Phase-Detection-Based Range Estimation With Robust Chinese Remainder Theorem

Li, Xiaoping; Wang, Wenjie; Zhang, Weile; Cao, Yunhe

doi:10.1109/tvt.2016.2550083

Cited by 14 publications

(19 citation statements)

References 23 publications

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“…We have conducted experiments on a hardware platform, and the results show that the DIFM technique which is based on the proposed algorithms can measure the carrier frequency from 0 to 5,000 MHz with a maximum of 0.8 MHz RMSE in less than 200 ns. Besides, the proposed deblurring algorithm can also be applied in phase unwrapping [24], DOA estimation [25], and SAR [26] as CRT.…”

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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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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“…Localization of nodes [3], [5] and frequency estimation [4] are two fundamental problems in sensor networks. Due to the restriction on precise synchronization and hardware resources such as high-rate analog to digital converters (ADC), the phase detection based ranging methods and sub-Nyquist sampling are two important approaches used in these kinds of applications.…”

Section: Introductionmentioning

confidence: 99%

“…Here X i m l denotes the residue of X i modulo m l and 1 is the indicator function. Similarly, in a localization system [3], [5], {X i } stand for the distances and {m l } denote the wavelengths, respectively. In a nutshell, addressing the ambiguity problems is equivalent to recover X i with the residue sets, {r il }, which is a generalized Chinese Remainder Theorem (CRT) problem.…”

Section: Introductionmentioning

confidence: 99%

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On Solving Ambiguity Resolution With Robust Chinese Remainder Theorem for Multiple Numbers

Xiao

2019

IEEE Trans. Veh. Technol.

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Chinese Remainder Theorem (CRT) is a powerful approach to solve ambiguity resolution related problems such as undersampling frequency estimation and phase unwrapping which are widely applied in localization. Recently, the deterministic robust CRT for multiple numbers (RCRTMN) was proposed, which can reconstruct multiple integers with unknown relationship of residue correspondence via generalized CRT and achieves robustness to bounded errors simultaneously. Naturally, RCRTMN sheds light on CRT-based estimation for multiple objectives. In this paper, two open problems arising that how to introduce statistical methods into RCRTMN and deal with arbitrary errors introduced in residues are solved. We propose the extended version of RCRTMN assisted with Maximum Likelihood Estimation (MLE), which can tolerate unrestricted errors and bring considerable improvement in robustness.

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“…It is widely used in the calculation of large integers, because it allows replacing a calculation for which one knows a bound on the size of the result by several similar computations on small integers. The CRT has many applications in various areas, like secret sharing [3,4], the RSA decryption algorithm [13], the discrete logarithm algorithm [14], and the radio interferometric positioning system [15], etc.…”

Section: Introductionmentioning

confidence: 99%

A Novel (t,n) Secret Sharing Scheme Based upon Euler’s Theorem

Chen

Chang

2019

Security and Communication Networks

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The t,n secret sharing scheme is used to protect the privacy of information by distribution. More specifically, a dealer splits a secret into n shares and distributes them privately to n participants, in such a way that any t or more participants can reconstruct the secret, but no group of fewer than t participants who cooperate can determine it. Many schemes in literature are based on the polynomial interpolation or the Chinese remainder theorem. In this paper, we propose a new solution to the system of congruences different from Chinese remainder theorem and propose a new scheme for t,n secret sharing; its secret reconstruction is based upon Euler’s theorem. Furthermore, our generalized conclusion allows the dealer to refresh the shared secret without changing the original share of the participants.

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Phase-Detection-Based Range Estimation With Robust Chinese Remainder Theorem

Cited by 14 publications

References 23 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

On Solving Ambiguity Resolution With Robust Chinese Remainder Theorem for Multiple Numbers

A Novel (t,n) Secret Sharing Scheme Based upon Euler’s Theorem

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