cs.SDSep 7, 2026

Frequency Estimation Based on SNR-adaptive Frequency Estimator Under Wide SNR Range

Authors: Hee-Yang Jung, Dong-Hee Paek, Woo-Jin Jung, Seung-Hyun Kong

Organizations: Graduate School of CCS Mobility, Korea Advanced Institute of Science and Technology, Daejeon 34051, South Korea · Department of Future Mobility, Korea University, Sejong 30019, Republic of Korea

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Abstract

Frequency estimation is the problem of estimating individual tone frequencies from noisy multi-tone sinusoidal signals. Existing frequency estimation methods have difficulty accurately estimating both the number of tone frequencies and the individual tone frequencies in low signal-to-noise ratio (SNR) environments, because weak tone frequency components are buried in noise. In addition, existing methods generally exhibit a trade-off between robustness at low SNR and frequency estimation precision at high SNR, making it difficult to achieve consistently superior frequency estimation performance over a wide SNR range. To overcome these limitations, this paper proposes an SNR-adaptive frequency estimator (SAFE). SAFE consists of a time-frequency image neural network (TFINet), which enhances weak tone frequency components at low SNR, and an SNR-based frequency selector (SFS), which selects an appropriate frequency estimator according to the SNR of the estimated tone frequencies. TFINet enhances tone frequency components even in the low-SNR range, while SFS estimates the SNR of each tone frequency and selects either a robust frequency estimator or a super-resolution frequency estimator according to the estimated SNR. This enables SAFE to achieve robustness at low SNR while preserving high precision at high SNR. Simulation results show that SAFE achieves an False Negative Rate (FNR) of 13.00% over the SNR range from -10 dB to 0 dB, corresponding to an 13.04% improvement over the state-of-the-art method. In addition, SAFE reduces the Nearest Neighbor-Root Mean Squared Error (NN-RMSE) by 56.67% compared with the state-of-the-art method, demonstrating that SAFE performs more accurate frequency estimation. Furthermore, experiments using real-world data demonstrate that SAFE provides robust frequency estimation performance even in practical environments with clutter.

Figures & tables

Fig. 1 : Overview of SAFE. SAFE takes a one-dimensional (1D) noisy signal as input and outputs the estimated frequency set {f^k}k=1K^\{\widehat{f}_{k}\}_{k=1}^{\widehat{K}} . TFINet generates a noise-suppressed frequency representation (FR), from which SFS detects the tone frequencies. PMCD takes the estimated number of frequencies, K^\widehat{K} , and the 1D noisy signal as inputs and outputs the frequency estimates {f^PMCD,k}k=1K^\{\widehat{f}_{\mathrm{PMCD},k}\}_{k=1}^{\widehat{K}} . In SFS, the SNR of each detected frequency is estimated, and either the frequency detected by TFINet or the corresponding estimate f^PMCD,k\widehat{f}_{\mathrm{PMCD},k} is selected.
Fig. 2 : Architecture of TFINet. TFINet takes TFIMLTS\mathbf{TFI}_{\mathrm{MLTS}} as input and outputs the noise-suppressed frequency representation FRMUL\mathbf{FR}_{\mathrm{MUL}} . In FSA, self-attention is performed along the frequency axis for each feature map FMdown(l)\mathbf{FM}_{\mathrm{down}}^{(l)} obtained from the corresponding downsampling layer.
Fig. 3 : Architecture of SFS. SFS estimates FR^SNR\widehat{\mathbf{FR}}_{SNR} , an FR representing the SNR information, from FRMUL\mathbf{FR}_{MUL} , and detects the frequency estimates {f^TFINet,k}k=1K^\{\widehat{f}_{\mathrm{TFINet},k}\}_{k=1}^{\widehat{K}} using OS-CFAR. The estimated number of detected frequencies, K^\widehat{K} , is provided to PMCD to obtain the set of super-resolution frequency estimates {f^PMCD,k}k=1K^\{\widehat{f}_{\mathrm{PMCD},k}\}_{k=1}^{\widehat{K}} . The SNR of each detected frequency is then estimated from FR^SNR\widehat{\mathbf{FR}}_{SNR} , and either f^TFINet,k\widehat{f}_{\mathrm{TFINet},k} or the corresponding f^PMCD,k\widehat{f}_{\mathrm{PMCD},k} is selected according to the estimated SNR.
Fig. 4 : FNR, FPR and NN-RMSE of the SAFE and existing methods for known KK .
Fig. 5 : FNR, FPR, and NN-RMSE of the SAFE and existing methods for unknown KK .
Fig. 6 : FNR, FPR, and NN-RMSE for each frequency-estimation method on the test dataset of real-world data.
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