Noise Vector Research Articles

Robust Sum MSE Optimization for Downlink Multiuser MIMO Systems With Arbitrary Power Constraint: Generalized Duality Approach

This paper considers linear minimum mean-square-error (MMSE) transceiver design problems for downlink multiuser multiple-input multiple-output (MIMO) systems where imperfect channel state information is available at the base station (BS) and mobile stations (MSs). We examine robust sum mean-square-error (MSE) minimization problems. The problems are examined for the generalized scenario where the power constraint is per BS, per BS antenna, per user or per symbol, and the noise vector of each MS is a zero-mean circularly symmetric complex Gaussian random variable with arbitrary covariance matrix. For each of these problems, we propose a novel duality based iterative solution. Each of these problems is solved as follows. First, we establish a novel sum average mean-square-error (AMSE) duality. Second, we formulate the power allocation part of the problem in the downlink channel as a Geometric Program (GP). Third, using the duality result and the solution of GP, we utilize alternating optimization technique to solve the original downlink problem. To solve robust sum MSE minimization constrained with per BS antenna and per BS power problems, we have established novel downlink-uplink duality. On the other hand, to solve robust sum MSE minimization constrained with per user and per symbol power problems, we have established novel downlink-interference duality. For the total BS power constrained robust sum MSE minimization problem, the current duality is established by modifying the constraint function of the dual uplink channel problem. And, for the robust sum MSE minimization with per BS antenna and per user (symbol) power constraint problems, our duality are established by formulating the noise covariance matrices of the uplink and interference channels as fixed point functions, respectively. We also show that our sum AMSE duality are able to solve other sum MSE-based robust design problems. Computer simulations verify the robustness of the proposed robust designs compared to the nonrobust/naive designs.

Performance analysis and improvement of dither modulation under the composite attacks

The first goal of this article is to analyze the performance of dither modulation (DM) against the composite attacks including valumetric scaling, additive noise and constant change. The analyzes are developed under the assumptions that the host vector and noise vector are mutually independent and both of them have independently and identically distributed components. We derive the general expressions of the probability density functions of several concerned signals and the decoding error probability. The specific theoretical results are provided for the case of generalized Gaussian host and noise. Based on the analyzes, the performance of DM is predicted for different scenarios with a high degree of accuracy and evaluated for different distribution models of host and noise signals. Numerical simulations confirm the validity of the given theoretical analyzes. Then, we address to improve the robustness of DM against valumetric scaling plus constant change. The normalized dither modulation (NDM) is presented, which works by constructing a gain-invariant vector with zero mean for quantization. Performance analysis shows that NDM is theoretically invariant to valumetric scaling and constant change and achieves similar performance to DM in other aspects. The performance of NDM is further improved by weighting the quantization errors. Experiments on real images also show the advantage of NDM over DM subject to amplitude scaling and constant change.

Evaluation of fermion loops applied to the calculation of the [formula omitted] mass and the nucleon scalar and electromagnetic form factors

The exact evaluation of the disconnected diagram contributions to the flavor-singlet pseudo-scalar meson mass, the nucleon σ-term and the nucleon electromagnetic form factors is carried out utilizing GPGPU technology with the NVIDIA CUDA platform. The disconnected loops are also computed using stochastic methods with several noise reduction techniques. Various dilution schemes as well as the truncated solver method are studied. We make a comparison of these stochastic techniques to the exact results and show that the number of noise vectors depends on the operator insertion in the fermion loop.

Critical Fluctuations in Cortical Models Near Instability

Computational studies often proceed from the premise that cortical dynamics operate in a linearly stable domain, where fluctuations dissipate quickly and show only short memory. Studies of human electroencephalography (EEG), however, have shown significant autocorrelation at time lags on the scale of minutes, indicating the need to consider regimes where non-linearities influence the dynamics. Statistical properties such as increased autocorrelation length, increased variance, power law scaling, and bistable switching have been suggested as generic indicators of the approach to bifurcation in non-linear dynamical systems. We study temporal fluctuations in a widely-employed computational model (the Jansen–Rit model) of cortical activity, examining the statistical signatures that accompany bifurcations. Approaching supercritical Hopf bifurcations through tuning of the background excitatory input, we find a dramatic increase in the autocorrelation length that depends sensitively on the direction in phase space of the input fluctuations and hence on which neuronal subpopulation is stochastically perturbed. Similar dependence on the input direction is found in the distribution of fluctuation size and duration, which show power law scaling that extends over four orders of magnitude at the Hopf bifurcation. We conjecture that the alignment in phase space between the input noise vector and the center manifold of the Hopf bifurcation is directly linked to these changes. These results are consistent with the possibility of statistical indicators of linear instability being detectable in real EEG time series. However, even in a simple cortical model, we find that these indicators may not necessarily be visible even when bifurcations are present because their expression can depend sensitively on the neuronal pathway of incoming fluctuations.

Disturbance rejection in space applications: Problems and solutions

Navigation, control and guidance of the propulsive phase of planetary landing, e.g. on Mars (or the Moon), with a soft landing being the only target, are driven by Inertial Measurement Units and a radar altimeter/velocimeter. Their measurements are affected by bias and scale errors. The latter ones are aggravated by the attitude navigation error as it accumulates during the ballistic (and aerodynamic) flight after orbiter separation and couples for most of the descent trajectory with the vehicle axis inclination from the local vertical direction. By complementing the center-of-mass dynamics with appropriate disturbance state equations driven by noise vectors and estimating the noise from the model error (plant measurements minus model output), scale errors and bias can be retrieved in real time in the form of disturbance state variables. Although a similar complement is adopted in the standard navigation algorithms, it takes the form of an output disturbance, which may lead to unobservability. In this paper instead, the disturbance complement is designed to be fully observable, which may require that the derivatives of smooth systematic errors be pushed up to the command channel (a form of back-stepping). It is then viable, unlike standard navigation, to eliminate them from position and velocity tracking errors through disturbance rejection, under appropriate convergence conditions and sensor layout. It will, however, be demonstrated in this paper that the same result cannot be achieved under pure feedback control. Since constant errors (bias) become zero through back-stepping, a well known fact derives: bias can only be eliminated by disposing of supplementary sensors. To further enlighten and solve the question of bias rejection, a further case study is treated. The attitude control of drag-free satellites is considered, where fine accelerometers allow for the rejection of wide-band aerodynamic torques (think of low-Earth orbit spacecrafts) at the price of attitude divergence because of accelerometer bias and drift. The spacecraft attitude can be made bounded and accurate, if bias and drift are modeled as angular accelerations, affecting the attitude. They are estimated by attitude sensors like star trackers and then are rejected by the attitude control. The results in the soft landing and drag free case studies are illustrated by simulated runs and Monte Carlo trials.

Multiuser Multi-Hop MIMO Relay Systems with Correlated Fading Channels

In this letter, we address multiuser multi-hop multiple-input multiple-output (MIMO) relay communication systems with correlated MIMO fading channels. In particular, we consider the practical scenario where the channel fading is fast and thus the instantaneous channel state information (CSI) is only available at the destination node, but unknown at all users and all relay nodes. We derive the structure of the optimal user precoding matrices and relay amplifying matrices that maximizes the users-destination ergodic sum mutual information. Compared with existing works, our results are more general, since we address multiuser scenarios, consider MIMO relays with a finite dimension, and take into account the noise vector at each relay node.

High-accuracy direction finding in multipath environment with short-wave antenna arrays comprising a small number of elements

A method for short-wave multipath direction finding is considered. The method allows high-accuracy determination of the directions of arrival and the amplitudes of a priori unknown arriving signals through the use of an antenna array comprising a small number of independent receiving elements with narrow-bandwidth filters placed at their inputs. An algorithm based on eigenvector decomposition of the correlation matrix of the complex signals arriving at the inputs of the radiating elements in each subband; separation of the eigenvectors into signal vectors and noise vectors; determination of the receiving-antenna eigenpatterns from the obtained vectors; and substantiation of the functional equation that allows, with the antenna eigenpatterns taken into account, the signals’ amplitudes and angles of arrival of the signals to be determined, is proposed. The results of a numerical simulation, which confirm the high accuracy of direction finding by the proposed method, are presented.

A Non-Iterative Technique for Phase Noise ICI Mitigation in Packet-Based OFDM Systems

A practical approach for detecting packet-based orthogonal-frequency-division multiplexing (OFDM) signals in the presence of phase noise is presented. An OFDM packet consists of several OFDM symbols with full-pilot symbols at the beginning followed by consecutive data symbols. Based on the full-pilot OFDM symbol, a frequency-domain joint phase noise and channel vector estimator is first derived. It is shown that the phase noise vector can be estimated by maximizing a constrained quadratic form without requiring knowledge of the channel vector. This estimated phase noise vector is then used to compute the least squares channel estimator. Assuming that the channel is constant during each packet, the estimated channel is used in subsequent data OFDM symbols for equalization and data detection. Since phase noise changes from one OFDM symbol to the next, the scattered pilots in each data OFDM symbol are used to non-iteratively estimate and mitigate the phase noise induced interference. A significant improvement in the signal-to-interference-plus-noise ratio is achieved using the proposed algorithm.

A Novel Delay- and Reliability- Aware Inter-Vehicle Routing Protocol

Intelligent transportation systems could improve transportation safety, driving assistance and traffic management system. Vehicular Ad hoc Network (VANET) is an emerging field of technology, embedding wireless communication networks into vehicles to achieve intelligent transportation systems. The development of such systems pose many unique challenges like designing routing protocols that not only forward packets with good end to end delay but also take into consideration the reliability and progress in data packets forwarding. In this article, we begin by presenting a review of recent unicast, geocast and broadcast routing protocols for message transmission. We then outline a novel Delay and Reliability aware Routing (DR 2 ) protocol that addresses these challenges (forwarding packets with low latency, high reliability and fast progress toward destination). Furthermore, our DR 2 protocol uses cross layer communication between MAC (Medium Access Control) and network layer. That is, the MAC layer observes the Signal to Noise (SNR), delay and velocity vector difference metrics for all paths of neighboring nodes, network layer then could select the best preferable path based on fuzzy inference system. We also used H∞ technique to optimize the membership functions and then tune it with rapid changing topology of VANET. To achieve a fair comparison with other routing protocols, we have implemented the proposed DR 2 protocol in Network Simulator 2 (NS 2). The preliminary results show that the proposed DR 2 protocol is able to improve end- to-end delay in sparse traffic conditions and packet delivery ratio in error prone urban vehicular scenarios.

Unscented Kalman filtering in the additive noise case

The unscented Kalman filter (UKF) has four implementations in the additive noise case, according to whether the state is augmented with noise vectors and whether a new set of sigma points is redrawn from the predicted state (which is so-called resampling) for the observation prediction. This paper concerns the differences of performances for those implementations, such as accuracy, adaptability, computational complexity, etc. The conditionally equivalent relationships between the augmented and non-augmented unscented transforms (UTs) are proved for several sampling strategies that are commonly used. Then, we find that the augmented and non-augmented UKFs have the same filter results with the additive measurement noise, but only have the same state predictions with the additive process noise. Resampling is not believed to be necessary in some researches. However, we find out that resampling can be helpful for an adaptive Kalman gain. This will improve the convergence and accuracy of the filter when the large scale state modeling bias or unknown maneuvers occur. Finally, some universal designing principles for a practical UKF are given as follows: 1) for the additive observation noise case, it’s better to use the non-augmented UKF; 2) for the additive process noise case, when the small state modeling bias or maneuvers are involved, the non-resampling algorithms with state whether augmented or not are candidates for filters; 3) the resampling and non-augmented algorithm is the only choice while the large state modeling bias or maneuvers are latent.

Fom classical to Bayesian estimators in the interpretation of MEG and EEG measurements

Event Abstract Back to Event Fom classical to Bayesian estimators in the interpretation of MEG and EEG measurements Jukka Sarvas1* and Risto Ilmoniemi2 1 Aalto University , Athena project team, Finland 2 Aalto University , Department of Biomedical Engineering and Computational Science, Finland MEG and EEG measurements can be modeled by the equation y = A x + e. Here y is the data vector, A is the observation matrix, x is the unknown parameter vector, and e is the noise vector. Due to noise or possible illposedness of A, the equation cannot be solved for x exactly, and the solution x(y) becomes an estimator to the true x. Now a practical question is how to choose a good solving method, i.e. a good estimator x(y). In this paper we show how a search for better estimators leads from the classical to Bayesian estimators. The usual choice is a least-squares estimator, which, however, due to the possible illposedness of A, is often unstable, and regularization is needed. The classical regularized estimators are the truncated-singular-value, Tikhonov and Wiener estimators. The amount of regularization can be determined, e.g., by Morozov's principle. Usually, however, one has prior knowledge on the unknown x, which can be used to find better estimators than Morozov's principle yields. We show that in a fairly elementary way one can, for these estimator types, find linear minimum mean square error (MMSE) estimators which make full use of both the data y and the prior knowledge on x.This result raises the question whether one can still find better estimators if linearity is not required. A complete answer is given by the Bayesian approach: the Bayesian posterior mean estimator always is the best possible MMSE estimator. If the prior knowledge and the noise are Gaussian, this estimator is linear and includes the MMSE Tikhonov and Wiener ones as special cases. We also show how the hierarchical Bayesian approach can be used to still improve the Tikhonov estimator. The various estimators will be illustrated by numerical examples with simulated measurement data. Conference: Biomag 2010 - 17th International Conference on Biomagnetism , Dubrovnik, Croatia, 28 Mar - 1 Apr, 2010. Presentation Type: Poster Presentation Topic: MEG Modeling Citation: Sarvas J and Ilmoniemi R (2010). Fom classical to Bayesian estimators in the interpretation of MEG and EEG measurements. Front. Neurosci. Conference Abstract: Biomag 2010 - 17th International Conference on Biomagnetism . doi: 10.3389/conf.fnins.2010.06.00063 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 21 Mar 2010; Published Online: 21 Mar 2010. * Correspondence: Jukka Sarvas, Aalto University, Athena project team, Espoo, Finland, jukka.sarvas@tkk.fi Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Jukka Sarvas Risto Ilmoniemi Google Jukka Sarvas Risto Ilmoniemi Google Scholar Jukka Sarvas Risto Ilmoniemi PubMed Jukka Sarvas Risto Ilmoniemi Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Color image denoising based on noise characteristic and vector median filtering

In order to effectively denoise the color image,while preserving image detail information,and increase processing speed,a new noise pinpointing method based on noise characteristic was proposed according to the analysis of noise characteristic of color images.Combined with the modified Vector Median Filtering(VMF)algorithm,the detected noise was denoised.Experimental results show that the algorithm can preserve the detail of image very well when restraining noise effectively,and its computation time is only half of the classical vector median filtering algorithm.

Spatial-frequency tuning in the pooling of one- and two-dimensional motion signals

Cortical neurons that initially extract motion signals have small receptive-fields, and narrow orientation- and bandpass-spatial-frequency tuning. Accurate extraction of the veridical motion of objects typically requires the global pooling of the output of multiple local-motion units across orientation and space. We examined whether the narrow spatial-frequency tuning present at the local-motion level is preserved at the global-motion-pooling stage. Stimuli consisted of numerous drifting Gabor or plaid elements that were either signal (carrier drift-speed consistent with a given global-motion vector) or noise (drift speed consistent with a random, noise vector). The carrier spatial-frequencies of the signal and noise elements were independently varied. Regardless of the frequency of the signal elements, broad low-pass masking functions were obtained for both Gabor (one-dimensional) and Plaid (two-dimensional) conditions when measuring the threshold signal ratio for identification of the global-motion direction. For the Gabor stimuli, this pattern of results was also independent of the relative orientations of the signal and noise elements. These results indicate that in the global-motion pooling of one-dimensional and two-dimensional signals, local-motion signals of all spatial frequencies are pooled into a single system that exhibits broadband, low-pass tuning.

Noise correlations and SNR in phased-array MRS

The acquisition of magnetic resonance spectroscopy (MRS) signals by multiple receiver coils can improve the signal-to-noise ratio (SNR) or alternatively can reduce the scan time maintaining a reliable SNR. However, using phased array coils in MRS studies requires efficient data processing and data combination techniques in order to exploit the sensitivity improvement of the phased array coil acquisition method. This paper describes a novel method for the combination of MRS signals acquired by phased array coils, even in presence of correlated noise between the acquisition channels. In fact, although it has been shown that electric and magnetic coupling mechanisms produce correlated noise in the coils, previous algorithms developed for MRS data combination have ignored this effect. The proposed approach takes advantage of a noise decorrelation stage to maximize the SNR of the combined spectra. In particular Principal Component Analysis (PCA) was exploited to project the acquired spectra in a subspace where the noise vectors are orthogonal. In this subspace the SNR weighting method will provide the optimal overall SNR. Performance evaluation of the proposed method is carried out on simulated (1)H-MRS signals and experimental results are obtained on phantom (1)H-MR spectra using a commercially available 8-element phased array coil. Noise correlations between elements were generally low due to the optimal coil design, leading to a fair SNR gain (about 0.5%) in the center of the field of view (FOV). A greater SNR improvement was found in the peripheral FOV regions.

Reliability Analysis in Kalman Filteirng

This manuscript centers on the reliability theory and its applications in Kalman filtering. Especially, it delivers a distinct derivation of the redundancy contribution - the key element of reliability theory for the Kalman filter algorithm that has not been comprehensively discussed in literature at present. A distinction is made between the system innovation vector and the measurement (or pseudo measurement) residual vector. This allows to directly analyse the observation vector and the process noise vector. Particular attention is paid not only to the theoretical fundamentals of the reliability, and also to the

Moments of nucleon’s parton distribution for the sea and valence quarks from lattice QCD

We extend the study of lowest moments, $<x>$ and $<x^2>$, of the parton distribution function of the nucleon to include those of the sea quarks; this entails a disconnected insertion calculation in lattice QCD. This is carried out on a $16^3 \times 24$ quenched lattice with Wilson fermion. The quark loops are calculated with $Z_2$ noise vectors and unbiased subtractions, and multiple nucleon sources are employed to reduce the statistical errors. We obtain 5$\sigma$ signals for $<x>$ for the $u,d,$ and $s$ quarks, but $<x^2>$ is consistent with zero within errors. We provide results for both the connected and disconnected insertions. The perturbatively renormalized $<x>$ for the strange quark at $\mu = 2$ GeV is $<x>_{s+\bar{s}} = 0.027 \pm 0.006$ which is consistent with the experimental result. The ratio of $<x>$ for $s$ vs. $u/d$ in the disconnected insertion with quark loops is calculated to be $0.88 \pm 0.07$. This is about twice as large as the phenomenologically fitted $\displaystyle\frac{< x>_{s+\bar{s}}}{< x>_{\bar{u}}+< x>_{\bar{d}}}$ from experiments where $\bar{u}$ and $\bar{d}$ include both the connected and disconnected insertion parts. We discuss the source and implication of this difference.

Time-domain equalisation for discrete multi-tone transceivers: new results and performance analysis

The time-domain equaliser (TEQ) is a commonly used device to shorten the channel impulse response in a discrete multitone (DMT) receiver. Many methods have been proposed to design the TEQ with a capacity maximisation criterion. An implicit assumption used by existing methods is that circular convolution can be conducted for the noise signal and the TEQ. This assumption is not valid because the noise vector, observed in a DMT symbol, does not have a cyclic prefix. A similar assumption is also made for the residual inter-symbol interference (ISI) signal. Because of these invalid assumptions, the TEQ-filtered noise and residual ISI powers in each subcarrier were not properly evaluated. As a result, optimum solutions derived are not actually optimal. This paper attempts to resolve this problem. We first analyse the statistical properties of the TEQ-filtered noise signal and the residual ISI signal in detail, and derive precise formulae for the calculation of the TEQ-filtered noise and residual ISI powers. Then, we re-formulate the capacity maximisation criterion to design the true optimum TEQ. Simulations show that the proposed method outperforms the existing ones, and its performance closely approaches the theoretical upper bound.

Optimum fuzzy filters for phase-contrast magnetic resonance imaging segmentation

To develop and validate a multidimensional segmentation and filtering methodology for accurate blood flow velocity field reconstruction from phase-contrast magnetic resonance imaging (PC MRI). The proposed technique consists of two steps: (1) the boundary of the vessel is automatically segmented using the active contour approach; and (2) the noise embedded within the segmented vector field is selectively removed using a novel fuzzy adaptive vector median filtering (FAVMF) technique. This two-step segmentation process was tested and validated on 111 synthetically generated PC MRI slices and on 10 patients with congenital heart disease. The active contour technique was effective for segmenting blood vessels having a sensitivity and specificity of 93.1% and 92.1% using manual segmentation as a reference standard. FAVMF was the superior technique in filtering out noise vectors, when compared with other commonly used filters in PC MRI (P < 0.05). The peak wall shear rate calculated from the PC MRI data (248 +/- 39 sec(-1)), was significantly decreased to (146 +/- 26 sec(-1)) after the filtering process. The proposed two-step segmentation and filtering methodology is more accurate compared to a single-step segmentation process for post-processing of PC MRI data.

Tug-of-war with noise: A game-theoretic view of the p-Laplacian

Fix a bounded domain Ω⊂Rd, a continuous function F:∂Ω→R, and constants ε>0 and 1<p,q<∞ with p−1+q−1=1. For each x∈Ω, let uε(x) be the value for player I of the following two-player, zero-sum game. The initial game position is x. At each stage, a fair coin is tossed, and the player who wins the toss chooses a vector v∈B̲(0,ε) to add to the game position, after which a random noise vector with mean zero and variance (q/p)|v|2 in each orthogonal direction is also added. The game ends when the game position reaches some y∈∂Ω, and player I's payoff is F(y). We show that (for sufficiently regular Ω) as ε tends to zero, the functions uε converge uniformly to the unique p-harmonic extension of F. Using a modified game (in which ε gets smaller as the game position approaches ∂Ω), we prove similar statements for general bounded domains Ω and resolutive functions F. These games and their variants interpolate between the tug-of-war games studied by Peres, Schramm, Sheffield, and Wilson [15], [16] (p=∞) and the motion-by-curvature games introduced by Spencer [17] and studied by Kohn and Serfaty [9] (p=1). They generalize the relationship between Brownian motion and the ordinary Laplacian and yield new results about p-capacity and p-harmonic measure

A Factor Graph Approach to the Iterative Detection of OFDM Signals in the Presence of Carrier Frequency Offset and Phase Noise

This paper provides a new iterative solution to the problem of the joint estimation of phase noise and residual carrier frequency offset in an orthogonal frequency division multiplexing transmission over a multipath fading channel, in the presence of known data and channel impulse response. The proposed technique results from the application of the sum-product algorithm to a factor graph representing the joint a posteriori probability density function of the carrier frequency offset and the phase noise vector affecting a given symbol. The resulting algorithm is shown to be exploited in a coherent receiver for both data-aided training and decision-directed tracking. Its performance is assessed by computer simulations and is compared with that provided by other strategies.