The random step frequency signal shares the characteristics of the step frequency radar and the wideband noise radar. It not only reduces the instantaneous band-width and data sampling rate, but also has the good characteristics of the low probability of intercept, the electromagnetic compatibility and the radio-frequency immunity. The statistic characteristics of correlation output and ambiguity function like first moment，second moment, and variance were analyzed, and the radio-frequency immunity of the random step frequency signal was compared with linear stepped frequency signal in this paper. The SAR imaging algorithm based on the Correlation-Output and Range-Doppler algorithm was presented and analyzed, and the simulation result verified the validity.