An algorithm using compressive sensing to blindly detect frequency hopping signals corrupted by white Gaussian noise is presented. The samples obtained through compressive sensing effectively maintain structures and information of the original signal, so detection tasks of the original signal could be solved by directly processing the sampling values. The algorithm is based on the difference in numerical characteristics of sampling values. According to the different characteristics of the expectation of sampling values under different hypothesis, detection is accomplished by using the deviation of the actual sampling values from the expectations under corresponding hypothesis as criterion. Without reconstructing the frequency hopping signal itself, hopping frequencies can be estimated with a tiny number of measurements by compressive sensing algorithm. Simulation results have proved that the proposed algorithm is adequate to the environments in which signal-to-noise ratio is higher than −6dB. Meanwhie, compared with other traditional algorithms, the proposed algorithm greatly reduces the amount of data and complexity, and significantly reduced the detection time.
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