Utilizing periodic phase modulation (PPM) can shift the echo spectrum, affecting matched filtering (MF) processing, leading to time delay shift or amplitude attenuation. The prior works on the impact of PPM on MF mainly consider an ideal phase modulation model, where the phase shift is considered to be sufficient. In practical applications, the phase shift capability achieved by physical devices for phase modulation is often insufficient due to factors such as hardware limitations, operating bandwidth, and cost constraints. To address this limitation, this paper investigates the quantitative impact of PPM on the MF under conditions of insufficient phase shift. Firstly, reflection coefficient models for PPM under insufficient phase shifts are established, considering 1-bit and 2-bit conditions. Furthermore, for commonly used radar waveforms such as linear frequency modulation (LFM) and phase-coded modulation (PCM), expressions for MF output results under different bit rates are derived, and a quantitative analysis of the time delay and amplitude attenuation compared with the unmodulated case is conducted. Finally, the correctness of the proposed theoretical model is validated through simulation and measured experiments.

In this paper, we address the online state estimation problem of linear discrete-time systems in the presence of inaccurate and slowly time-varying non-Gaussian measurement noise (NGMN). Recently, the variational Bayesian (VB) method has been successfully used to jointly estimate the system state along with the statistics of the unknown Gaussian measurement noise. However, we prove that the original VB method for the non-Gaussian state-space models, modeled by the Gaussian mixture distributions, is analytically intractable. To overcome this problem, we propose a partial variational Bayesian based adaptive Gaussian sum Kalman filter (PVB-GSKF), which uses a feedback-based filtering framework to calculate the posterior distribution of the state and posterior distribution of the NGMN in an independent way. Experimental results demonstrate the effectiveness of the proposed filter.

Metasurfaces can alter radar echo characteristics by dynamically modulating the phase of incident electromagnetic waves, thereby degrading radar signal processing performance. Recovering the time-varying phase modulation signal of metasurfaces from radar echoes is crucial for understanding modulation patterns or suppressing modulation effects. To address this problem, we introduce an optimization-based deconvolution approach in this paper. Firstly, an optimization model for recovering phase modulation signals from metasurfaces is established by combining the least squares deconvolution principle, total variation of the modulating signal, and imaginary part constraint. Furthermore, a composite optimization approach (COA) to solve the deconvolution optimization problem is developed, in which the alternating minimization and alternating direction method of multipliers (ADMM) frameworks are integrated to estimate the complex propagation loss and the modulation phase sequence. In addition, the convergence and computational complexity analysis of the proposed COA is conducted. Finally, the effectiveness of the proposed method is validated through simulation and measured experiments.