Correlated Noise Environments Research Articles

Multiantenna Spectrum Sensing for Correlated Signal in Spatially Correlated Noise Environments

The multiantenna spectrum sensing (MSS) problem for correlated signal is addressed in this correspondence. First, the zero-lag and non-zero-lag covariance matrices are established, respectively, to capture the correlation feature of primary signals. Then, two scenarios are considered: 1) the noises at different antennas are spatially white; 2) the noises at different antennas are spatially correlated. Afterward, two variants of the covariance detection method are devised to detect the presence of primary user. Also, we derive the approximate closed-form expressions to calculate the decision thresholds of the proposed two methods. Simulation results are presented to demonstrate the superiority of the proposed two methods over the conventional MSS methods.

Generic Deep Learning-Based Linear Detectors for MIMO Systems Over Correlated Noise Environments

To support the and development and application of the fifth-generation (5G) communication and internet of things (IoT) networks, high data-rate wireless transmission is required. To meet the demand of high data-rate, multiple antennas are equipped at the transmitter and receiver, forming multiple-input multiple-output (MIMO) systems. A big challenge of MIMO is the detector design in correlated noise environments, which should achieve a fine performance with moderate computational complexity. To this end, we employ an iterative framework of a deep convolutional neural network (DCNN) and a linear detector for MIMO systems over correlated noise environments. In this framework, the linear detector can be zero-forcing (ZF), minimum mean square error (MMSE), ZF with successive interference cancellation (ZF-SIC), or MMSE-SIC, which produces an initial estimate of transmitted signals. The DCNN is used to capture the local correlation among noise, and it can produce a more accurate estimate of transmitted signals. Simulation results are finally provided to show that the proposed detector can outperform the conventional linear detectors substantially through capturing the local correlation characteristics among noise.

Experimental quantum verification in the presence of temporally correlated noise

Growth in the capabilities of quantum information hardware mandates access to techniques for performance verification that function under realistic laboratory conditions. Here we experimentally characterise the impact of common temporally correlated noise processes on both randomised benchmarking (RB) and gate-set tomography (GST). Our analysis highlights the role of sequence structure in enhancing or suppressing the sensitivity of quantum verification protocols to either slowly or rapidly varying noise, which we treat in the limiting cases of quasi-DC miscalibration and white noise power spectra. We perform experiments with a single trapped 171Yb+ ion-qubit and inject engineered noise left( { propto hat sigma _z} right) to probe protocol performance. Experiments on RB validate predictions that measured fidelities over sequences are described by a gamma distribution varying between approximately Gaussian, and a broad, highly skewed distribution for rapidly and slowly varying noise, respectively. Similarly we find a strong gate set dependence of default experimental GST procedures in the presence of correlated errors, leading to significant deviations between estimated and calculated diamond distances in the presence of correlated hat sigma _z errors. Numerical simulations demonstrate that expansion of the gate set to include negative rotations can suppress these discrepancies and increase reported diamond distances by orders of magnitude for the same error processes. Similar effects do not occur for correlated hat sigma _x or hat sigma _y errors or depolarising noise processes, highlighting the impact of the critical interplay of selected gate set and the gauge optimisation process on the meaning of the reported diamond norm in correlated noise environments.

Joint DOD and DOA Estimation for Bistatic MIMO Radar in Unknown Correlated Noise

In this paper, joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation for bistatic multiple-input–multi-output (MIMO) radar in an unknown spatially correlated noise environment is investigated. The signal model is based on the assumption that the waveforms are transmitted by two separated subarrays having $M_1$ and $M_2$ sensors and received by two separated subarrays having $N_1$ and $N_2$ sensors, respectively. The received data are pulse-compressed using a matching matrix consisting of $M=M_1+M_2$ orthogonally transmitted waveforms. The joint covariance matrix of unknown correlated noise is analyzed. A novel algorithm is proposed by jointly estimating the DOD and DOA with transmitter and receiver subarrays in unknown noise. The joint estimation algorithm is based on the canonical correlation decomposition (CCD) and exploits the shift-invariance properties in the Kronecker product structure of each column of the various steering matrices. The estimated DOA and DOD can be automatically paired correspondingly. In addition, the formulas of stochastic Cramer–Rao bounds (CRB) for DOD and DOA estimation are derived. Simulations show that our method can effectively improve the performance of estimation in unknown correlated noise environments and is insensitive to having different noise environments in the two subarrays.

Estimation of Toeplitz Covariance Matrices in Large Dimensional Regime With Application to Source Detection

In this article, we derive concentration inequalities for the spectral norm of two classical sample estimators of large dimensional Toeplitz covariance matrices, demonstrating in particular their asymptotic almost sure consistence. The consistency is then extended to the case where the aggregated matrix of time samples is corrupted by a rank one (or more generally, low rank) matrix. As an application of the latter, the problem of source detection in the context of large dimensional sensor networks within a temporally correlated noise environment is studied. As opposed to standard procedures, this application is performed online, i.e. without the need to possess a learning set of pure noise samples.

Multi-antenna assisted spectrum sensing in spatially correlated noise environments

A significant challenge in spectrum sensing is to lessen the signal to noise ratio needed to detect the presence of primary users while the noise level may also be unknown. To meet this challenge, multi-antenna based techniques possess a greater efficiency compared to other algorithms. In a typical compact multi-antenna system, due to small interelement spacing, mutual coupling between thermal noises of adjacent receivers is significant. In this paper, unlike most of the spectrum sensing algorithms which assume spatially uncorrelated noise, the noises on the adjacent antennas can have arbitrary correlations. Also, in contrast to some other algorithms, no prior assumption is made on the temporal properties of the signals. We exploit low-rank/sparse matrix decomposition algorithms to obtain an estimate of noise and received source covariance matrices. Given these estimates, a Semi-Constant False Alarm Rate (S-CFAR) detector, in which the probability of false alarm is constant over the scaling of the noise covariance matrix, to examine the presence of primary users is proposed. In order to analyze the efficiency of our algorithm, we derive approximate probability of detection. Numerical simulations show that the proposed algorithm consistently and considerably outperforms state-of-the-art multi-antenna based spectrum sensing algorithms.

Recursive inverse adaptive algorithm: a second-order version, a fast implementation technique, and further results

A variable step-size and first-order recursive estimate of the autocorrelation matrix have been used in the update equation of the recently proposed recursive inverse (RI) algorithm. These lead to an improved performance of the RI algorithm compared with some well-known adaptive algorithms. In this paper, the RI algorithm is first briefly reviewed. An improved version of the RI algorithm, which uses a second-order recursive estimation of the correlations, is introduced. A general fast implementation technique for the RI algorithms is presented. The performances of the fast RI and fast second-order RI algorithms are compared to that of the RLS algorithm in stationary white and correlated noise environments in a noise cancellation setting. The simulation results show that the fast RI algorithms outperform the others compared either in speed of convergence and/or the computational complexity when the MSE is held constant. The performance of the original RI algorithms is compared to that of the RLS algorithm in a system identification setting. Simulations show that the RI algorithms perform similar or better than the other algorithms.

Circular contour retrieval in real-world conditions by higher order statistics and an alternating-least squares algorithm

Abstract In real-world conditions, contours are most often blurred in digital images because of acquisition conditions such as movement, light transmission environment, and defocus. Among image segmentation methods, Hough transform requires a computational load which increases with the number of noise pixels, level set methods also require a high computational load, and some other methods assume that the contours are one-pixel wide. For the first time, we retrieve the characteristics of multiple possibly concentric blurred circles. We face correlated noise environment, to get closer to real-world conditions. For this, we model a blurred circle by a few parameters--center coordinates, radius, and spread--which characterize its mean position and gray level variations. We derive the signal model which results from signal generation on circular antenna. Linear antennas provide the center coordinates. To retrieve the circle radii, we adapt the second-order statistics TLS-ESPRIT method for non-correlated noise environment, and propose a novel version of TLS-ESPRIT based on higher-order statistics for correlated noise environment. Then, we derive a least-squares criterion and propose an alternating least-squares algorithm to retrieve simultaneously all spread values of concentric circles. Experiments performed on hand-made and real-world images show that the proposed methods outperform the Hough transform and a level set method dedicated to blurred contours in terms of computational load. Moreover, the proposed model and optimization method provide the information of the contour grey level variations.

Optimum array design to maximize fisher information for bearing estimation in spatially correlated noise environment.

Source bearing estimation is a common application of linear sensor arrays. The Cramer–Rao bound (CRB) sets a lower bound on the achievable mean square error (MSE) of any unbiased bearing estimate. In the white noise case, the CRB is minimized by placing half of the sensors at each end of the array [MacDonald and Schultheiss, JASA (1969)]. However, many realistic ocean environments have a mixture of both white noise and correlated noise. In many shallow water environments, the correlated ambient noise can be modeled as cylindrically (two‐dimensionally) isotropic. This research designs a fixed aperture linear array to maximize the fisher information for bearing estimation under these noise conditions. The optimum array is designed to maximize the minimum fisher information over an a priori bearing range. The elements of the optimal array are located closer to the array ends than uniform spacing, but are not so extreme as in the white noise case. The optimal array results from a trade off between minimizing the measured noise and maximizing the array bearing sensitivity. Depending on the source bearing, the resulting improvement in MSE performance over a uniform array is equivalent to a 3 to 5 dB improvement in input SNR. [Work supported by ONR.]

Generalized Correlation Decomposition-Based Blind Channel Estimation in DS-CDMA Systems With Unknown Wide-Sense Stationary Noise

A new blind subspace-based channel estimation technique is proposed for direct-sequence code-division multiple access (DS-CDMA) systems operating in the presence of unknown wide-sense stationary noise. Unlike most of the blind techniques developed for unknown correlated noise environments so far, the proposed algorithm is applicable to an arbitrary symbol constellation and does not require any auxiliary antennas at the receiver or any prior knowledge of the interfering user spreading codes. Our approach exploits the centro-Hermitian property of the unknown noise covariance matrix and makes use of the generalized correlation decomposition (GCD) to obtain an accurate estimate of the noise subspace and, consequently, of the user-of- interest channel vector. We also obtain optimal values of the GCD weighting matrices which maximally preserve the orthogonality of the estimated noise subspace to the actual signal subspace in the high signal-to-noise ratio (SNR) regime. It is shown that such an optimal choice of the weighting matrices transforms GCD to an extended form of the conventional canonical correlation decomposition (CCD). Simulation results further demonstrate that if such an extended CCD-based approach is used to estimate the user-of-interest channel vector, then the estimation performance can be substantially improved as compared to earlier SVD-based blind channel estimation techniques.

Noncoherent Communication in Multiple-Antenna Systems: Receiver Design and Codebook Construction

In this paper, we address the problem of space-time codebook design for noncoherent communications in multiple-antenna wireless systems. In contrast with other approaches, the channel matrix is modeled as an unknown deterministic parameter at both the receiver and the transmitter, and the Gaussian observation noise is allowed to have an arbitrary correlation structure, known by the transmitter and the receiver. In order to handle the unknown deterministic space-time channel, a generalized likelihood ratio test (GLRT) receiver is considered. A new methodology for space-time codebook design under this noncoherent setup is proposed. It optimizes the probability of error of the GLRT receiver's detector in the high signal-to-noise ratio (SNR) regime by solving a high-dimensional nonlinear nonsmooth optimization problem in a two-step approach. First, a convex semidefinite programming (SDP) relaxation of the codebook design problem yields a rough estimate of the optimal codebook. This is then refined through a geodesic descent optimization algorithm that exploits the Riemannian geometry imposed by the power constraints on the space-time codewords. The results obtained through computer simulations illustrate the advantages of our method. For the specific case of spatio-temporal white observation noise, our codebook constructions replicate the performance of state-of-the-art known solutions. The main point here is that our methodology permits extending the codebook construction to any given correlated noise environment. The simulation results show good performance of these new designed codes in colored noise setups.

Contrast techniques for line detection in a correlated noise environment

A new class of line detectors based on the theory of linear contrasts is developed. By incorporating the F-statistic and the shape test, the new algorithm detects and locates line features simultaneously, and thereby increases the detection power substantially. Many classes of detectors, including the step edge detector, naturally becomes subclasses of the proposed detector. Mathematical analysis indicates that the new algorithm that accounts for noise dependence performs better than its counterpart that neglects the dependence of noise. A symmetrical balanced incomplete-blocks (SBIB) design is introduced to model real-world images in terms of a treatment group that is associated with preexistent, conspicuous, features such as lines, edges, etc., and an incomplete treatment group that is randomized to accommodate image textures. The new algorithm in conjunction with the SBIB design is applied in the four main directions, perpendicularly to the line under investigation. It is robust, simple, efficient, and amenable to real-time applications. All pertinent statistics for the implementation of the procedure are estimated from data. Extensive computer simulations demonstrate the performance of the proposed detector.

Estimation of DOA in unknown noise: performance analysis of UN-MUSIC and UN-CLE, and the optimality of CCD

In a previous paper, a new approach was proposed for the consistent estimation of the directions of arrival (DOA) of signals in an unknown spatially correlated noise environment using generalized correlation decomposition (GCD). Based on the various interesting properties of the eigenspace structure obtained by GCD, two effective methods (UN-MUSIC and UNCLE) of estimating the DOA in an unknown correlated noise were developed, In this paper, the performance of the two methods are analyzed. It is shown that the performance of these two methods can be optimized by assigning optimum weighting matrices in their respective criteria. Furthermore, and more importantly, it is also shown that of all the correlation decompositions, the canonical correlation decomposition (CCD) leads to the optimum performance of the methods. Computer simulations confirm these conclusions and show that the use of CCD is robust even under variable spatially correlated noise conditions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Information theoretic criteria for the determination of the number of signals in spatially correlated noise

The problem of determining the number of signals in high-resolution array processing when the noise is spatially correlated (having an unknown covariance matrix) is examined. By considering a model in which two sensor arrays are well separated such that their noise outputs are uncorrelated, the authors develop a likelihood function whose maximum can be expressed in a very simple form involving the canonical correlation coefficients. This likelihood function and a choice of penalty functions constitute a number of new information theoretic criteria suitable for the determination of the number of signals in an unknown correlated noise environment. Furthermore, it is demonstrated that the new criteria are applicable in the case when only one sensor array is available.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Variable time delay estimation in colored and correlated noise environment

A new iterative algorithm for variable time delay estimation (TDE) is presented. The algorithm is based on a system model where two received signals of the form r/sub 1/(i)=s(i)+n/sub 1/(i) and r/sub 2/(i)=s(i-D(i))+n/sub 2/(i) are used to estimate the delay. In the model i is the discrete-time index, s(i) is the source signal, D(i) is the (integer) delay waveform, and n/sub 1/(i) and n/sub 2/(i) are colored and correlated noises. An iterative delay estimator is devised based on the minimum mean-square error criterion and a linearized observation model. The estimator involves a weighting function that is designated to facilitate the convergence to delay estimate. Simulations are run to test the performance of the algorithm. Results of the simulations are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>