Towards the use of learned dictionaries and compressive sensing in wideband signal detection

Detection and estimation of wideband radio frequency signals are major functions of persistent surveillance systems and rely heavily on high sampling rates dictated by the Nyquist-Shannon sampling theorem. In this paper we address the problem of detecting wideband signals in the presence of AWGN and interference with a fraction of the measurements produced by traditional sampling protocols. Our approach uses learned dictionaries in order to work with less restriction on the class of signals to be analyzed and Compressive Sensing (CS) to reduce the number of samples required to process said signals. We apply the K-SVD technique to design a dictionary, reconstruct using a recently developed signal-centric reconstruction algorithm (SSCoSaMP), then use maximum likelihood estimation to detect and estimate the carrier frequencies of wideband RF signals while assuming no prior knowledge of the frequency location. This solution relaxes the assumption that signals are sparse in a fixed/predetermined orthonormal basis and reduces the number of measurements required to detect wideband signals all while having comparable error performance to traditional detection schemes. Simulations of frequency hopping signals corrupted by additive noise and chirp interference are presented. Other experimental results are included to illustrate the flexibility of learned dictionaries whereby the roles of the chirps and the sinusoids are reversed.