Frequency Estimation For Undersampled Signals In Low SNR Circumstances

Signal frequency estimation is an important problem in the field of radar,communication,earthquake monitoring and sensor network.However,Nyquist's law requires to sample at least two sampling points in one sampling period.For the high-frequency signal measurements,it requires a very high sampling rate,so the hardware cost is high.In addition,in low SNR circumstances,the difficulty of estimating the undersampled frequency is further increased.In order to solve the problem,this paper proposes four measures,such as Chinese remainder theorem(CRT),frequency offset recognition,remainder selection and spectrum correction.1)Chinese remainder theorem: Decomposed the single-frequency estimation into a number of undersampled signals,and take the frequency estimation results of each channel as remainders and the sampling rates as moduli.Then substituted the remainders and moduli into the framework of closed robust CRT to reconstruct the signal frequency.2)Frequency offset recognition: In view of the fact that the DFT spectrum peak is easy to be submerged by noise interference in low SNR circumstances,this paper proposes to use frequency shift and frequency offset recognition to make the DFT spectral peak value more prominent,so as to reduce the error of remainder acquiring and improve the anti-noise robustness of the algorithm.3)Remainder selection: For the remainders obtained by the frequency offset recognition and spectrum correction,the algorithm adopts the remainder error correcting and selection method to eliminate the remainder of excessive error.Thus the robustness of the undersampled frequency estimator to noise is further improved.4)Spectrum correction: Compared to the original frequency corrector,the paper proposed the method of frequency shift compensation to improve the performance of the all-phase time-shift phase difference frequency estimator,which reduced the threshold of all undersampled channels.Then the frequency estimator based on Tsui frequency correction is used to compare the performance with all-phase frequency estimator.After comparing the two methods,they have the almost same RMSE property in low SNR circumstances.However,in the case of reconstructed threshold,the reconstruction threshold of the frequency estimator based on Tsui frequency correction is lower.The simulation results show that when reconstruction probability is up to 90%,the SNR threshold can be as low as-15 dB when the DFT points are 512.It can be applied as reference to radar,sonar and other related detection fields.