Conjugate Symmetry Research Articles

DOA estimation in the presence of unknown non‐uniform noise with coprime array

The aim is to present a new direction-of-arrival (DOA) estimation algorithm, which is better suited for dealing with unknown non-uniform noise, as well as estimating more sources with less sensors. To achieve this goal, three key steps are exploited: a first step is to extend the array aperture by using coprime array and conjugate symmetry strategy, a second step is to avoid phase ambiguity via vector element reorganisation and a third step is to obtain a full-rank covariance matrix through subvector division, which has the same form with the covariance matrix obtained in uniform Gaussian white noise. Simulation results show that the proposed algorithm can provide better DOA estimation performance than the compared algorithms.

Two‐dimensional DOA estimation for L‐shaped array with nested subarrays without pair matching

Non-uniform L-shaped array consisting of two nested arrays and its computationally efficient two-dimensional direction-of-arrival (DOA) estimation method are developed in this study. The basic idea of the proposed method is to utilise the property of nested arrays and the conjugate symmetry property of the signal auto-correlation function for different time lags to construct a conjugate augmented spatial–temporal cross-correlation matrix (CAST-CCM) and form joint diagonalisation structure from the signal subspace corresponding to the CAST-CCM. Hence, the DOAs are estimated and paired automatically via signal subspace joint diagonalisation technique. The proposed method can handle underdetermined DOA estimation with automatic matching and deal with the angle ambiguity problem when multiple sources have the same azimuth or elevation angles. Meanwhile, the proposed method is computationally efficient without multidimensional search. The effectiveness of the proposed method is verified through computer simulations.

Signal Periodic Decomposition With Conjugate Subspaces

In this paper, we focus on hidden period identification and the periodic decomposition of signals. Based on recent results on the Ramanujan subspace, we reveal the conjugate symmetry of the Ramanujan subspace with a set of complex exponential basis functions and represent the subspace as the union of a series of conjugate subspaces. With these conjugate subspaces, the signal periodic model is introduced to characterize the periodic structure of a signal. To achieve the decomposition of the proposed model, the conjugate subspace matching pursuit (CSMP) algorithm is proposed based on two different greedy strategies. The CSMP is performed iteratively in two stages. In the first stage, the dominant hidden period is chosen with the periodicity strategy. Then, the dominant conjugate subspace is chosen with the energy strategy in the second stage. Compared with the current state-of-the-art methods for hidden period identification, the main advantages provided by the CSMP are the following: (i) the capability of identifying all the hidden periods in the range from $1$ to the maximum hidden period $Q$ of a signal of any length, without truncating the signal; (ii) the ability to identify the time-varying hidden period with its shifted version; and (iii) the low computational cost, without generating and using a large over-complete dictionary. Moreover, we provide examples and applications to demonstrate the abilities of the proposed two-stage CSMP algorithm, which include hidden period identification, signal approximation, time-varying period detection, and pitch detection of speech.

Accelerated electron paramagnetic resonance imaging using partial Fourier compressed sensing reconstruction

PurposeElectron paramagnetic resonance (EPR) imaging has evolved as a promising tool to provide non-invasive assessment of tissue oxygenation levels. Due to the extremely short T2 relaxation time of electrons, single point imaging (SPI) is used in EPRI, limiting achievable spatial and temporal resolution. This presents a problem when attempting to measure changes in hypoxic state. In order to capture oxygen variation in hypoxic tissues and localize cycling hypoxia regions, an accelerated EPRI imaging method with minimal loss of information is needed. MethodsWe present an image acceleration technique, partial Fourier compressed sensing (PFCS), that combines compressed sensing (CS) and partial Fourier reconstruction. PFCS augments the original CS equation using conjugate symmetry information for missing measurements. To further improve image quality in order to reconstruct low-resolution EPRI images, a projection onto convex sets (POCS)-based phase map and a spherical-sampling mask are used in the reconstruction process. The PFCS technique was used in phantoms and in vivo SCC7 tumor mice to evaluate image quality and accuracy in estimating O2 concentration. ResultsIn both phantom and in vivo experiments, PFCS demonstrated the ability to reconstruct images more accurately with at least a 4-fold acceleration compared to traditional CS. Meanwhile, PFCS is able to better preserve the distinct spatial pattern in a phantom with a spatial resolution of 0.6mm. On phantoms containing Oxo63 solution with different oxygen concentrations, PFCS reconstructed linewidth maps that were discriminative of different O2 concentrations. Moreover, PFCS reconstruction of partially sampled data provided a better discrimination of hypoxic and oxygenated regions in a leg tumor compared to traditional CS reconstructed images. ConclusionsEPR images with an acceleration factor of four are feasible using PFCS with reasonable assessment of tissue oxygenation. The technique can greatly enhance EPR applications and improve our understanding cycling hypoxia. Moreover this technique can be easily extended to various MRI applications.

Widely Linear Sphere Decoder in MIMO Systems by Exploiting the Conjugate Symmetry of Linearly Modulated Signals

This paper investigates the widely linear processing (WLP) for the detection of circular signals, such as M-ary phase-shift keying (MPSK) signals and M-ary quadrature amplitude modulation (MQAM) signals. First, a unified mathematical model is derived to describe the conjugate symmetry of general MPSK/MQAM signals. In the unified model, a phase-rotation matrix (PRM) is introduced to partition the constellation of multiple-input multiple-output (MIMO) signals into subsets. Signals in a subset share the same PRM. Second, a widely linear receiver is proposed in each subset for MIMO detection. To avoid repetitive WLP in each subset, a widely linear sphere decoder (WLSD) is further proposed for MIMO systems. WLSD transforms the traditional sphere decoder (SD) searching for a true transmitted vector into a shrunk one by searching for the corresponding phase-rotation vector. Finally, the diversity order of WLSD is proven to be more than $N_R-\frac{N_T-1}{2}$ and less than $N_R$ , where $N_T$ (or $N_R$ ) denotes the number of transmitting (or receiving) antennas. Additional performance analysis is also conducted to quantify the signal-to-noise ratio improvement. The complexity analysis reveals that the candidate phase-rotation vectors of WLSD are no more than $(\frac{1}{2})^{N_T}$ of the SD candidates. Simulation results show that the proposed WLSD can achieve quasi-optimal bit error rate performance, while the computational complexity is reduced by more than a half compared with the Schnorr–Euchner sphere decoder.

Comparison of Two Simulation Methods in Electron Crystallography: BW Method and a Modified Direct Product Method of Scattering Matrix

In this paper, a modified direct product method of scattering matrix (DPSM) was presented and the calculation formula was derived as follows: ϕ ( z ) = ∑ n 1 n ! ( M z ) n ϕ ( 0 ) and ϕ ( z + e j ) = ∑ n 1 n ! ( M e j ) n ϕ ( z ) , where M is the scattering matrix of which the dimension can be reduced by ‘Bethe potential method’ drastically and therefore the calculation speed can be increased tremendously without losing accuracy very much. The results calculated with the DPSM method are in almost exact agreement with those calculated with BW method. However, the calculation speed for the modified DPSM method is approximately three times faster than that for the BW method. Furthermore, the DPSM is suitable for computing all types of matrices without requiring symmetry or conjugate symmetry.

An Efficient POCS Interpolation Method in the Frequency-Space Domain

Sampling irregularity in observed seismic data may cause a significant complexity increase in subsequent processing. Seismic data interpolation helps in removing this sampling irregularity, for which purpose complex-valued curvelet transform is used, but it is time-consuming because of the huge size of observed data. In order to improve efficiency as well as keep interpolation accuracy, I first extract principal frequency components using forward Fourier transform. The size of the principal frequency-space domain data is at least halved compared with that of the original time-space domain data because the complex-valued components of the representation of a real-valued signal (i.e., a complex-valued signal with zero as its imaginary component) exhibit conjugate symmetry in the frequency domain. Then, the projection onto convex projection (POCS) method is used to interpolate frequency-space data based on complex-valued curvelet transform. Finally, interpolated seismic data in the time-space domain can be obtained using inverse Fourier transform. Synthetic data and field data examples show that the efficiency can be improved more than two times and the performance is slightly better in the frequency-space domain compared with the POCS method directly performed in the time-space domain, which demonstrates the validity of the proposed method.

Recovery of Failed Element Signal with a Digitally Beamforming Using Linear Symmetrical Array Antenna

An antenna array element failure problem is one of the practical and challenging issues in the field of adaptive beamforming. The complete radiation pattern of the array is distorted when any one of the elements fails. Sidelobes level increases, nulls are shifted and null depth is also decreased tremendously. In order to mitigate the problem, we have given a new and easy approach coined as conjugate symmetry approach of the array. In this, the failed element is given a conjugate of the output from its symmetrical counterpart element in the array. The Classical Dolph-Chebyshev and Taylor pattern are taken as the test antenna. The simulation results of both patterns show the validity and presentation of the proposed approach.

Estimating absolute-phase maps using ESPIRiT and virtual conjugate coils.

To develop an ESPIRiT-based method to estimate coil sensitivities with image phase as a building block for efficient and robust image reconstruction with phase constraints. ESPIRiT is a new framework for calibration of the coil sensitivities and reconstruction in parallel magnetic resonance imaging. Applying ESPIRiT to a combined set of physical and virtual conjugate coils (VCC-ESPIRiT) implicitly exploits conjugate symmetry in k-space similar to VCC-GRAPPA. Based on this method, a new post-processing step is proposed for the explicit computation of coil sensitivities that include the absolute phase of the image. The accuracy of the computed maps is directly validated using a test based on projection onto fully sampled coil images and also indirectly in phase-constrained parallel-imaging reconstructions. The proposed method can estimate accurate sensitivities which include low-resolution image phase. In case of high-frequency phase variations VCC-ESPIRiT yields an additional set of maps that indicates the existence of a high-frequency phase component. Taking this additional set of maps into account can improve the robustness of phase-constrained parallel imaging. The extended VCC-ESPIRiT is a useful tool for phase-constrained imaging. Magn Reson Med 77:1201-1207, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Robust and fast beamforming with magnitude response constraints for multiple‐input multiple‐output radar

In this study, a new robust and fast beamformer is developed for multiple-input multiple-output radar to improve the robustness against steering vector (SV) mismatches. A convex robust model with magnitude response constraints (MRC) is established by using the conjugate symmetry characteristic of the transmitted–received SV. To reduce the computational complexity and the number of samples required, the full-dimensional weight vector (WV) is expressed as the Kronecker product of the transmitted and received array WVs. Thus, the convex problem is converted into a bi-quadratic cost function and it is solved by combining the bi-iterative algorithm and convex quadratic program. The proposed beamformer can flexibly control the beamwidth of the robust region and achieve high output signal-to-interference-plus-noise ratio. Moreover, the proposed method has lower computational complexity and faster sample convergence rate as compared with the traditional MRC-iterative second-order cone programming and MRC-semi-definite programming beamformers. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of the proposed beamformer.

Computationally Efficient 2-D DOA Estimation for L-Shaped Array With Automatic Pairing

As L-shaped array can provide good angle estimation performance and is easy to implement, many two-dimensional (2-D) direction-of-arrival (DOA) estimation algorithms have been developed. In this letter, we present a low-computation-complexity DOA estimation method for L-shaped array that exploits the conjugate symmetry property of the array manifold matrix to increase the effective array aperture and improve the angle estimation performance. Hence, the DOA estimation is obtained via combining propagator method (PM) with ESPRIT algorithm, which does not need spectrum peak search or additional angle pair matching procedure. Simulation results demonstrate the effectiveness of the proposed method.

Model of the Neutrino Mass Matrix With δ=-π/2 and θ_(23)=π/4

Experimental data have provided stringent constraints on the neutrino mixing parameters. In the standard parameterization the mixing angle θ_(23) is close to π/4. There is also evidence which shows that the CP violating phase is close to -π/2. We study the neutrino mass matrix reconstructed using this information and find several interesting properties. We show that a theoretical model based on the A_4 symmetry naturally predicts δ = -π/2 and θ_(23) = π/4 when the Yukawa couplings and scalar vacuum expectation values are real, reaching a μ－τ exchange and CP conjugate symmetry limit. In this case CP violation solely comes from the complex group theoretical Clebsh-Gordan coefficients. The model also predicts |V_(e2)| = 1/√3, consistent with the data. With complex Yukawa couplings the values for δ and θ_(23) can significantly deviate away from the symmetry values -π/2 and π/4, respectively. But |V_(e2)| = 1/√3 is not altered. This matrix is an excellent lowest order approximation for theoretical model buildings of the neutrino mass matrix.

CP violation in neutrino mixing with [formula omitted] in [formula omitted] Type-II seesaw model

We study a class of models for neutrino mass matrix in Type-II seesaw with A4 family symmetry. The resulting neutrino mass matrix can be naturally made to respect a μ–τ exchange plus CP conjugate symmetry (GLS) with the CP violating phase δ and the mixing angle θ23 predicted to be ±π/2 and π/4, respectively. When GLS is explicitly broken by complex Yukawa couplings, the model predictions for δ and θ23 can be significantly modified. Should future experiments indeed determine θ23 and δCP away from the GLS limit values, one then had to consider models with broken GLS. We study several simple scenarios to show how the modifications arise w̱hen GLS is broken and how future experiments can test this class of models.

A universal symmetry detection algorithm.

Research on symmetry detection focuses on identifying and detecting new types of symmetry. The paper presents an algorithm that is capable of detecting any type of permutation-based symmetry, including many types for which there are no existing algorithms. General symmetry detection is library-based, but symmetries that can be parameterized, (i.e. total, partial, rotational, and dihedral symmetry), can be detected without using libraries. In many cases it is faster than existing techniques. Furthermore, it is simpler than most existing techniques, and can easily be incorporated into existing software. The algorithm can also be used with virtually any type of matrix-based symmetry, including conjugate symmetry.

Canonical linearized Regge calculus: Counting lattice gravitons with Pachner moves

We afford a systematic and comprehensive account of the canonical dynamics of 4D Regge Calculus perturbatively expanded to linear order around a flat background. To this end, we consider the Pachner moves which generate the most basic and general simplicial evolution scheme. The linearized regime features a vertex displacement (`diffeomorphism') symmetry for which we derive an abelian constraint algebra. This permits to identify gauge invariant `lattice gravitons' as propagating curvature degrees of freedom. The Pachner moves admit a simple method to explicitly count the gauge and `graviton' degrees of freedom on an evolving triangulated hypersurface and we clarify the distinct role of each move in the dynamics. It is shown that the 1-4 move generates four `lapse and shift' variables and four conjugate vertex displacement generators; the 2-3 move generates a `graviton'; the 3-2 move removes one `graviton' and produces the only non-trivial equation of motion; and the 4-1 move removes four `lapse and shift' variables and trivializes the four conjugate symmetry generators. It is further shown that the Pachner moves preserve the vertex displacement generators. These results may provide new impetus for exploring `graviton dynamics' in discrete quantum gravity models.

Equiaffine structure and conjugate Ricci-symmetry of a statistical manifold

A condition for a statistical manifold to have an equiaffine structure is studied. The facts that dual flatness and conjugate symmetry of a statistical manifold are sufficient conditions for a statistical manifold to have an equiaffine structure were obtained in [4] and [5]. In this paper, a fact that a statistical manifold, which is conjugate Ricci-symmetric, has an equiaffine structure is given, where conjugate Ricci-symmetry is a weaker condition than conjugate symmetry. A condition for conjugate symmetry and conjugate Ricci-symmetry to coincide is also given.

Accurate fast field formulation for a uniformly moving source traveling above an impedance plane

The Lorentz transform, which can be applied to a uniformly moving source, effectively converts the time-domain wave equation to an equivalent problem in frequency-domain due to a stationary source. Standard fast field program (FFP) implementations apply the property of conjugate symmetry in the wavenumber domain for improved efficiency. Recent literature [D. Dragna et al., AIAA 52, 1928–1939 (2014)] suggests the use of a Dopplerized frequency-dependent impedance model to account for the effects of source motion. Consequently, the FFP kernel function is no longer identical for the positive and negative wavenumbers. Additional complications are introduced by the necessity to compute the positive and negative horizontal separation distances in the Lorentz frame to obtain a complete time history of sound pressures for the source approaching and receding from the receiver. Further development of the FFP algorithm in the Lorentz frame is explored such that a frequency-dependent impedance model is developed. Both moving line and point monopole sources are considered in the current investigation. Results are validated against direct numerical integration schemes and with the published time-domain solutions. Applications for an aircraft operating in cruise condition is also examined in the present study. [Work Sponsored by the Federal Aviation Administration.]

Conjugate Augmented Spatial Temporal Technique for 2-D DOA Estimation With L-Shaped Array

To solve the angle ambiguity problem when multiple sources have the same azimuth or elevation angles, a novel two-dimensional direction of arrival (2-D DOA) estimation method with L-shaped array based on conjugate augmented spatial temporal technique is developed in this letter. The basic idea of the proposed method is to utilize the conjugate symmetry property of the signal auto-correlation function with different delays to construct a conjugate augmented spatial-temporal cross-correlation matrix (CAST-CCM) and form joint diagonalization structure from the signal subspace corresponding to the CAST-CCM. Hence, the DOAs are estimated and paired automatically via joint diagonalization technique. The proposed method can handle the angle ambiguity problem efficiently and can also work in the underdetermined case. The effectiveness of the proposed method is verified through computer simulations.

Coarse Symbol Timing Synchronization Improved Algorithm for CMMB Mobile TV

There are some multipath and frequency offset in wireless transmission environment, in order to determine the correct starting position of each OFDM symbol, CMMB system must achieve accurate symbol synchronization for send- ing and receiving data, making FFT data transform window position in receiver consistent with IFFT window position in sender. This paper combined the specific frame structure of CMMB standard protocol, analyzed some influences of sym- bol synchronization timing errors in system, discussed the traditional ML (Maximum Likelihood) algorithm, the non data aided algorithm and the reverse conjugate symmetry direct algorithm, and based on the characteristics of these algorithm, proposed a coarse symbol timing synchronization improved algorithm according to CMMB mobile TV, the feasibility of this algorithm is verified in AWGN and multipath channel. Simulation results show that the performance of improved al- gorithm is better, there is no multi-peak of ML algorithm, and don't worry about appearing lat roof phenomenon like no data aided algorithm, and it also eliminates adjacent peak interference of the reverse conjugate symmetry direct algorithm, this algorithm is not limited by SNR, even in bad multipath channel condition, the approximate starting position of sym- bol can be estimated.

A Computationally Efficient Subspace Algorithm for 2-D DOA Estimation with L-shaped Array

In this letter, a computationally efficient subspace algorithm is developed for two-dimensional (2-D) direction-of-arrival (DOA) estimation with L-shaped array structured by two uniform linear arrays (ULAs). The proposed method requires neither constructing the correlation matrix of the received data nor performing the singular value decomposition (SVD) of the correlation matrix. The problem is solved by dealing with three vectors composed of the first column, the first row and diagonal entries of the correlation matrix, which reduces the computational burden. Simultaneously, the proposed method utilizes the conjugate symmetry to enlarge the effective array aperture, which improves the estimation precision. The simulation results are presented to validate the effectiveness of the proposed algorithm.