Method for Estimating the Key Parameters of Phase-Coded Signals With Low Sampling Rate Based on Wavelet Analysis and Periodic Annihilating Filtering

To achieve the estimation of key parameters of phase-coded signals under low sampling rate conditions, a detailed derivation and analysis of the signal after anti-aliasing filtering were conducted. The analysis shows that when the signal is subjected to a certain frequency offset and analyzed using a fixed-scale Haar wavelet transform, the integral value reaches a local minimum when the frequency offset is equal to the carrier frequency. Moreover, the envelope spectrum of the signal exhibits a strong discrete spectral line at the frequency corresponding to the symbol rate, which enables the estimation of the carrier frequency and symbol period. When estimating the signal reception delay, considering the periodic modulation characteristics of the signal, the symbol period was incorporated into the Finite Rate of Innovation (FRI) sampling theory. An improved periodic annihilating filtering method was proposed. This method transforms the estimation of individual unknown pulse positions in the annihilating filter into the estimation of the common delay of periodic pulses, thereby significantly enhancing the estimation accuracy. Additionally, the symbol period is utilized to denoise the signal through singular value decomposition, thus completing the delay estimation. Simulation experiments have demonstrated the effectiveness of the proposed method.