Noise Correlation Matrix Research Articles

New resolution independent approach to noise estimation in Minimum Noise Fraction denoising of tissues measured with Infrared Imaging

The Minimum Noise Fraction (MNF) was originally developed for remote sensing data denoising. However, due to the hyperspectral character of Infrared (IR) imaging data, MNF is becoming increasingly popular in this field. IR imaging obtains data rich in biochemical information, therefore, it is extensively applied in tissue analysis and classification. It is popular to use different IR objectives of different magnification, which combined with Focal Plane Array (FPA) detector of fixed pixels size, give varying projected pixel sizes and as a result – different spatial resolutions. The MNF method proposed by Green et al. uses a noise correlation matrix that is calculated based on neighboring pixel difference, which heavily depends on the registered image magnification and thus spatial resolution, leading to different denoising efficiencies and signal loss. Here, we presented a new resolution-independent approach to noise matrix estimation (MNF2) based on the 2 sequential scans of the sample. In this way, the data acquisition step is only minimally changed, while offering a uniform denoising step. We decided to test our method on representative breast tissue biopsy, due to its spatial and biochemical heterogeneity. We compared the performance of the new method for data measured using objectives giving different spatial pixel projections: low - 11.4 μm (3.5x), standard - 2.7 μm (15x), and high - 1.1 μm (36x). Results of this study show that conventional MNF for standard and low resolutions produces an altered denoised signal, while MNF2 gives a denoised signal of very good quality. In the case of high resolution data, standard MNF gives reasonable results, likewise proposed MNF2.

Performance evaluation of sound source localisation and tracking methods using multiple drones

This study evaluates methods to improve sound source localisation and tracking performance using microphone arrays from multiple drones. Previous studies have demonstrated the feasibility of multi-drone sound source tracking by triangulating their respective direction estimations using the MUltiple SIgnal Classification (MUSIC) algorithm. In addition, we evaluate techniques to reduce the influence of rotor noise. Namely, this includes a Wiener filter that utilises rotor noises' power spectral density (PSD) estimations and a noise correlation matrix (NCM) estimation scheme exploiting the geometries of the drone and the microphone array. This is to reduce the rotor noise's influence on the microphone array input correlation matrix prior to localising with MUSIC. Results show that applying the rotor noise reduction method improves localisation and tracking accuracy under a wider range of signal-to-noise ratios, regardless of the sound source tracking method.

Exact Noise Statistics in Equalized Polarization Multiplexing Systems in the Presence of Polarization Dependent Loss

In polarization multiplexing systems, signal and noise have different correlation matrices in the presence of polarization dependent loss (PDL). Therefore, the noise will be correlated after the signal equalization process, and the statistical characteristics of the noise correlation matrix is vital for the system capacity evaluation. In this paper, a stochastic differential equation (SDE) for the evolution of the noise correlation matrix after equalization is derived and the statistics of the correlation matrix elements are obtained by the related ordinary differential equations (ODEs). A threshold of the link gain, which equals half of the local PDL vector variance, exists. If the gain is above the threshold, one may ensure the average accumulated noise power not to grow exponentially. Monte Carlo simulations are conducted to verify the proposed theory and an excellent agreement is observed.

Robust superdirective beamforming for arbitrary sensor arrays

This paper presents a method of designing robust superdirective beamformers for arbitrary sensor arrays. First, the optimal weighting vector is transformed into an equivalent form based on the eigen–decomposition of the noise correlation matrix in an isotropic uniform noise field, and its entries will be indexed using mode orders instead of element numbers. Second, a parameter is weighted at the maximum–order entry in the modified weighting vector. The beampattern, directivity factor, and error sensitivity function can be expressed as functions of the parameter. Adjusting the parameter will achieve arbitrary–order superdirective beampatterns with different directivity factors or error sensitivity functions. Third, the closed–form expression of the parameter can be derived given a desired directivity factor or error sensitivity function. The final robust broadband superdirective beampatterns can then be readily synthesized. The proposed method, which is an extension of that previously proposed for circular sensor arrays, provides flexible schemes to designing robust broadband superdirective beamformers for arbitrary arrays in simulations and experiments.

A New Beamforming Approach Using 60 GHz Antenna Arrays for Multi-Beams 5G Applications

Recent studies and research have centred on new solutions in different elements and stages to the increasing energy and data rate demands for the fifth generation and beyond (B5G). Based on a new-efficient digital beamforming approach for 5G wireless communication networks, this work offers a compact-size circular patch antenna operating at 60 GHz and covering a 4 GHz spectrum bandwidth. Massive Multiple Input Multiple Output (M–MIMO) and beamforming technology build and simulate an active multiple beams antenna system. Thirty-two linear and sixty-four planar antenna array configurations are modelled and constructed to work as base stations for 5G mobile communication networks. Furthermore, a new beamforming approach called Projection Noise Correlation Matrix (PNCM) is presented to compute and optimise the fed weights of the array elements. The key idea of the PNCM method is to sample a portion of the measured noise correlation matrix uniformly in order to provide the best representation of the entire measured matrix. The sampled data will then be utilised to build a projected matrix using the pseudoinverse approach in order to determine the best fit solution for a system and prevent any potential singularities caused by the matrix inversion process. The PNCM is a low-complexity method since it avoids eigenvalue decomposition and computing the entire matrix inversion procedure and does not require including signal and interference correlation matrices in the weight optimisation process. The suggested approach is compared to three standard beamforming methods based on an intensive Monte Carlo simulation to demonstrate its advantage. The experiment results reveal that the proposed method delivers the best Signal to Interference Ratio (SIR) augmentation among the compared beamformers.

Noise and Conversion Analyses for High-T c Superconducting Harmonic Mixers: Theoretical Modeling and Experimental Verification

High- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> superconducting (HTS) harmonic mixers are attractive frontends for terahertz wireless communication and sensing applications. However, the investigation of HTS harmonic mixers has long been hindered by the lack of effective theoretical method in device modeling. This article presents a modeling approach for analyzing the noise and conversion properties of HTS harmonic mixers. By quantitively analyzing the contribution of the parasitic components to frequency conversion, a parasitics-selection based equivalent circuit model is built with the architecture complexity reduced to a six-port network. Besides, a fast hybrid-solution method that combines the single-tone current excitation and perturbation-derivation processing techniques, is developed for efficiently calculating the conversion impedance matrix for harmonic mixing. Detailed derivations are then carried out to acquire the semianalytic expressions of noise temperature and conversion gain after solving the noise correlation matrix for harmonic mixing. The presented modeling method has been verified by the fourth harmonic mixing experiments for a dual-band antenna-coupled HTS Josephson-junction mixer module. The measured and simulated results are in good agreement in terms of the noise temperature and conversion gain as well as their dependance on dc biasing, local oscillator pumping, and operating temperatures. The results have validated the effectiveness of the presented modeling method for analyzing the properties of HTS Josephson junction mixers.

Left–Right Ambiguity Resolution Methods for Closely Spaced Arrays

One linear array with omnidirectional sensors cannot discriminate between the azimuth angle and its complementary angle due to axisymmetry about the array axis. This article examines solutions to the bearing ambiguity problem known as left–right (LR) ambiguity resolution using two closely spaced parallel arrays. We design a second-order nulling (SoN) beamformer to produce a cardioid-type spatial response with a null electronically steered to the complementary angle of the direction of interest. Three methods—namely, SoN, null constrained beamformer (NCB), and 2-D direct beamformer (2-DDB), are studied. The performance is evaluated in correlated noise conditions modeled by a first-order auto-regressive process. This work establishes analytical results for the bound on the detection gain (DG) of the two parallel arrays in terms of the Rayleigh quotient of the circulant noise correlation matrix. A closed-form expression is developed for estimating the loss due to cardioid processing at closer inter-array spacing. The expressions are validated based on the deflection criterion. Twin-array processing using the 2-DDB method results in a higher DG, while cardioid-based beamformers give a higher rejection ratio (RR). Data from an at-sea experiment using a towed array are analyzed. Field results show that the deeper null achieved by the cardioid method results in a higher RR compared to 2-D direct beamformer. From the field data, approximately 19-dB LR discrimination is demonstrated at 1650 Hz for the broadside. Experimental results from a towed array corroborate theory and simulations.

Performance of a Flexible 12-Channel Head Coil in Comparison to Commercial 16- And 24-Channel Rigid Head Coils.

To compare the performance of a 12-channel flexible head coil (HFC12) with commercial 16-channel (HRC16) and 24-channel (HRC24) rigid coils. The phantom study was performed on a 1.5 T MR scanner with HFC12, HRC16, and HRC24. The SNR and noise correlation matrix of T1WI, T2WI, and diffusion weighted imaging (DWI) were measured. The SNR profiles were created according to the SNR. In addition, 1/g-factors were calculated in different acceleration directions. In the in vivo study, T1WI, T2WI, and DWI were performed in one healthy volunteer with three different coils. The SNR and noise correlation matrix were measured. In the phantom study and in vivo study, the SNR of HFC12 in the transverse, sagittal, and coronal planes was the highest, followed by HRC24, and that of HRC16 was the lowest. The SNR profiles showed that the SNR at the edge of HFC12 was the highest. The mean value of the noise correlation matrix of HFC12 was the highest. The 1/g-factor results showed that HFC12 obtained the best acceleration ability in the head-foot acceleration direction when the reduction factor was set to two. The SNR of HFC12 in most cortices was significantly higher than that of HRC16 and HRC24, except in the occipital cortex. The SNR of HRC24 in the occipital cortex was higher than that of HFC12. The SNR of HFC12 in T1WI, T2WI, and DWI was better than that of the HRC24 and HFC16. The SNR of HFC12 in the cortex was significantly higher than that of the commercial rigid head coil, except in the occipital cortex.

Экспериментальное исследование двумерного подавления помех в активном радаре на базе адаптивной антенной решетки для случая короткой выборки

The paper analyzes an experiment on two-dimensional (in azimuth and elevation) noise suppression in an active radar in the decimeter wavelength range. The radar includes an adaptive antenna array, the canvas of which has a rectangular topology. As jammers, a continuous tone generator is used, as well as a phase-shift keyed signal generator – a Barker code of length 11. In both cases, the interference can be considered narrowband. As a useful signal (reflected from the target), a Barker code of length 11, generated by the simulator, was used. The noise suppression was carried out by the power vector method, as well as by the method of direct inversion of the noise correlation matrix. The case of a short sample when evaluating the correlation matrix is considered separately, as the most interesting for practice in conditions of limited computing resources of digital signal processors. A set of scenarios is considered both in azimuth and in elevation. In all scenarios, there was one interference and one useful signal. For each of them, the estimation of losses in relation to signal-tonoise, the interference suppression coefficient was performed, and the directivity diagrams of the adaptive antenna array were formed. The processing of the experimental data showed the high efficiency of the power vector method. In all scenarios, interference is suppressed almost to the level of thermal noise.

Method of description for the dynamics of the signal delay change in discrete time with changing aircraft position in space

The article presents an innovative approach to the description of the aircraft range parameter in discrete time when simulating the process of its repositioning in space. A method of describing the dynamics of changes in signal delay in discrete time when the aircraft is changing its spatial position is proposed. Such a model adequately describes the change in signal delay in discrete time. The direction of estimation for the adequacy of radio signal delay change simulation in algorithms of optimum filtration is defined in accordance with the aerodynamic properties of the aircraft. Simulation of the signal delay dynamic change is carried out (it is completely described by the dynamics of change in the distance to the aircraft). The transformation stages of simulation data for the initial model in continuous time with realization of the standard Gaussian random numbers are justified. Information on the simulation data transformation taking into account the correlation matrix of discrete white noise is provided. A method of calculating the transition matrix through the Laplace transform is proposed. The scientific-applied direction of research is determined – it lies in the development of a method for the legitimate representation for the mathematical model of aircraft’s changing range in discrete time within one-dimensional space: the longitudinal and the transverse dimensions. This approach takes into account the continuous description for a system of stochastic differential equations. A comprehensive algorithm for modeling the values of discrete white noise on modern computer equipment and calculating the dynamics of the aircraft range parameter changes is proposed. This algorithm allows to correctly form the a priori information about the change of the vector parameters of the aircraft spatial position at discrete moments of time. As a result, it was shown that the use of the obtained information in the optimal filtering algorithms minimizes the error when determining distance to the aircraft and, accordingly, allows to increase the accuracy and adequacy of the signal delay simulation in discrete time. The results of this research can be used in modernization of the existing models and development of promising on-board radar stations, integrated rangefinders, systems of radio technical reconnaissance and electronic warfare systems, as well as in technical implementation of aircraft flight simulation systems.

Efficient learning of quantum noise

Noise is the central obstacle to building large-scale quantum computers. Quantum systems with sufficiently uncorrelated and weak noise could be used to solve computational problems that are intractable with current digital computers. There has been substantial progress towards engineering such systems1–8. However, continued progress depends on the ability to characterize quantum noise reliably and efficiently with high precision9. Here, we describe such a protocol and report its experimental implementation on a 14-qubit superconducting quantum architecture. The method returns an estimate of the effective noise and can detect correlations within arbitrary sets of qubits. We show how to construct a quantum noise correlation matrix allowing the easy visualization of correlations between all pairs of qubits, enabling the discovery of long-range two-qubit correlations in the 14-qubit device that had not previously been detected. Our results are the first implementation of a provably rigorous and comprehensive diagnostic protocol capable of being run on state-of-the-art devices and beyond. These results pave the way for noise metrology in next-generation quantum devices, calibration in the presence of crosstalk, bespoke quantum error-correcting codes10 and customized fault-tolerance protocols11 that can greatly reduce the overhead in a quantum computation. A protocol for the reliable, efficient and precise characterization of quantum noise is reported and implemented in an architecture consisting of 14 superconducting qubits. Correlated noise within arbitrary sets of qubits can be easily detected.

Technical Note: A custom-designed flexible MR coil array for spine radiotherapy treatment planning.

To assess the performance and optimize the MR image quality when using a custom-built flexible radiofrequency (RF) spine coil array fitted between the immobilization device and the patient for spine radiotherapy treatment planning. A 32 channel flexible custom-designed receive-only coil array has been developed for spine radiotherapy simulation for a 3T Philips MR scanner. Coil signal-to-noise performance and interactions with standard vendor hardware were assessed. In four volunteers, immobilization molds were created with a dummy version of the array within the mold, and subjects were scanned using the custom array in the mold. Phantoms and normal volunteers were scanned with both the custom spine coil array and the vendor's FDA-approved in-table posterior coil array to compare performance. The superior-inferior field of view for the custom spine array was ~30cm encompassing at least 10 vertebrae. A noise correlation matrix showed at least 25dB isolation between all coil elements. Signal-to-noise ratio (SNR) calculated on a phantom scan at the depth of the spinal cord was a factor of 3 higher with the form-fit spine array as compared to the vendor's posterior coil array. The body coil B1 transmit map was equivalent with and without the spine array in place demonstrating that the elements are decoupled from the body coil. Volunteer imaging showed improved SNR as compared to the vendor's posterior coil array. The custom array permitted a high degree of acceleration making possible the acquisition of isotropic high-resolution 1.1×1.1×1.1mm3 three-dimensional data set over a 30-cm section of the spine in less than 5min. The custom-designed form-fitting flexible spine coil array provided enhanced SNR and increased acceleration compared to the vendor's posterior array. Future studies will assess MR-based spinal cord imaging with the custom coil in comparison to CT myelogram.

Computational Analysis of a Dual Loop Dipole Antenna and Its Interleaving Array for Improving Transceiver ∣B1∣-field for MRI

This article intends to present the electromagnetic (EM) insight of the operation of a double loop shaped dual loop dipole (DLD) antenna as a single-channel transceiver coil and in an array configuration of multi-channel transceiver coil, designed to provide high signal-to-noise ratio (SNR) by using numerical simulations for 300 MHz magnetic resonance imaging (MRI). Thus, this section includes the comparison of DLD antenna and commonly used loop coils through EM simulations. The use of a DLD antenna is proposed to address the length issue that traditional straight dipole have by making a spiral type in a loop style, while having the same effective physical length of the straight dipole. The magnetic flux density (∣B1∣)-fields of the DLD antenna and the traditional loop coil are compared by field maps acquired by EM simulations. In addition, the DLD antenna has been extended to a 7-channels array, for which the magnetic field coupling between each coil is analyzed and presented through the noise correlation matrix. The use of the DLD antenna exhibits higher ∣B1∣-field intensity while keeping the similar uniformity than a surface loop coil. We use the DLD antenna 7-channel array to observe its utility as multi-channel with short distance overlap between elements; each element is approximately 37 mm away from neighboring element. Transceiver array arrangements also show improved coil performance, especially the interleaving configuration with loop coil indicates lowered mutual inductance coupling at calculated noise correlation matrix. The proposed DLD antenna is expected to induce rapid imaging and high ∣B1∣-field, when expanded to multi-channel planar or volume configuration since it can maximize the number of configuring coil elements within limited imaging area leading effective parallel imaging and deeper penetration depth due to the traveling wave.

Spectral-spatial Classification of Hyperspectral Images Using Signal Subspace Identification and Edge-preserving Filter

Hyperspectral images in remote sensing include hundreds of spectral bands that provide valuable information for accurately identify objects. In this paper, a new method of classifying hyperspectral images using spectral spatial information has been presented. Here, using the hyperspectral signal subspace identification (HYSIME) method which estimates the signal and noise correlation matrix and selects a subset of eigenvalues for the best representation of the signal subspace in order to minimize the mean square error, subsets from the main sample space have been extracted. After subspace extraction with the help of the HYSIME method, the edge-preserving filtering (EPF), and classification of the hyperspectral subspace using a support vector machine (SVM), results were then merged into the decision-making level using majority rule to create the spectral-spatial classifier. The simulation results showed that the spectral-spatial classifier presented leads to significant improvement in the accuracy and validity of the classification of Indiana, Pavia and Salinas hyperspectral images, such that it can classify these images with 98.79%, 98.88% and 97.31% accuracy, respectively.

Noise Wave Modeling of an SIS Mixer and Its IF Circuit Using Tucker's Quantum Theory of Mixing

Tucker's Quantum Theory of Mixing (QTM) is widely used to model the conversion gain and noise temperature of SIS mixers. In particular, the theory describes the phenomenon of non-classical conversion gain and that of infinite or even negative output impedances in inductively tuned SIS mixers. Common microwave noise theory is inadequate to describe the operation of the IF circuit connected to such mixers. In this paper, we report the use of the noise wave formalism to model the noise properties of a Double-Side-Band SIS mixer together with an IF isolator and low noise amplifier cascade. Starting from QTM, we derive the 4 noise parameters of the SIS mixer, together with an approximate 2-port chain matrix with an upper-side-band RF input port and an IF output port. These matrices are cascaded with the noise correlation matrix of the IF circuit to form a complete noise model of the SIS receiver. Optimum source impedance for the receiver can be derived from this noise model, which can be used in efficient CAD modeling of a complete SIS receiver.

A combined 32-channel receive-loops/8-channel transmit-dipoles coil array for whole-brain MR imaging at 7T.

PurposeMultichannel receive arrays provide high SNR and parallel‐imaging capabilities, while transmit‐only dipole arrays have been shown to achieve a large coverage of the whole‐brain including the cerebellum. The aim of this study was to develop and characterize the performances of a 32‐channel receive‐only loop array combined with an 8‐channel dipole coil array at 7T for the first time.MethodsThe 8Tx‐dipoles/32Rx‐loops coil array was characterized by the SNR, g‐factors, noise correlation matrix, accelerated image quality, and B1+ maps, and compared with a commercial 1Tx‐birdcage/32Rx‐loops array. Simulated and measured B1+ maps were shown for the 8Tx‐dipoles/32Rx‐loops coil array and compared with the 8Tx/Rx dipole array.ResultsThe in‐house built 32‐channel receive coil demonstrated a large longitudinal coverage of the brain, particularly the upper neck area. G‐factors and accelerated MR acquisitions demonstrated robust performances up to R = 4 in 2D, and R = 8 (4 × 2) in 3D. A 83% increase in SNR was measured over the cerebellum with the in‐house built 8Tx/32Rx coil array compared to the commercial 1Tx/32Rx, while similar performances were obtained in the cerebral cortex.ConclusionsThe combined 32‐channel receive/8‐channel transmit coil array demonstrated high transmit‐receive performances compared to the commercial receive array at 7T, notably in the cerebellum. We conclude that in combination with parallel transmit capabilities, this coil is particularly suitable for whole‐brain MR studies at 7T.

Distributed Rate-Constrained LCMV Beamforming

In this letter, we propose a decentralized framework for rate-distributed linearly constrained minimum variance (LCMV) beamforming in wireless acoustic sensor networks. To save the energy usage within the network, we propose to minimize the transmission cost and put a constraint on the noise reduction performance. Subsequently, we decentralize the obtained LCMV filter structure by exploiting an imposed block diagonal form of the noise correlation matrix. As a result, the beamformer weights are calculated in a decentralized fashion and each node can determine its quantization rate locally. Finally, numerical results validate the proposed method.

The Theory of Special Noise Invariants

This paper reports a novel systematic theory of the noise invariants of two-port linear noisy networks under lossless reciprocal input and output impedance transformations. The theory clarifies the relationship between the circuit theory of linear noisy networks and the theory of four noise parameters, which are widely applied in the design of low-noise amplifiers (LNAs). In particular, we prove that the fundamental noise invariants under input and output impedance transformations are the eigenvalues of a permuted version of the noise correlation matrix and that there is no feedback operation that preserves them. Known invariants, such as the minimum equivalent noise temperature ${T}_{{N}{min}}$ and ${N}$ , may be expressed in terms of such eigenvalues. In addition, we provide a complete characterization of the four noise parameters of two-port passive dissipative networks in terms of their gain parameters and derive the condition under which the invariant ${4N}{T}_{{0}}{/}{T}_{{N}{min}}$ of passive nonreciprocal networks is lower than two. We also extend the theory of special noise invariants to LNAs with lossy input matching network. Overall, the impact of the findings emerging from the theory is highlighted through theorems, remarks, circuit examples, and studies on widespread design methodologies.

잡음지수분석기의 새로운 교정방법과 잡음상관행렬 측정

잡음지수분석기의 새로운 교정방법과 잡음상관행렬 측정

Computer‐aided noise analysis of a multiwall carbon nanotube

In this work, a novel approach for the computer-aided noise analysis of a multiwall carbon nanotube (MWCNT) is proposed. A transmission line model of the MWCNT and a noise correlation matrix based on admittance representation are used for the computer-aided noise analysis. This work presents a simple, fast and effective noise analysis approach for the MWCNT. The noise figure is computed for different values of the parameters of the MWCNT for determining the effects of parameter values on the noise figure of the MWCNT. The results of the computer-aided noise analysis of the MWCNT are given and discussed in detail. According to the results, the variation of the distance from the ground plane of the outer shell has little effect on the value of noise figure, when the value of inner radius or the total number of shells increases the value of noise figure decreases. Therefore the noise figure decreases with increasing diameter because the diameter increases with the increasing value of inner radius and the total number of shells. The value of noise figure increases when the value of nanotube length or physical absolute temperature increases. The value of noise figure decreases with the decreasing value of source admittance.