Phase Ambiguity Problem Research Articles

An Improved Unfolded Coprime Linear Array Design for DOA Estimation with No Phase Ambiguity

In this paper, the direction of arrival (DOA) estimation problem for the unfolded coprime linear array (UCLA) is researched. Existing common stacking subarray-based methods for the coprime array are invalid in the case of its subarrays, which have the same steering vectors of source angles. To solve the phase ambiguity problem, we reconstruct an improved unfolded coprime linear array (IUCLA) by rearranging the reference element of the prototype UCLA. Specifically, we design the multiple coprime inter pairs by introducing the third coprime integer, which can be pairwise with the other two integers. Then, the phase ambiguity problem can be solved via the multiple coprime property. Furthermore, we employ a spectral peak searching method that can exploit the whole aperture and full DOFs of the IUCLA to detect targets and achieve angle estimation. Meanwhile, the proposed method avoids extra processing in eliminating ambiguous angles, and reduces the computational complexity. Finally, the Cramer–Rao bound (CRB) and numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed method.

Improved calibration method based on phase-slope description in phase-shift deflectometry

Phase-shift deflectometry is a widely used high-precision gradient measurement method for assessing the topography of specular objects. The calibration of phase-shift deflectometry measurement systems involves establishing the phase-slope mapping relationship. This paper analyzes the causes of phase variations at different calibration points in existing phase-slope analysis models. Based on the fact that changes in height simultaneously produce phase variations in two perpendicular directions, a decoupling method is proposed to address the phase ambiguity problem to some extent. Through simulation, the variation in height phase and slope distribution were quantitatively analyzed for a unidirectional inclined plane to validate the proposed algorithm. Additionally, measurement experiments were performed on a unidirectional inclined plane with an inclination angle of −2.584° and a concave mirror with a curvature radius of 779.87 mm. Based on the findings, the decoupling method reduced the relative root-mean-square error of the gradient measurement for the inclined plane in the inclined direction by 2.206% and improved the error range of the curvature radius for the concave mirror from [0.55%, 4.1%] to [0.22%, 3.86%]. By comparing with the existed method, the decoupling method showed a certain advantage in practicality.

BD-CVSA: A Broadband Direction Finding Method Based on Constructing Virtual Sparse Arrays

As the electromagnetic environment becomes more complex, radio direction finding systems need to cover a wide frequency range. However, the phase ambiguity of high frequency limits the development of broadband direction finding technology. The existing methods in solving the phase ambiguity problem heavily rely on designing the precise actual sparse array structure by theoretical derivation, which is expensive and time-consuming. To solve this problem, we propose a broadband direction finding method based on constructing virtual sparse arrays. First, we perform the convolutional operation on the direction feature matrix to achieve the weighted summation of the original baselines, which generates numerous virtual array elements and virtual baselines with different directions. The virtual array elements are combined to form virtual sparse arrays with different aperture sizes. Second, we optimize the parameters through the error backpropagation algorithm and obtain the optimal combination of virtual sparse arrays, which eliminates the phase ambiguity. Meanwhile, the virtual sparse arrays can maintain the advantages of sparse arrays, which can accomplish high-precision broadband direction finding. The experimental results demonstrate that the proposed method can solve the phase ambiguity problem effectively. It has high accuracy and strong robustness in simulation environment.

Energy receiver positioning using a spatial search strategy in MWPT

This paper proposes a space search method combining the Г-type layout of receiving antenna array of pilot signal for energy receiver positioning in MWPT systems. Based on the retrodirective technology, the spatial coordinate identification function (SCIF) of the energy receiver is generated. The study also investigates how to determine the spatial search range and search point interval. In addition, we propose a Criss-cross space search strategy (CSSS) to accelerate target positioning by summarizing the distribution features of the results obtained by SCIF. The simulation and physical experiment results demonstrate that the proposed method effectively overcomes the phase ambiguity problem and greatly improves the speed and accuracy of energy receiver positioning.

Sparse Stripmap SAR Autofocusing Imaging Combining Phase Error Estimation and L₁-Norm Regularization Reconstruction

Various reasons can induce phase error during synthetic aperture radar (SAR) data collection. If phase error is ignored during SAR imaging, the defocused image will be obtained. Although conventional autofocusing methods can eliminate phase error in the full-sampled case, they are not suitable for down-sampled data. Sparse SAR imaging is a technique that combines sparse signal processing with SAR imaging. It can deal with both full- and down-sampled data if the underlying scene admits a sparse representation in a particular domain. Autofocusing methods based on sparse SAR have been developed in the last decades. However, they are known to be developed for spotlight mode. Furthermore, there is a phase ambiguity problem in existing methods, which will affect the uniqueness of the solution if not handled properly. In this paper, we propose a sparse SAR autofocusing imaging method suitable for stripmap mode and give a solution to phase ambiguity problem. The method jointly estimate phase error and reconstruct sparse SAR image in an iterative way. Each iteration consists of sparse imaging based on the phase error corrected echo and an update of the phase error estimation. Experimental results based on simulated and real data verify the effectiveness of the proposed method in coping with the full- or down-sampled data corrupted by the phase error.

A phase shift group delay-based approach to resolving the phase ambiguity problem in plasma microwave diagnostics

In the diagnosis of plasma microwave transmission, when the plasma size is large and the electron density is high, the microwave will cause a phase period ambiguity problem. In order to solve the phase ambiguity, a novel method of using the phase shift group delay (PSGD) to recover the true phase shift is proposed. The PSGD method is used to recover the simulated phase shift and diagnose the plasma. The diagnostic accuracy is all greater than 91%, which verifies the method. And the new method is used to diagnose the real inductively coupled plasma with high precision. Through analysis, the method of group delay recover phase shift is more suitable for stable plasma or slow-varying plasma.

2π ambiguity-free digital holography method forstepped phase imaging.

It is known that phase ambiguity is always an inherent problem in digital holography. In this paper, a 2π ambiguity-free digital holography method is proposed. The method naturally avoids phase ambiguity by a quasianalytic method. This quasianalytic method accurately calculates the true phase by constructing an equation and solving the solution of the equation. Thus, the inherent wrapping problem in digital holography is eliminated. For example, our experimental result shows that the true phase of the stepped specimen with the phase distributed in [0, 16π] can be obtained unambiguously. Since the proposed method naturally avoids the phase ambiguity problem, it may be beneficial to enlarge the application potential of the digital holography. The effectiveness and accuracy of the proposed method are verified by both numerical simulations and experimental results.

OFDM Network Optimization Using a QPSK Based on a Wind-Driven Genetic Algorithm

Quadrature phase shift keying (QPSK) is a digital modulation technique that transmits data at a constant frequency whilst varying the phases of the carrier signal. QPSK is one of the fundamental modulation schemes for orthogonal frequency division multiplexing systems (OFDM). It is a stable modulation technique with good spectral efficiency. However, during transmission, the carrier signal can undergo numerous phase changes. This creates phase ambiguity problems at the receiver end. This results in inter-symbol interference (ISI) and a high bit error rate (BER). In this paper, the wind-driven optimization was incorporated into the genetic algorithm (GA) as its population selection function. This hybrid algorithm was used to determine the phase assignments for the QPSK. The developed QPSK was implemented on an OFDM network and the message signal was recovered at more than 92% accuracy in a noisy Rayleigh fading channel and 100% accuracy in a noiseless channel. The enhancements greatly mitigated phase ambiguity and bit errors.

Error analysis and correction equations for a real-time phase-shifting method using circular polariscope-based photoelasticity

The use of a polarization camera to achieve real-time phase shifting in circular polariscope-based photoelasticity is limited due to quantitative error analysis and correction. In particular, the primary factor limiting this method is the mismatch between the quarter-wave plate and the wavelength of the light source. In this regard, this study proposes error correction equations for the instantaneous phase-shifting method based on theoretical analysis and simulation of a diametrically stressed disc. First, the error distributions of the stress direction angle and phase retardation are discussed, and the correction equations of the isochromatic and isoclinic lines are deduced. Subsequently, we consider the phase ambiguity problem caused by the phase absolutization. Finally, the error analysis and correction methods are verified experimentally on the diametrically compressed disc.

Phase extraction of optical carrier-based microwave interferometry with all-phase fast Fourier transform for distance measurement

Optical carrier-based microwave interferometry (OCMI) has been recognized as a striking tool for various sensing applications. In this study, distance measurement is realized by a novel and cost-effective phase extraction method for OCMI. Based on all-phase fast Fourier transform (apFFT), the proposed method can effectively suppress spectral leakage and accurately extract phase information, resulting to a better distance estimation performance. Additionally, a phase unwrapping procedure using multiple modulation frequencies is designed and implemented to solve the phase ambiguity problem, avoiding undelightful trade-offs between measurement range and resolution. Theoretical analysis and experimental results verify the validity for distance measurement. At modulation frequency of 1.5 GHz, the measurement results show good linearity with a relative error lower than 10−3. Discussions mainly focus on the anti-noise performance and signal analysis applications of apFFT. This article may provide fresh insights for OCMI researchers and contribute to future development of OCMI sensing.

A Configurable and Real-Time Multi-Frequency 3D Image Signal Processor for Indirect Time-of-Flight Sensors

3D time-of-flight (ToF) cameras have recently attracted widespread attention because of their potential in wide applications. However, the lack of versatile 3D image signal processor (ISP) is still an obstacle that hinders their popularity. The main challenges lie in the management of high-throughput raw data and the complexity of 3D image processing in hardware. To address these challenges, this paper presents a top-down 3D ISP with high real-time performance and high energy efficiency for indirect ToF (IToF) imaging. First, we propose configurable cache strategies to improve the efficiency of non-streaming memory accesses and support different IToF sensors. Then, to resolve the phase ambiguity problem commonly existing in IToF sensors, we develop a hardware-optimized cascaded multi-frequency fusion method, which not only supports up to six modulation frequencies but also facilitates the pixel-wise detection of multipath interference. Moreover, we propose a scalable calculation engine for depth calculation and calibration, 3D image enhancement, and post-processing. The pipeline is prototyped on a Xilinx ZCU102 FPGA board. Results show that the 3D ISP has negligible precision loss and low latency, achieving <inline-formula> <tex-math notation="LaTeX">$53.35\times $ </tex-math></inline-formula> energy efficiency improvement compared with the implementation on Intel CPU and <inline-formula> <tex-math notation="LaTeX">$55.45\times $ </tex-math></inline-formula> improvement over the ARM CPU implementation. When running at 75 MHz, the 3D ISP can support <inline-formula> <tex-math notation="LaTeX">$1280\times 960$ </tex-math></inline-formula> depth, intensity, and point cloud output at a frame rate of 30 f/s.

An Algorithm for Solving the Phase Ambiguity Problem of SAW Delay-Line Sensor Systems.

Solving the phase ambiguity problem is crucial to achieving a wide-range and high-precision measurement for the frequency-domain sampling (FDS)-based surface acoustic wave (SAW) delay-line sensor systems. This study proposes an improved phase estimation algorithm called dual-band phase estimation (DBPE) to solve the problem. By using DBPE, the SAW sensor system can obtain an extensive and alterable measuring range without further requirements for sensor design or transmitted signals. Thus, it can be widely used in various FDS-based SAW delay-line sensor systems. Monte Carlo simulations and temperature measuring experiments, based on a YZ-cut LiNbO3 SAW delay-line sensor and a switched frequency-stepped continuous wave (S-FSCW) reader, are performed to demonstrate the algorithm's validity. The Monte Carlo simulations show that DBPE can effectively solve the phase ambiguity problem and has better performance than frequency estimation in measuring precision at a low signal-to-noise ratio (SNR). The temperature-sensing experiments show that DBPE has a good performance in measuring range and precision, serving as a phase ambiguity solver in the temperature sensor system.

Discussion on Piston-Type Phase Ambiguity in a Coherent Beam Combining System

Coherent beam combining (CBC) with closely arranged centrosymmetric arrays is a promising way to obtain a high-brightness laser. An essential task in CBC is to actively control the piston phases of the input beams, maintaining the correct phasing to maximize the combination efficiency. By applying the neural network, the nonlinear mapping relationship between the far-field image and the piston phase could be established, so that the piston phase can be corrected quickly with one step, which caused widespread concern. However, there exists a piston-type phase ambiguity problem in the CBC system with centrosymmetric arrays, which means that multiple different piston phases may generate the same far-field image. This will prevent the far-field image from correctly reflecting the phase information, which will result in a performance degradation of the image-based intelligent algorithms. In this paper, we make a theoretical analysis of phase ambiguity. A method to solve phase ambiguity is proposed, which requires no additional optical devices. We designed simulations to verify our conclusions and methods. We believe that our work solves the phase ambiguity problem in theory and is conducive to improving the performance of image-based algorithms.

Computationally Efficient Direction-of-Arrival Estimation Algorithms for a Cubic Coprime Array.

In this paper, we investigate the problem of direction-of-arrival (DOA) estimation for massive multi-input multi-output (MIMO) radar, and propose a total array-based multiple signals classification (TA-MUSIC) algorithm for two-dimensional direction-of-arrival (DOA) estimation with a coprime cubic array (CCA). Unlike the conventional multiple signal classification (MUSIC) algorithm, the TA-MUSIC algorithm employs not only the auto-covariance matrix but also the mutual covariance matrix by stacking the received signals of two sub cubic arrays so that full degrees of freedom (DOFs) can be utilized. We verified that the phase ambiguity problem can be eliminated by employing the coprime property. Moreover, to achieve lower complexity, we explored the estimation of signal parameters via the rotational invariance technique (ESPRIT)-based multiple signal classification (E-MUSIC) algorithm, which uses a successive scheme to be computationally efficient. The Cramer–Rao bound (CRB) was taken as a theoretical benchmark for the lower boundary of the unbiased estimate. Finally, numerical simulations were conducted in order to demonstrate the effectiveness and superiority of the proposed algorithms.

A Polar Coding With a Q-Section NBC Property for Managing Phase Ambiguity and PAPR in Multi-Carrier Communications

For an orthogonal frequency division multiplexing (OFDM) communication system which requires channel estimation for each sub-carrier without using pilot signals, there may exist the problem of phase ambiguity. By extending the conventional concept of noncoherent block coding (NBC), we propose a $Q$ -section polar code that has the NBC property in such a way that each codeword is divided into $Q$ sections and reversing the code bits in some sections results in another codeword which is encoded by the same desired message. The polar coded OFDM with a $Q$ -section NBC property enables us to solve the problem of phase ambiguity that exists in each sub-carrier. In addition, the $Q$ -section NBC property also enables us to employ the multiple-candidate method for reducing the peak-to-average-power ratio (PAPR).

Array shape calibration with phase unwrapping techniques for highly deformed arrays

Flexible sensor arrays, such as towed and bottom-mounted arrays, typically suffer from large shape deformations, which seriously affect the results of array processing. In this article, an innovative array shape calibration method with phase unwrapping techniques for highly deformed arrays is proposed. The deformed array is divided into several subarrays, and the first subarray is assumed to suffer from slight shape deformations which can be pre-calibrated. With the consideration of highly deformed arrays, uncalibrated sensors in other subarrays would have serious position mismatches. The phase differences between uncalibrated and pre-calibrated sensors are probably larger than 2 π , which lead to phase ambiguity problems. A phase unwrapping technique is proposed to efficiently solve the phase ambiguity problem by considering the physical structure constraints of the deformed array, such as intersensor distance and bending angle. Then, sensor positions in highly deformed arrays are calibrated with multiple target directions. Simulation results evaluate the performance of the proposed calibration method, and the SwellEx-96 shallow water experiment data set is utilised to demonstrate the effectiveness of the proposed method.

Phase and Amplitude Calibrations of Rotating Equispaced Circular Array for Geostationary Microwave Interferometric Radiometers— Theory and Methods

The calibration strategy for synthetic aperture interferometric radiometers based on noise injection has been successfully demonstrated in the Microwave Imaging Radiometer with Aperture Synthesis (MIRAS) instrument onboard the Soil Moisture and Ocean Salinity (SMOS) mission of the European Space Agency (ESA). With the emerging demands of increasing both array size and frequency bands, the internal calibration hardware becomes more difficult to implement. Although several external calibration methods have been proposed, the so-called phase ambiguity problem was not carefully considered. In this article, a novel calibration strategy for both phase and amplitude calibrations based on redundant space calibration is proposed, which utilizes the unique structure of equispaced circular array and rotational sampling strategy. The original irregular phase ambiguity degenerates to the fixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -ambiguity, where only two possible solutions to phases are introduced. Both phase and amplitude of visibility can be simultaneously calibrated by the proposed strategy, and no cooperative calibration target is needed.

Coherent Target Direction‐of‐Arrival Estimation for Coprime Arrays: From Spatial Smoothing Perspective

In this paper, we investigate the issue of direction‐of‐arrival (DOA) estimation of multiple signals in coprime arrays. An algorithm based on multiple signal classification (MUSIC) and forward and backward spatial smoothing (FBSS) is used for DOA estimation of this signal caused by multipath and interference. The large distance between adjacent elements of each subarray in the coprime arrays will bring phase ambiguity issues. According to the feature of the coprime number, the ambiguity problem can be eliminated. The correct DOA estimation can be obtained by searching for the common peak of the spatial spectrum and finding the overlapping peaks in the MUSIC spectrum of the two subarrays. For the rank deficit problem caused by the coherent signal, the FBSS algorithm is used for signal preprocessing before the MUSIC algorithm. Theoretical analysis and simulation results show that the algorithm can effectively solve the rank deficiency and phase ambiguity problems caused by coherent signals and sparse arrays in the coprime arrays.

Accurate Respiration Monitoring for Mobile Users With Commercial RFID Devices

Vital signs (e.g., respiration rate or heartbeat rate) sensing is of great importance to implement pervasive in-home healthcare. Traditional vital signs monitoring approaches usually require users to wear some dedicated sensors. These approaches are intrusive and inconvenient to use, especially for elderly people. Some non-intrusive vital signs monitoring approaches based on wireless sensing have been proposed in recent years. However, these approaches require the target user to be in situ during the monitoring process, which greatly limits their utilization in practical scenarios where the target users usually move around. In this paper, we propose RF-RMM, an RFID-based approach to accurate and continuous respiration monitoring for mobile users. The major challenge in respiration monitoring for moving people is that the tiny body displacement caused by the user's respiration is overwhelmed by the user's entire body movement. To address this issue, we propose a novel approach that uses a pair of tags to eliminate the effect of the user's body movement. We fuse the data from the paired tags to cancel the effect of the user's entire body movement and retain only the displacement caused by the user's respiration. Another challenging issue in implementing RF-RMM is how to resolve the phase ambiguity problem when the target user moves around, which becomes more serious than in the static case. We propose a distance tracking algorithm to track the phase transition during the user's movement, according to which the phase ambiguity problem can be well handled. We implement RF-RMM on commercial RFID devices and conduct extensive real-world experiments to evaluate its performance. The results show that RF-RMM achieves accurate respiration rate monitoring with an average error of 0.54 BPM in estimating different users' respiration rate and an average relative error of less than 13% in estimating the user's individual breath length.

Fast Angle-of-Arrival Estimation via Virtual Subarrays in Analog Antenna Array

Angle-of-arrival (AoA) estimation is a challenging problem for analog antenna arrays. Typical schemes use time-consuming beam scanning, and the resolution is limited to the scanning beam width. In this paper, we propose a virtual-subarray based AoA (ViSA) estimation scheme, which divides an analog array into two virtual subarrays and exploits phase difference between one pair of measurements for AoA estimation. The basic ViSA algorithm can obtain a direct AoA estimate from every two temporal measurements. We propose different subarray constructions which can lead to different accuracy of estimation. We provide closed-form expressions for the statistics of the estimation error. Based on the basic ViSA estimator, we develop two methods to combine multiple pairs of measurements, when they are obtained via sequential and multi-resolution scanning, respectively. Near-optimal estimators are derived for both methods, employing the maximum likelihood principle. Novel techniques are also proposed to address the typical phase ambiguity problem due to the periodic phase function. Simulation results demonstrate that the proposed scheme significantly outperforms existing ones.