Quantitative Analysis of Metasurface With Random Phase Modulation on Complex HRRP: A Statistical Perspective

Analyzing the influence of metasurface phase encoding on high-resolution range profile (HRRP) is essential for the design of modulation strategies and interference suppression. Periodic phase modulation (PPM) and random phase modulation (RPM), as the primary phase encoding methods of metasurfaces, have been extensively studied in recent years for their influence on HRRP. Compared to PPM, analyzing the influence of RPM on HRRP is challenging due to its inherent randomness. Existing research has primarily provided qualitative analyses of the influence of RPM on HRRP, without investigating the underlying quantitative relationships. In this article, the main approach is to analyze the quantitative influence of RPM on complex HRRP from a statistical perspective, examining its influence on the complex HRRP, the energy of the complex HRRP, and the autocorrelation between the energy of the complex HRRP. First, a joint probability density function (JPDF) is constructed with the real and imaginary parts of complex HRRP as random variables, and the quantitative relationship between the corresponding statistical parameters and modulation parameters is provided. Secondly, the expression for the average complex HRRP energy is derived, which quantitatively relates it to the modulation pulse signal and the number of modulation segments. Third, the expression for the autocorrelation function of the average complex HRRP energy is presented, which quantitatively relates it to the modulation pulse signal and the number of modulation segments. Finally, simulations and experiments are conducted to validate the conclusions provided.