Abstract: ‍ ‍To address the challenge of estimating key parameters of a root-raised cosine pulse-shaped Binary Phase Shift Keying （BPSK） signal in non-cooperative communication， the signal is innovatively modeled as a periodic modulation signal. A necessary analysis of the singular value decomposition results of the segmented observation matrix for the periodic modulation signal was conducted， clarifying the structural characteristics of singular value decomposition in both mono-component and multi-component cases. Based on this analysis and leveraging the characteristics of the signal itself， new methods were proposed for estimating key parameters such as symbol rate， carrier frequency， roll-off coefficient， and delay. First， by analyzing the power spectrum and its histogram of the received signal and utilizing the constant noise power spectrum， a rough estimation of the symbol rate and carrier frequency of the signal was achieved. Based on this， the Chirp-Z transform spectrum of the squared signal was analyzed to obtain a more precise carrier frequency estimate. A novel approach was introduced to obtain the normalized waveform of the root-raised cosine pulse by utilizing the power spectrum of the signal， effectively eliminating the influence of the carrier frequency on the estimation of the roll-off coefficient estimation. Second， an analysis of the envelope spectrum revealed distinct spectral lines at integer multiples of the symbol rate， enabling an accurate estimate of the symbol period. Waveform similarity measurement indicators combined with the estimation of the normalized waveform of the root-raised cosine pulse were introduced to estimate the roll-off coefficient for the first time. Finally， based on the periodic modulation signal model， a dynamic delay-segmented observation matrix was designed to analyze the segmentation of the basic waveform of the root-raised cosine pulse under different delay conditions. The proposed improved singular value ratio spectrum was then employed to achieve an accurate estimation of the signal reception delay. Simulation results demonstrate that the proposed method achieves high estimation accuracy.