Abstract: Based on the theory of sensing matrix optimization and the characteristics of step frequency waveform, this paper proposes a sensing matrix optimization method for sparse random step frequency signal based on autocorrelation function. Firstly, on the basis of constructing sparse reconstruction model, the internal relationship between the waveform parameters of sparse random step frequency signal and the construction mode of sensing matrix is given. Secondly, the relationship between the mutual coherence matrix and the autocorrelation function matrix of signal is analyzed, and the conclusion that under specific conditions, these two matrices are the same. Therefore, the optimal design of sensing matrix is transformed into the optimal design of sparse random stepped frequency signal based on autocorrelation function. Finally, a sparse waveform design method based on the joint constraint of the maximum and average sidelobes of the autocorrelation function is proposed. Simulation experiments verify the relationship between the mutual coherence matrix and the autocorrelation function matrix of signal, and through waveform design, the sensing matrix optimization and the improving performance of signal sparse recovery are realized.