Sparse Recovery of Intermittent Frequency Hopping Signals Aided by DOA

Radio frequency sources with frequency hopping (FH) are observed at a fusion center via sensor measurements made over additive white Gaussian noise channels. The number of sources may be larger than the number of sensors, but their activity is sparse and intermittent with bursty transmission patterns accounted for by hidden Markov models. Blind source estimation of intermittent FH signals is solved via a proposed algorithm, consisting of a direction of arrival (DOA) estimation step, an FH estimation step, and a pairing step. The DOA estimation step is achieved by merging the FH effect and the complex amplitude of the signal, and FH estimation step is completed by estimating likewise by merging the DOA effect and the complex amplitude of the signal. After DOA and FH are estimated, a crucial procedure of pairing is operated by picking a pair of estimated DOA and estimated FH patterns that provides the best fit to the data at each time sample over all possible pairs. To this end, a smooth least absolute shrinkage and selection operator (LASSO) algorithm is integrated with DOA and FH estimation steps, while a standard LASSO algorithm is utilized for pairing step. It is shown that the proposed algorithm can separate FH signals with high accuracy and the pairing step can effectively eliminate false alarms during previous DOA and FH estimation steps.