Phase Ambiguity Problem Research Articles

Time-Difference-of-Arrival Estimation Algorithms by Employing Cyclostationary Property of LFM Signals

In this letter, two time-difference-of-arrival (TDOA) estimation algorithms are studied by employing the cyclostationary property of LFM signals. First, the multicycle frequency phase TDOA (MCFP-TDOA) estimation algorithm is developed by using the phase difference of the cyclic auto-correlation function of each cycle frequency, followed by an analysis on the phase ambiguity problem. By taking advantage of multiple cycle frequencies and the linear relationship between each cycle frequency, it was found to have smaller estimation error compared with the traditional cyclic phase difference (CPD) method. Second, based on the characteristics of LFM signals in the cyclic frequency domain, the spectral correlation TDOA (SC-TDOA) estimation algorithm is devised, which has good antinoise ability. The improved performances of the proposed algorithms are demonstrated through detailed theoretical analysis and simulations.

Performance Enhancement of Coherent Optical OFDM System Using LMS Algorithm

Instability of the local oscillator causes phase noise – a phenomenon that is a disadvantage and is considered to be a major obstacle in the functioning of coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. An attempt has been made in this paper to reduce the effects of common phase errors generated by phase noise. In this paper, a least mean square (LMS) based algorithm is proposed for estimation of phase noise. Using this proposed algorithm, the major problem of phase ambiguity caused by cycle slip is avoided and the bit error rate is greatly improved. Further, there is no requirement for modifying the frame structure of OFDM using this algorithm. A CO-OFDM system with the 8-PSK technique is used to implement the algorithm concerned. Furthermore, the algorithm, using the 8-PSK modulation technique, is analyzed and compared with the existing QPSK technique and with other algorithms. The investigations reveal that 8-PSK outperforms existing LMS algorithms using other techniques and significantly reduces the bit error rate.

Structured-light-field 3D imaging without phase unwrapping

Directly using wrapped phases may cause a problem of phase ambiguity in fringe-projection-based three-dimensional (3D) imaging. In our previous work, the phase ambiguity was addressed by introducing light-field imaging to associate a wrapped phase-encoded field in the image space with several candidates of spatial points in the object space to identify the correct fringe orders for absolute phase unwrapping. The candidate spatial points with absolute phases can be reconstructed by satisfying the mandatory requirements of system fixation and pre-calibration, which may lack flexibility and applicability. Since we also illustrated that the correspondence cue in an unwrapped phase-encoded field could be used for accurate light-field depth estimation, an instructive question is whether or not depth cues of the light-field imaging can provide constraint conditions to deal with the phase ambiguity without these systematic requirements. To this end, a method for structured-light-field 3D imaging is proposed. The wrapped phase-encoded field was processed to be locally continuous with respect to the phases in specific angular coordinates. After that, the correspondence cue focusing on the local angular variance of the processed wrapped phase-encoded field was used to estimate depths correctly without the requirement of system pre-calibration. Furthermore, comparative experiments under different measurement conditions, including the changes of the fringe period of projected patterns, the focal length of the projector, and the relative orientation among system components, produced the consistent measurement results. Consequently, the proposed method is proved to adapt to the changes in the measurement environment and be a flexible way for structured-light-field 3D imaging without the need for phase unwrapping.

Method of fiber transfer delay measurement based on phase quantization and delay synthesis.

A novel method, to the best of our knowledge, of fiber transfer delay (FTD) measurement based on phase quantization and delay synthesis is proposed and demonstrated. By detecting the differential phase shifts of a set of frequency-multiplied RF signals transmission through the fiber link with and without the FTD under the test, the ${2}\pi $2π phase ambiguity problem can be solved. To avoid the phase quantization error near the digital quantization boundary, a self-check and error-correction method is proposed so as to greatly improve the reliability of measurement. In the experiment, the measurement repeatability around 0.018 ps within a period of 80 s is achieved for a back-to-back fiber link, and a test resolution of 0.03 ps is proved with a motorized tunable delay line. The system is available for measurement of a large FTD range up to 100 µs with no dead zone.

Precision Position Measurement of PMSLM Based on ApFFT and Temporal Sinusoidal Fringe Pattern Phase Retrieval

To improve the accuracy of the mover position detection with longer measurement range, a linear motor displacement measurement method is proposed based on digital image measurement and temporal sinusoidal fringe pattern phase retrieval. A simple computer-generated sinusoidal fringe pattern is designed as the target image, and sequences of fringe signals are recorded by a line scan camera that moves with the linear motor. Fourier phase analysis is employed to extract the initial phase of each signal curve, and then temporal phase unwrapping is applied to reconstruct the mover displacement evolution according to the system magnification parameter and fringe width. This method removes the phase ambiguity problem of traditional temporal phase analysis, and can be used in complex motion of permanent magnet synchronous linear motors. To suppress the spectrum leakage of fast Fourier transform (FFT), all-phase FFT with double Hanning windows is used to improve the detection accuracy of initial phase and fringe width. Simulation and experimental results demonstrate that the proposed method can estimate the mover position with longer measurement range precisely and robustly under different working conditions.

Three-Dimensional Coprime Array for Massive MIMO: Array Configuration Design and 2D DOA Estimation

In massive multiple-input multiple-output (MIMO) systems, it is critical to obtain the accurate direction of arrival (DOA) estimation. Conventional three-dimensional array mainly focuses on the uniform array. Due to the dense arrangement of the sensors, the array aperture is limited and severe mutual coupling effects arise. In this paper, a coprime cubic array (CCA) configuration design is presented, which is composed of two uniform cubic subarrays and can extend the interelement spacing with a selection of three pairs of coprime integers. Compared with uniform cubic array (UCA), CCA achieves the larger array aperture and less MC effects. And the analytical expression of Cramer–Rao Bound (CRB) for CCA is derived which verifies that the proposed CCA geometry outperforms the conventional UCA in two-dimensional (2D) DOA estimation performance in massive MIMO systems. Meanwhile, we propose a computationally efficient 2D DOA estimation algorithm with high accuracy for CCA. Specifically, we utilize array mapping to extract two uniform arrays from the nonuniform array by exploiting the relation derived from the signal subspace and the two directional matrices. Then, we operate a reduced dimension process on the uniform arrays and convert the 2D spectrum peak searching (SPS) problem into one-dimensional (1D) one, which significantly reduces the computational complexity. In addition, we employ the polynomial root finding technique with a lower complexity instead of 1D SPS to further relieve the computational complexity. Simultaneously, with coprime property, the phase ambiguity problem is solved, which results from the large interelement spacing. Numerical simulation results demonstrate that the proposed algorithm is very computationally efficient without degradation of DOA estimation performance.

High-Precision OMP-Based Direction of Arrival Estimation Scheme for Hybrid Non-Uniform Array

Most of compressive sensing Direction of Arrival (DoA) estimation schemes in the literature employ a uniform array for the simplicity and mathematical tractability. Non-uniform array geometries can enhance the resolution performance, substantially. However, they suffer from the problem of phase ambiguity. In this letter, we suggest a novel hybrid non-uniform and linear array and propose an efficient DoA estimation scheme. This scheme can distinguish adjacent signal sources with high accuracy. In addition, the proposed scheme tackles the problem of phase ambiguity.

Maximum likelihood approach to DoA estimation using lens antenna array

Massive antenna array has been proposed to improve the spectral efficiency and link reliability in wireless communication systems. However, using large antenna arrays incurs additional cost in terms of signal processing and hardware complexity. The electromagnetic (EM) lens-focusing antennas are introduced as a promising technique to reduce the hardware complexity and cost. On the other hand, determining the location of users in terms of their direction-of-arrival (DoA) using these lens array becomes of great interest for different 5G services. This paper addresses the issue of DoA estimation by adopting lens antenna array (LNA). We firstly derive an expression for the received signal with the adoption of LNA, and then a maximum likelihood (ML) estimator for the DoA has been obtained. Depending on the ability of the lens array to focus the signal power on a subset of antennas as a function of DoA. We propose using the antenna selection (AS) technology to select an antenna subset aiming to reduce the number of radio frequency (RF) chains and accordingly reducing the hardware cost. The simulation results show the the capability of the proposed method to avoid the phase ambiguity problem and provide high accurate DoA estimation of signals.

Surface profile measurement of doped silicon using near-infrared low-coherence light.

A scanning interferometry system based on near-infrared low-coherence interferometry by using a superluminescent diode (SLD) as the light source is presented. The system cannot only measure the surface profile of doped double-sided polished silicon but also measure its optical thickness and refractive index. The measurement system uses near-infrared CCD to detect interferometric light in the near infrared, based on the Michelson interference principle. SLD has low temporal and high spatial coherence and high penetration to doped silicon wafers; thus, higher visibility can be obtained when measuring the rear side. Meanwhile, the optical thickness measured by low coherent scanning interference is compared with the optical thickness obtained by spectrally resolved interferometry to verify the accuracy of the system. Due to the periodic characteristics of interference fringes, the coherence length of the narrowband light source is usually greater than the path length difference of the interferometer. It gives the measurement a phase ambiguity of 2π, which may severely limit the application of the measurement. However, the short coherent length SLD light source used in the project can avoid 2π phase ambiguity problems. Besides, this system can perform full scanning in a larger step and achieve rapid on-line measurement of the target surface.

Unfolded coprime bistatic MIMO radar for joint DOD and DOA estimation: from viewpoint on aperture augment for sum coarray

ABSTRACTGenerally, the coprime linear array (CLA) consisting of two interleaved uniform linear subarrays can enlarge the array aperture to attain the better angle estimation performance compared with the uniform linear array (ULA). In this paper, we ulteriorly study the virtual sum coarray of the unfolded coprime (UC) bistatic multiple-input multiple-output (MIMO) radar whose transmitter and receiver array are both unfolded CLA from the viewpoint on the geometry and array aperture. The UC MIMO radar can be exploited to obtain the better joint direction of departure (DOD) and direction of arrival (DOA) estimation performance due to the larger array aperture. Furthermore, we propose an all sum coarray multiple signals classification (ASCA-MUSIC) algorithm for the UC MIMO radar. ASCA-MUSIC can fully exploit all the degrees of freedom (DOFs) in the sum coarray and can obtain the better estimation performance. We also prove that ASCA-MUSIC can avoid the phase ambiguity problem due to the coprime property. In addition, we devise a reduced complexity scheme for ASCA-MUSIC to reduce the high computational complexity and utilize Cramer–Rao Bound (CRB) as a benchmark for the lower bound on the root-mean-square error (RMSE) of unbiased angle estimation. Finally, the numerical simulations verify the effectiveness and superiority of the UC MIMO radar, ASCA-MUSIC and the reduced complexity scheme.

Ambiguity Analysis and Resolution for Phase-Based 3D Source Localization under Given UCA

Under uniform circular array, by employing some algebraic schemes to exploit the phase information of receiving data and further estimate the source’s three-dimensional (3D) parameters (azimuth angle, elevation angle, and range), a series of novel phase-based algorithms with low computational complexity have been proposed recently. However, when the array diameter is larger than source’s half-wavelength, these algorithms would suffer from phase ambiguity problem. Even so, there always exist certain positions, where the source’s parameters can still be determined with nonambiguity. Therefore, this paper first investigates the zone of ambiguity-free source 3D localization using phase-based algorithms. For the ambiguous zone, a novel ambiguity resolution algorithm named ambiguity traversing and cosine matching (ATCM) is presented. In ATCM, the phase differences of centrosymmetric sensors under different ambiguities are utilized to match a cosine function with sensor number-varying, and the source’s unambiguous rough angles can be derived from amplitude and initial phase of the cosine function. Then, the unambiguous angles are employed to resolve the phase ambiguity of the phase-based 3D parameter estimation algorithm, and the source’s range as well as more precise angles can be achieved. Theoretical analyses and numerical examples show that, apart from array diameter and source’s frequency, the sensor number and spacing of employed sensors are two key factors determining the unambiguous zone. Moreover, simulation results demonstrate the effectiveness and satisfactory performance of our proposed ambiguity resolution algorithm.

Power efficient dual‐dependent pilots' channel estimation for filter bank multi‐carrier with offset quadrature amplitude modulation

The channel estimation for a filter bank multi-carrier with offset quadrature amplitude modulation has been considered an attractive scheme alternative to the conventional cyclic prefix (CP)-orthogonal frequency-division multiplexing. However, all the advantages come at the price of the real-field orthogonality conditions, which gives rise to the intrinsic imaginary. Especially the channel estimation algorithm with a scattered-pilot structure, which neutralises the interference by increasing power or reducing spectrum efficiency to get accurate channel estimation coefficients. In this work, dual-dependent pilot (DDP) channel estimation algorithm is studied. By analysing the interference at the pilot position and pilot power, the authors propose an improved power efficient scattered DDP channel estimation method. The proposed method regards the interference as a part of the pilot rather than cancelling it. Moreover, in order to fully utilise intrinsic interference, phase ambiguity is introduced into predefined pilots to adapt to different intrinsic interference values, combined with the reference pilot and DFT iteration to solve phase ambiguity problems at the receiver. Theoretical analysis shows that the improved method can effectively improve the power efficiency. Furthermore, numerical results show the validity of the theoretical analysis and the reliability of the new method.

Phase Matching of Coincident Pulses for Range-Doppler Estimation of Multiple Targets

Range-Doppler estimation algorithms that use the phase of the returned signal face the 2 $\pi$ phase ambiguity problem. In this letter, we eliminate phase wrapping by using two coincident opposite polarity chirps but equal starting frequencies. The returns for both chirps from the same target have near equal phases. The phase wrap is present in both returns but they are the same. Therefore, the differential phase matching used to pair the returns from the same target cancels out the phase wrap. No phase unwrapping is needed. The proposed method has no inherent maximum unambiguous range or velocity, works in multitarget theaters, requires a much lower sampling rate, is not affected by range migration, decouples the Doppler cycle from the pulse repetition frequency and is computationally more efficient than FFT-based methods.

Phase noise analysis of proposed PFD and CP switching circuit and its advantages over various PFD/CP switching circuits in phase-locked loops

This paper presents the design of a new phase frequency detector (PFD) and different type of charge pump (CP) circuits for phase-locked loops. A proposed phase frequency detector circuit can eliminate the effect of missing edge and phase ambiguity problems in many PFDs. A novel CP circuit with a special switching scheme has been incorporated to reduce the current mismatch error, charge injection error and clock feed through effect in many CP circuits using a new and unique clocking scheme of up delay (UPD) and down bar-delay (DNBD) signals in place of the conventional UPD and DNB clock pulses. Output noise, input referred phase noise, and phase noise performance (with 10 fF load capacitance) of the proposed PFD and true single phase clock (TSPC) PFD have been studied with different CP circuits. The effect of CP current mismatch and DC offset current at any of the current source or sink has been incorporated to check the effect on spur and phase noise performance of the ΔΣ fractional-N PLL frequency synthesizer. In addition, PFD and charge pump circuit phase noise estimation theory has been illustrated and it has been verified through the transistor level simulation. PLL locking response has been verified through the transistor level simulation in Cadence SpectreRF for the different CPs configuration with the proposed PFD and it shows that the proposed PFD and different CP circuits lock much faster than other works in literature. This condition also holds for the automatic frequency control unit along with the loop bandwidth calibration circuit and in special case of both loop bandwidth calibration and phase noise cancellation circuit. According to our knowledge this work shows a new state of the art performances for this proposed charge pump circuit and phase noise analysis of the charge pump circuit in presence of an error amplifier and many switching circuits.

DOA Estimation for Generalized Three Dimensional Coprime Arrays: A Fast-Convergence Quadrilinear Decomposition Algorithm

In this paper, we construct the generalized 3-D coprime array (G-TDCA) configuration, which consists of two 2-D uniform subarrays, by selecting three pairs of coprime integers to obtain the extension of inter-element spacing. Meanwhile, we derive the analytical expression of Cramer–Rao bound for G-TDCA and verify that G-TDCA outperforms the conventional 3-D uniform array (TDUA) in the direction of arrival (DOA) (i.e., azimuth and elevation angles) estimation performance and resolution with numerical simulations. In addition, we propose a fast convergence quadrilinear decomposition (FC-QD) algorithm to extract the DOA estimates for G-TDCA. In the FC-QD algorithm, we first employ propagator method (PM) to achieve rough DOA estimates that are utilized to initialize the steering matrices. Subsequently, the received signal is constructed as two quadrilinear models and quadrilinear alternating least square algorithm is operated to attain fine DOA estimates. Moreover, phase ambiguity problem, caused by large adjacent distance between array sensors, is eliminated based on coprime property, where the uniqueness of DOA estimates can be achieved. Specifically, the proposed FC-QD algorithm has a fast convergence due to initialization via PM, and hence, FC-QD can significantly lower the computational cost without degrading the DOA estimation performance, which is demonstrated by extensive simulation results.

P048 NGS performance on a transplanted liver biopsy sample: A case study

A male pediatric patient was diagnosed with biliary atresia and was transplanted with liver from a deceased donor. The surgery went well, but years later the patient developed antibodies to Cw12, DR14, DQ7 and DQA1∗04:01 and various DP alleles. The need for high resolution typing to determine the identity of de novo DSA and the lack of any remaining pre-transplant sample on a deceased donor led to the use of NGS to determine chimeric typing. Genomic DNA was extracted from a post-transplant liver biopsy from this patient by using Gentra Puregene Tissue kit. We used the Immucor NGS FLEX HLA typing system for amplification and sequencing of HLA genes HLA -A, B, C, DRB1, DRB3/4/5, DQA1, DQB1, DPA1, and DPB1 followed by analysis with MIA FORA software. The NGS methodology is a clonal sequencing approach which solves the phase ambiguity problems inherent with Sanger-based sequencing when alleles are amplified and sequenced together. The genomic DNA extracted from the transplanted liver biopsy is chimeric, with residual recipient DNA at very low but detectable levels. The presence of chimeric reads is the result of co-amplification of both donor and recipient HLA genes. The majority of sequencing reads with zero mismatches belonged to the donor and were concordant with the deceased donor HLA type provided by UNOS. Unclaimed sequencing reads appeared as grey background and derived from the recipient HLA type (previously obtained with pre-transplant samples). In this case and a few other chimeric cases examined in our laboratory, the MIA FORA NGS software detected the HLA type of donor as the called alleles and showed some unclaimed reads that did not align to the donor type but rather to the HLA type of recipient. We note that if the donor and recipient HLA genes are perfectly matched in one or both alleles then they are indistinguishable. The clonal sequencing nature of the NGS reveals PCR primer specificity by identifying the sequences of all co-amplified genomic regions within the intended target region in the same biopsy sample. This case demonstrates the clinical utility of high resolution HLA typing by NGS technology in the clinical setting to de convolute a solid organ biopsy admixture i.e. the ability to do chimeric typing.

Ambiguity Resolution for Phase-Based 3-D Source Localization under Fixed Uniform Circular Array.

Under fixed uniform circular array (UCA), 3-D parameter estimation of a source whose half-wavelength is smaller than the array aperture would suffer from a serious phase ambiguity problem, which also appears in a recently proposed phase-based algorithm. In this paper, by using the centro-symmetry of UCA with an even number of sensors, the source’s angles and range can be decoupled and a novel algorithm named subarray grouping and ambiguity searching (SGAS) is addressed to resolve angle ambiguity. In the SGAS algorithm, each subarray formed by two couples of centro-symmetry sensors can obtain a batch of results under different ambiguities, and by searching the nearest value among subarrays, which is always corresponding to correct ambiguity, rough angle estimation with no ambiguity is realized. Then, the unambiguous angles are employed to resolve phase ambiguity in a phase-based 3-D parameter estimation algorithm, and the source’s range, as well as more precise angles, can be achieved. Moreover, to improve the practical performance of SGAS, the optimal structure of subarrays and subarray selection criteria are further investigated. Simulation results demonstrate the satisfying performance of the proposed method in 3-D source localization.

Depth estimation of water column objects using interferometric synthetic aperture sonar

Synthetic Aperture Sonar (SAS) is a technique which delivers sonar images of the seabed with both high resolution and large area coverage rate. SAS is therefore a well suited sensor for search of small objects on the seafloor, and is an important tool in many emerging mine countermeasures (MCM) systems. An interferometric SAS system can also resolve the angle of arrival in the vertical plane, and thus estimate the depth of an object. In this talk, we present techniques using SAS imaging for depth estimation of small objects, not on the seafloor, but located in the water column. We consider the effect of geometry, sensor settings and processing parameters. For objects of interest, we present a belief propagation inspired method for estimating the depth of the objects. This method is CPU intensive, but avoids the phase ambiguity problem encountered in standard SAS interferometry. We compare this method to a coarse depth estimate acquired from the multipath response in the SAS images as well as to ground truth. We show example images and depth estimates from the Kongsberg HISAS interferometric SAS collected by a HUGIN autonomous underwater vehicle.

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

The radio interferometric positioning system can measure distance by using the wavelength of the carried radio wave from the relative phase offset of the interference signal. All of these measurements suffer from the phase ambiguity problem and are inevitably corrupted by noise in systems. In this paper, we propose to resolve the given problems by the robust Chinese remainder theorem (CRT). By exploiting the angular circular distance between two vectors, we propose the vector-based robust CRT (Vec-CRT). To further improve estimation performance, we propose the maximum-likelihood-estimation-based robust CRT (MLE-CRT). Compared with the existing range estimation algorithms, both of the proposed algorithms provide better performances. In particular, the robust MLE-CRT achieves the best performance and the least computational complexity among all the competitors. Simulations are presented to verify the effectiveness and robustness of the proposed algorithms.

Increasing the robustness and applicability of full-waveform inversion: An optimal transport distance strategy

Full-waveform inversion starts being used as a standard stage of the seismic-imaging workflow, at the exploration scale, for the reconstruction of high-resolution wave velocity models. However, its successful application still relies on the estimation of an accurate enough initial velocity model, as well as on the design of a suitable hierarchical workflow, allowing it to feed the inversion process progressively with data. These two requirements are mandatory to avoid the cycle-skipping or phase-ambiguity problem when comparing observed and synthetic data. This difficulty is due to the definition of the full-waveform inversion problem as the least-squares minimization of the data misfit. The resulting misfit function has local minima, which correspond to the interpretation of the seismic data up to one or several phase shifts. In this article, we review an alternative formulation of full-waveform inversion based on the optimal transport distance we have proposed in recent studies. We propose to use a particular instance of the optimal transport problem, which is adapted to the interpretation of real seismic data and for which we design an efficient low-complexity numerical strategy. Numerical results in 2D and 3D configurations (BP 2004, Chevron 2014 benchmark model, SEG/EAGE overthrust model) show that this reformulation should yield a more convex misfit function, less prone to cycle skipping. In this study, we present a simple illustration on the Marmousi model, which illustrates how this new distance strongly relaxes the requirement on the initial model design. Starting from a rather simplistic approximation of the initial model, the method is able to reconstruct a meaningful estimation of the Marmousi model, while the standard least-squares formulation is trapped into a local, meaningless minimum.