe a method of integrating Karhunen-Loève Transform (KLT) into compressive sensing, which can as a result improve the compression ratio without affecting the accuracy of decoding. We present two complementary results: 1) by using KLT to find an optimal basis for decoding we can drastically reduce the number of measurements for compressive sensing used in applications such as radio spectrum analysis; 2) by using compressive sensing we can estimate and recover the KLT basis from compressive measurements of an input signal. In particular, we propose CS-KLT, an online estimation algorithm to cope with nonstationarity of wireless channels in reality. We validate our results with empirical data collected from a wideband UHF spectrum and eld experiments to detect multiple radio transmitters, using software-defined radios.en-USConference Paper2012-12-0610.1109/GLOCOM.2012.6503977