Digital Frequency Determination of Real Waveforms Based on Multiple Sensors With Low Sampling Rates

Maroosi, Ali; Bizaki, Hossein Khaleghi

doi:10.1109/jsen.2011.2173482

Cited by 14 publications

(24 citation statements)

References 14 publications

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“…Usually, M k will not be too large as the limitation of full power bandwidth (FPBW) of ADC. In [28], the authors proposed and demonstrated a theorem that gives the relationship between the sampling rates and the maximum unambiguous frequency. e maximum unambiguous frequency determined by K channels is derived and can be expressed as…”

Section: Frequency-band Divisionmentioning

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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Section: Frequency-band Divisionmentioning

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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“…Maroosi and Bizaki proposed a searching-matching based frequency estimator [4], [5] for undersampled real-valued waveforms, in which the frequency estimate is determined by applying the the minimax-distance criterion (see [4]) to find out an optimal remainder combination among a pre-set searching space. Nevertheless, this space consists of all the direct remainders and their derived eligible remainders (i.e., plus integers times of the corresponding undersampling rate) and thus it is very large, which renders heavy searching complexity to this estimator.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, this space consists of all the direct remainders and their derived eligible remainders (i.e., plus integers times of the corresponding undersampling rate) and thus it is very large, which renders heavy searching complexity to this estimator. Moreover, as [4] pointed out, the upper bound of realizable frequency estimator of this estimator is a bit low. Besides, Huang and Zhang [6] derived a three sub-Nyquist channels based estimator.…”

Section: Introductionmentioning

confidence: 99%

“…To solve these two problems, this paper proposes an improved CRT-based estimator, which can sift the desired remainders from the DFT spectra of real-valued signals through combining spectrum correction with phase matching, rendering our estimator with the ability of dealing with real-valued sinusoidal waveforms. Due to the consideration of detecting an undersampled waveform's zero crossing point (not required by the determination algorithm addressed in [4]), the recoverable frequency can reach the same upper bound as the determination case of complex exponential waveforms.…”

Section: Introductionmentioning

confidence: 99%

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Frequency Estimator Based on Spectrum Correction and Remainder Sifting for Undersampled Real-Valued Waveforms

et al. 2019

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Frequency estimation of undersampled waveforms receives increasing attention in communication, radar signal processing, instrumentation and measurements, and so on. However, due to the lack of recognizing the correct remainder between two side spectra, the existing Chinese Remainder Theorem (CRT)-based frequency estimators can hardly deal with real-valued signals. To achieve this goal, this paper proposes an estimator combining spectrum correction (aiming to enhance reconstruction accuracy by incorporating the fractional parts of DFT remainders), closed-form CRT, and a remainder sifting approach. Based on the detection of an undersampled waveform's zero crossing point, this solution can pick out the correct remainder between two side spectra, which ensures that the CRT achieves a valid reconstruction. Compared with the existing Maroosi-Bizaki estimator, the proposed method not only enlarges the upper bound of frequency recovery but also possesses higher reconstruction accuracy (the relative error is less than 0.002%) with lower consumption of computational complexity. The numerical results verify the superior performances of our estimator.

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“…Many Doppler ambiguity resolution methods have been proposed in [1][2][3][4][5][6][7]. The so-called robust refinement Chinese Remainder Theorem (CRT) algorithm under noisy environment is proposed in [1][2][3][4]. The staggered PRF is proposed in [5] for overcoming Doppler ambiguity.…”

Section: Introductionmentioning

confidence: 99%

Doppler Ambiguity Resolution Based on Random Sparse Probing Pulses

Zhang

Deng

Shi

et al. 2015

Journal of Electrical and Computer Engineering

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A novel method for solving Doppler ambiguous problem based on compressed sensing (CS) theory is proposed in this paper. A pulse train with the random and sparse transmitting time is transmitted. The received signals after matched filtering can be viewed as randomly sparse sampling from the traditional fixed-pulse repetition frequency (PRF) echo signals. The whole target echo could be reconstructed via CS recovery algorithms. Through refining the sensing matrix, which is equivalent to increase the sampling frequency of target characteristic, the Doppler unambiguous range is enlarged. In particular, Complex Approximate Message Passing (CAMP) algorithm is developed to estimate the unambiguity Doppler frequency. Cramer-Rao lower bound expressions are derived for the frequency. Numerical simulations validate the effectiveness of the proposed method. Finally, compared with traditional methods, the proposed method only requires transmitting a few sparse probing pulses to achieve a larger Doppler frequency unambiguous range and can also reduce the consumption of the radar time resources.

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Digital Frequency Determination of Real Waveforms Based on Multiple Sensors With Low Sampling Rates

Cited by 14 publications

References 14 publications

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

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

Frequency Estimator Based on Spectrum Correction and Remainder Sifting for Undersampled Real-Valued Waveforms

Doppler Ambiguity Resolution Based on Random Sparse Probing Pulses

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