Theoretical Analysis of Random Phase Modulation Effects on Radar Pulse Compression by the Time-Modulated Metasurface

Metasurfaces can degrade radar pulse compression (PC) performance by encoding radar echoes with time-domain random phase modulation (RPM), which alters the correlation between the echo signal and the reference signal. Analyzing the quantitative impact of metasurface RPM on radar PC is crucial for designing encoding strategies and modulation suppression. However, due to the random nature of encoding, quantitatively analyzing its impact on radar PC is challenging. To address this problem, a quantitative analysis of the impact of RPM on radar PC performance from a statistical perspective is conducted in this work. First, from the frequency-domain analysis, a theoretical model of the average energy spectrum (AES) under RPM is introduced. This model determines the extent of the time-domain spread during PC and quantifies the reduction in PC energy compared with an unmodulated case. Second, from the time-domain analysis, a mapping relationship between the PC output amplitude and the RPM is established. It is found that the statistical properties of the modulus of the sum of the modulation sequence determine the magnitude of the matched filter output. On this basis, the analytical expressions for the average amplitude loss ratio (ALR) for PC output of the target for both 1-bit and 2-bit RPM cases are derived. In addition, we further consider the potential existence of insufficient phase shift conditions in practical time modulation metasurface (TMM) applications and analyze their quantitative impact on AES and ALR. Finally, the effectiveness of the proposed models is validated through simulation and measured experiments.