Aliasing-free micro-Doppler analysis based on short-time compressed sensing

Time-frequency distribution (TFD) has been widely used for micro-Doppler analysis in radar signal processing. However, the spectrogram will suffer from aliasing if the maximum Doppler frequency exceeds half of the pulse repetition frequency, which may lead to false estimation of the targets' kinematic properties. In this study, by transmitting a series of random pulse repetition interval (RPRI) pulses, a concise TFD approach named short-time compressed sensing (STCS) is proposed for aliasing-free micro-Doppler analysis. In STCS, precise analysis and synthesis of the random sampling time series can be achieved by exploiting the signal's sparsity in the frequency domain. Furthermore, adaptive to the data, the widths of the particular rectangle windows are determined by sequential processing with a proper optimisation rule. To speed up the STCS procedure, the smoothed L0 algorithm is chosen for sparse recovery, where the pseudoinverse of the dictionaries can be calculated iteratively. The simulation results indicate that the proposed STCS approach can achieve both preferable TFD and acceptable computational cost. The effectiveness of the STCS is finally verified by the application for micro-Doppler estimating in RPRI radar.