Effect of Periodic Phase Modulation on the Matched Filtering With Insufficient Phase-Shift Capability

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 article investigates the quantitative impact of PPM on the MF under conditions of insufficient phase shift. First, 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 modulatio and phase-coded modulation, 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.