The ambiguity range of the traditional stepped-frequency waveform is decided by the frequency step

which result in range aliasing. To solve the above problem

a compressive sensing-based anti-range aliasing method for random sparse chirp frequency-stepped (RSCFS) signal is proposed. In the method

the sub pluses are dechirped firstly. Then the echoes are treated as the measurement data of the equivalent bandwidth LFM signal. Secondly

the corresponding measurement matrix is constructed according to the random transmission mode of the sub pulses

and then the compressed sensing reconstruction model of the RSCFS signal is built. At the same time

the high resolution range profile can be obtained by the compressed sensing reconstruction algorithm. At last

the ambiguity range of the proposed method is analyzed

and the factors that influence the size of the ambiguity range and the parameter setting criteria are given. In this method

the range profile synthesis process of the RSCFS signal is regarded as the process of the equivalent bandwidth LFM signal. It can not only reduce the restriction of the carrier frequency step to ambiguity range

effectively overcome the range aliasing problem

but also improve the range profile synthetic performance. Simulation results show the effectiveness of the proposed method.