Frequency estimation of multiple sinusoids with three sub-Nyquist channels

Huang, Shongming; Zhang, Haijian; Sun, Hui; Yu, Lei; Chen, Liwen

doi:10.1016/j.sigpro.2017.04.013

Cited by 26 publications

(10 citation statements)

References 31 publications

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“…the range of f), the value of K' and K'' can be determined to solve f. This approach can be extended to multiple input signals and interpolation between FFT bins can be used to improve frequency estimation accuracy [20][21]. It should be pointed out that to avoid possible ambiguity when determining signal frequencies more sampling rates might be used and it has been shown that three ADC with different sampling rates are sufficient [9][10]. In this study, as the main purpose is to demonstrate the capability of a sub-Nyquist linear array, for simplicity, only two sampling rates are used in simulation.…”

Section: A Sub-nyquist Methods Using Adc With Different Sampling Ratesmentioning

confidence: 99%

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A Sub-Nyquist Uniform Linear Array Receiver Design

Cheng

2021

IEEE Access

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A design of sub-Nyquist uniform linear array receiver with different sampling rates is proposed, investigated, and reported in this paper. The proposed architecture increases functionality of conventional linear array receiver with modest modifications. Simulation results show that the proposed receiver is capable of determining angle of arrival (AOA) and signal frequencies of multiple continuouswave/chirp signals over several Nyquist zones.

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Section: A Sub-nyquist Methods Using Adc With Different Sampling Ratesmentioning

confidence: 99%

“…It has also been shown that a wideband receiver using multiple ADC with different sampling rates can cover several Nyquist zones [6][7][8][9][10]. Such a method is usually classified as a sub-Nyquist method.…”

Section: Introductionmentioning

confidence: 99%

A Sub-Nyquist Uniform Linear Array Receiver Design

Cheng

2021

IEEE Access

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“…Table 4 compares the computation complexity between the frequency-band division algorithm and robust CRT and closed-form CRT. rough careful analysis (17), (18), and (28) in [16], we find that the robust CRT method needs to calculate 4Γ 3…”

Section: Performance Comparison Between Frequency-bandmentioning

confidence: 99%

“…K is the number of channels) folding into the first Nyquist region and solve the frequency ambiguity in a short time. Usually, a fast Fourier transform (FFT) [16,17] algorithm is used to analyse the frequency to obtain high accuracy. However, the FFT algorithm has obvious shortcomings in processing time.…”

Section: Introductionmentioning

confidence: 99%

Digital Instantaneous Frequency Measurement of a Real Sinusoid Based on Three Sub-Nyquist Sampling Channels

Jiang

2020

Mathematical Problems in Engineering

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Multichannel sub-Nyquist sampling is an efficient technique to break through the limitation of the Nyquist sampling theorem for the wideband digital instantaneous frequency measurement (DIFM) receiver. The significant challenge is calculating the folding frequency and solving the ambiguity quickly and accurately. Usually, the researchers adopt a fast Fourier transform (FFT) to calculate the folding frequency and a Chinese remainder theorem (CRT) to solve the ambiguity caused by undersampling. However, these algorithms have the drawback of long response time. In this paper, we use a frequency deduction algorithm based on the total least-squares estimation to measure the folding frequency accurately within a few clocks. We propose a frequency-band division algorithm by dividing the measurable frequency range into a few sub-bands to solve the frequency ambiguity. This deblurring algorithm is more efficient and faster than CRT. We analyse the performance of our algorithms by numerical simulations and functional hardware simulations and compare them with FFT and CRT. We also conduct experiments on a hardware platform to confirm the effectiveness of our algorithms. The simulation results show that our algorithms have better performance than FFT and CRT in accuracy and response time. Board-level measurement results verify that the proposed DIFM technique can capture the frequency from 0 to 5,000 MHz with a maximum of 0.8 MHz root-mean-squared error in less than 200 ns.

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“…On the other side, their disadvantage is that they require the number of sinusoids to be known in advance, restricting their use in more general cases. One recent contribution that uses the MUSIC-based approach on the undersampled data is proposed in [15]. A numerical implementation of the ML estimator has been proposed in [16].…”

Section: Introductionmentioning

confidence: 99%

Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids

Djukanović

Popovic-Bugarin

2019

IEEE Access

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The method for detection of complex sinusoids in additive white Gaussian noise and estimation of their frequencies is proposed. It contains two stages: 1) sinusoid detection (model order estimation) and coarse frequency estimation, and 2) fine frequency estimation. The proposed method operates in the frequency domain, i.e., it uses the discrete Fourier transform (DFT) as the main tool. Sinusoid detection is performed so that a fixed probability of false alarm is provided (Neymann-Pearson criterion). For both coarse and fine frequency estimations, the three-point periodogram maximization approach is used. Simulations are carried out for variable signal-to-noise ratio, variable frequency displacement between the sinusoids and variable offset from the frequency grid. The proposed method meets the Cramér-Rao lower bound in frequency estimation and practically does not depend on the frequency displacement except for very small displacement values. In terms of model order estimation accuracy, it outperforms the state-of-the-art approaches. The most expensive operation in the method is the calculation of the DFT. Therefore, in terms of calculation complexity, the proposed method is on par with the most efficient algorithms for multiple frequency estimations. INDEX TERMS Cramér-Rao lower bound, discrete Fourier transform, model order estimation, multiple frequency estimation, Neymann-Pearson criterion.

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Frequency estimation of multiple sinusoids with three sub-Nyquist channels

Cited by 26 publications

References 31 publications

A Sub-Nyquist Uniform Linear Array Receiver Design

A Sub-Nyquist Uniform Linear Array Receiver Design

Digital Instantaneous Frequency Measurement of a Real Sinusoid Based on Three Sub-Nyquist Sampling Channels

Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids

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