Polynomial Phase Estimation by Least Squares Phase Unwrapping

McKilliam, Robby G.; Quinn, B. G.; Clarkson, I. Vaughan L.; Moran, Bill; Vellambi, Badri N.

doi:10.1109/tsp.2014.2306178

Cited by 53 publications

(29 citation statements)

References 75 publications

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“…Therefore, it is not possible to use this method in this solution. In general, there are other algorithms for estimating the phase described by a polynomial, examples of which can be found in [36,37,38].…”

Section: State Of the Artmentioning

confidence: 99%

A Block Method Using the Chirp Rate Estimation for NLFM Radar Pulse Reconstruction

Abratkiewicz

Samczyński

2019

Sensors

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This paper presents a novel approach to fast and accurate non-linear pulse signal reconstruction dedicated for electromagnetic sensors and their applications such as ELectronic INTelligence (ELINT), electronic warfare (EW), electronic reconnaissance (ER) systems, as well as for passive bistatic radar purposes in which other pulse radars are used as a source of illumination. The method is based on the instantaneous chirp rate (CR) estimation in the time-frequency (TF) domain providing a calculation of the frequency rate between every two consecutive samples. Such a new method allows for the precise reconstruction of the non-linear frequency modulated (NLFM) signal to be carried out in significantly shorter time in comparison to methods known in the literature. The presented approach was tested and validated using both simulated and real-life radar signals proving the usability of the proposed solution in practical applications. The results were compared with the precise extended generalized chirp transform (EGCT) method as a reference technique, using optimal matched filtration as the main concept.

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Section: State Of the Artmentioning

confidence: 99%

A Block Method Using the Chirp Rate Estimation for NLFM Radar Pulse Reconstruction

Abratkiewicz

Samczyński

2019

Sensors

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“…. , 35 as dual time scale, dt = k, with the Chern-Simons current generated from each k as J μ=k by using the docking operator 35 ) is the sequence of V3 loop time series data and y t is the sequence of host cell CD4 time series data. The transition of solitary wave function is just the evoluationary Chern-Simons gauge field induced from intersection of these two fields in the context of adaptive behavior of machine learning.…”

Section: Generator Of Hiv Gene and All Proteinsmentioning

confidence: 99%

“…We visualize all transition states in developmental biology by using modified path integral along ribbon graph produced from Laurent polynomial [35,36] in complex projective plane. In the new quantum field theory for biology with Khovanov cohomology and Grothendieck topology, we define Laurent polynomial [37,38] in the knotted time series data with the characteristic class over 35 amino acids in V3 loop HIV viral glycoprotein by taking the functor from the ribbon graph of the tensor network to categories of knots and links in the secondary protein structure.…”

Section: Introductionmentioning

confidence: 99%

Forecasting Laurent Polynomial in the Chern–Simons Current of V3 Loop Time Series

2019

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The genetic variation in the V3 loop obstruction component of gp120 HIV glycoprotein is defined as a solitary standing wave function with the transition state between the interaction of wave function in the DNA and RNA hidden states. It is a parasitism co-state generated from the coupling between two pairs of hidden 8 states of Laurent polynomial in the Chern-Simons current of HIV genotypes. A modified Nahm equation for a biology with Lax pairs is defined as the pairs of viral glycoprotein states with the transition between DNA and RNA in the reverse transcription process. The direction in the spinor field with genetic variation in 30 samples of the V3 loop time series with hidden 8 states of Laurent polynomial over the Chern-Simons current is predicted using a support spinor machine and convolutional neural network based on the imaging technique generated from tensor correlation network.We assume that the transcription process from the DNA to RNA and to a protein is a chain with the exact sequence in cohomology theory for biology. We cannot separate the DNA from RNA and the protein. It also happens in the transition state, which means that every state of an amino acid is a mixed state. One amino acid is linked with the other amino acids with an affine Poincare group with modulo SO(3, 1). [40] The derivation of a distribution in gene expression shows us the coupling transition protein states as an interaction of

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“…Once this is done we will be able to prove the normality of √ Lm L . Recall thatλ L is the maximiser of the function G L defined in (20). The proof is complicated by the fact that G L is not differentiable everywhere due to the function · not being differentiable at multiples of π M .…”

Section: Proof Of Asymptotic Normality (Theorem 2)mentioning

confidence: 99%

Carrier Phase and Amplitude Estimation for Phase Shift Keying Using Pilots and Data

McKilliam

Pollok

Cowley

et al. 2014

IEEE Trans. Signal Process.

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Abstract-We consider least squares estimators of carrier phase and amplitude from a noisy communications signal that contains both pilot signals, known to the receiver, and data signals, unknown to the receiver. We focus on signaling constellations that have symbols evenly distributed on the complex unit circle, i.e., M -ary phase shift keying. We show, under reasonably mild conditions on the distribution of the noise, that the least squares estimator of carrier phase is strongly consistent and asymptotically normally distributed. However, the amplitude estimator is not consistent, but converges to a positive real number that is a function of the true carrier amplitude, the noise distribution and the size of the constellation. Our theoretical results can also be applied to the case where no pilot symbols exist, i.e., noncoherent detection. The results of Monte Carlo simulations are provided and these agree with the theoretical results.

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Polynomial Phase Estimation by Least Squares Phase Unwrapping

Cited by 53 publications

References 75 publications

A Block Method Using the Chirp Rate Estimation for NLFM Radar Pulse Reconstruction

A Block Method Using the Chirp Rate Estimation for NLFM Radar Pulse Reconstruction

Forecasting Laurent Polynomial in the Chern–Simons Current of V3 Loop Time Series

Carrier Phase and Amplitude Estimation for Phase Shift Keying Using Pilots and Data

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