Compressive Sensing with Directly Recoverable Optimal Basis and Applications in Spectrum Sensing

We describe a method of integrating KarhunenLoève 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.