低采样率下相移键控信号符号周期估计方法

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

  • 摘要: 针对矩形脉冲成型相移键控(Phase Shift Keying,PSK)信号频谱收敛性差,现有符号周期估计方法依赖高采样率的问题,开展低采样率下该类信号的符号周期估计方法研究,旨在突破高过采样率限制,实现低采样率下精准高效的符号周期估计。先构建矩形脉冲成型PSK信号的数学模型与接收采样模型,推导证明该类信号经抗混叠低通滤波器后,包络谱会在符号率整数倍处呈现显著离散谱线。进一步经数学推导与谱线幅度分析发现,当接收信号中心频率近似等于抗混叠滤波器带宽的一半时,包络谱中符号率处的谱线幅度必然大于其整数倍处的谱线幅度。基于这一核心发现,本文提出两种低采样率符号周期估计方法:一是无需本振重调的“部分谱置零法”,通过估计信号中心频率并对单侧频谱置零,构造满足谱线幅度条件的信号,使采样率下限降至符号率的2倍,即每个符号周期至少需2个离散采样点;二是结合本振重调的“本振调谐法”,通过两轮信号接收与采样,将采样率下限进一步降至符号率的1倍,即每个符号周期仅需1个离散采样点。为验证方法有效性,本文以二进制相移键控(Binary Phase Shift Keying,BPSK)、正交相移键控(Quadrature Phase Shift Keying,QPSK)信号为对象设计多组仿真实验,分析中心频率估计误差概率、不同中心频率范围的估计精度,并与循环谱法、小波法等现有方法进行性能对比。仿真结果表明,功率谱粗估计中心频率可高概率满足估计误差容忍要求,所提两种方法的估计性能均随参与估计符号数的增加而提升,且在低采样率条件下,其估计精度显著优于现有方法。

     

    Abstract: 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.

     

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