Truncated Nuclear Norm Matrix Completion for Random Stepped-Frequency Waveforms in Multi-Radar Cooperative Sensing Systems

Random Stepped Frequency (RSF) waveform, known for its superior anti-interference capability, effectively mitigates mutual interference issues commonly encountered in multi-radar cooperative sensing scenarios. However, its sparse sampling pattern in the time-frequency domain results in incomplete echo signal, degrading the range-Doppler spectrum estimation quality. This paper proposes a coherent processing approach for RSF waveform echoes based on matrix completion (MC), significantly enhancing RSF waveform practical value in multi-radar sensing. The proposed method first incorporates a Hankel matrix structure to strengthen the low-rank characteristics of time-frequency data matrix. Subsequently, we utilize the MC approach that combines truncated nuclear norm regularization with an accelerated proximal gradient linear algorithm to effectively address noisy data and improve the completion performance. The efficacy of the proposed method is verified via numerical simulations and further validated with real-collected sensing data.