Method for Estimating the Symbol Period of PSK Signals with Low Sampling Rate

Rectangular pulse-shaped phase shift keying （PSK） signals have poor spectral convergence and the existing symbol period estimation methods rely on high sampling rates. To solve these problems， this study investigated the symbol period estimation methods for signals at low sampling rates， with the aim of overcoming the limitation of high oversampling rates and achieving accurate and efficient symbol period estimation at low sampling rates. To this end， a mathematical model and receiving sampling model of rectangular pulse-shaped PSK signals were constructed and it was proven that after passing through an anti-aliasing low-pass filter， the envelope spectra of such signals exhibited significant discrete spectral lines at integer multiples of the symbol rate. Through mathematical derivation and spectral line amplitude analysis， it was found that when the central frequency of the received signal was approximately equal to half of the bandwidth of the anti-aliasing filter， the amplitude of the spectral line at the symbol rate in the envelope spectrum must be greater than that at its integer multiples. Based on this core finding， two symbol period estimation methods at low sampling rates were proposed in this study. The first was the “partial spectrum zeroing method” without local oscillator retuning， in which a signal meeting the spectral line amplitude condition was constructed by estimating the central frequency of the signal and zeroing the single-side spectrum， thus reducing the lower limit of the sampling rate to twice the symbol rate， that is， at least two discrete sampling points were required per symbol period. The second was the “local oscillator tuning method” combined with local oscillator retuning， which further reduced the lower limit of the sampling rate to the symbol rate through two rounds of signal receiving and sampling， that is， only one discrete sampling point was needed per symbol period. To verify the effectiveness of the proposed methods， a series of simulation experiments was designed with the binary and quadrature PSK signals as the research objects， the probability of the central frequency estimation error and the estimation accuracy in different central frequency ranges were analyzed， and their performance was compared with the existing methods such as the cyclic spectrum and wavelet methods. The simulation results showed that the rough estimation of the central frequency using the power spectrum could meet the estimation error tolerance requirement with a high probability， the estimation performance of the two proposed methods improved with the increase in the number of symbols involved in the estimation， and their estimation accuracy was significantly better than that of the existing methods under the condition of low sampling rates. The proposed methods provide an effective solution for the symbol period estimation of rectangular pulse-shaped PSK signals at low sampling rates and make up for the limitations of the traditional estimation methods in low-sampling-rate scenarios.