Robust and Efficient Frequency Estimator for Undersampled Waveforms Based on Frequency Offset Recognition.

Xiangdong Huang,Xukang Jin,Haipeng Fu,Ruipeng Bai,Xiaofeng Wang

doi:10.1371/journal.pone.0163871

Abstract

This paper proposes an efficient frequency estimator based on Chinese Remainder Theorem for undersampled waveforms. Due to the emphasis on frequency offset recognition (i.e., frequency shift and compensation) of small-point DFT remainders, compared to estimators using large-point DFT remainders, it can achieve higher noise robustness in low signal-to-noise ratio (SNR) cases and higher accuracy in high SNR cases. Numerical results show that, by incorporating a remainder screening method and the Tsui spectrum corrector, the proposed estimator not only lowers the SNR threshold of detection, but also provides a higher accuracy than the large-point DFT estimator when the DFT size decreases to 1/90 of the latter case.

Highlights

IntroductionFrequency estimation of undersampled waveforms is widely encountered in radar detection [1] and distance estimation [2] etc
This paper proposes an efficient frequency estimator based on Chinese Remainder Theorem for undersampled waveforms
Frequency estimation of undersampled waveforms is widely encountered in radar detection [1] and distance estimation [2] etc

Summary

Introduction

Frequency estimation of undersampled waveforms is widely encountered in radar detection [1] and distance estimation [2] etc. For the CRT-based frequency estimators [3,4,5,6], the remainders are directly acquired from DFT peak bins of multiple channels, which means that the estimation accuracy heavily relies on the DFT frequency resolution. Small-point DFT brings a coarse frequency resolution and degrades the accuracy To overcome these two difficulties, this paper proposes a scheme based on frequency offset recognition, which was ignored by the existed estimators [4,5,6]. In low SNR cases, for any individual undersampled waveform, we use a performance index to recognize the value range of the frequency offset and implement frequency-shift operation to highlight the peak DFT bin buried in noise.

Procedure of the Proposed Estimator

G G1Gi mod

Numerical Results

Conclusions