Knowledge Of Noise Variance Research Articles

CFAR based NOMP for Line Spectral Estimation and Detection

The line spectrum estimation and detection problem are considered in this paper. We propose a CFAR-based Newtonized OMP (NOMP-CFAR) method which can maintain a desired false alarm rate without the knowledge of the noise variance. The NOMP-CFAR consists of two steps, namely, an initialization step and a detection step. In the initialization step, NOMP is employed to obtain candidate sinusoidal components. In the detection step, CFAR detector is applied to detect each candidate frequency, and provides the “soft” thresholds. After removing the most unlikely target, the Newton refinements are used to refine the remaining parameters. The relationship between the false alarm rate and the required threshold is established. Compared with NOMP, NOMP-CFAR has only 1 dB performance loss in additive white Gaussian noise scenario with false alarm probability <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-2}$</tex-math></inline-formula> and detection probability 0.8 without knowledge of noise variance. For varied noise variance scenario, NOMP-CFAR still preserves its CFAR property, while NOMP violates the CFAR. Besides, real experiments are also conducted to demonstrate the detection performance of NOMP-CFAR, compared to CFAR and NOMP.

Sparse signal detection without reconstruction based on compressive sensing

This paper considers the problem of compressive detection of sparse signals without signal reconstruction. In the compressed detection model, we present the design of measurement matrix by using the sparsity of a signal, and prove that the variances of the compressive measurements follow two different Gaussian distributions under the binary hypothesis testing. A single measurement vector (SMV) detector is proposed when the knowledge of noise variance is available. Nevertheless, the theoretical analysis shows that the SMV detector has an inferior perfornance in the low signal-noise-ratio regime. To address this situation, the SMV model is extended to the multiple measurement vectors (MMV) model. In the scenario of unknown noise (UN) variance, we propose the UN-MMV detector which requires less prior knowledge. Moreover, the closed-form expressions for the probabilities of false alarm and detection of each detector are derived, respectively. Numerical simulations are conducted to illustrate the performance of the proposed detectors.

Adaptive Neuro-Filtering Based Visual Servo Control of a Robotic Manipulator

This paper focuses on the solutions to flexibly regulate robotic by vision. A new visual servoing technique based on the Kalman filtering (KF) combined neural network (NN) is developed, which need not have any calibration parameters of robotic system. The statistic knowledge of the system noise and observation noise are first given by Gaussian white noise sequences, the nonlinear mapping between robotic vision and motor spaces are then on-line identified using standard Kalman recursive equations. In real robotic workshops, the perfect statistic knowledge of the noise is not easy to be derived, thus an adaptive neuro-filtering approach based on KF is also studied for mapping on-line estimation in this paper. The Kalman recursive equations are improved by a feedforward NN, in which the neural estimator dynamic adjusts its weights to minimize estimation error of robotic vision-motor mapping, without the knowledge of noise variances. Finally, the proposed visual servoing based on adaptive neuro-filtering has been successfully implemented in robotic pose regulation, and the experimental results demonstrate its validity and practicality for a six-degree-of-freedom (DOF) robotic system which the hand-eye without calibrated.

Using generalized cross validation to select regularization parameter for total variation regularization problems

The regularization approach is used widely in image restoration problems. The visual quality of the restored image depends highly on the regularization parameter. In this paper, we develop an automatic way to choose a good regularization parameter for total variation (TV) image restoration problems. It is based on the generalized cross validation (GCV) approach and hence no knowledge of noise variance is required. Due to the lack of the closed-form solution of the TV regularization problem, difficulty arises in finding the minimizer of the GCV function directly. We reformulate the TV regularization problem as a minimax problem and then apply a first-order primal-dual method to solve it. The primal subproblem is rearranged so that it becomes a special Tikhonov regularization problem for which the minimizer of the GCV function is readily computable. Hence we can determine the best regularization parameter in each iteration of the primal-dual method. The regularization parameter for the original TV regularization problem is then obtained by an averaging scheme. In essence, our method needs only to solve the TV regulation problem twice: one to determine the regularization parameter and one to restore the image with that parameter. Numerical results show that our method gives near optimal parameter, and excellent performance when compared with other state-of-the-art adaptive image restoration algorithms.

A Novel Blind Event Detection Method for Wireless Sensor Networks

Student'st-distribution is utilized to derive a novel method for event detection in wireless sensor networks. Numerical analysis is used to show that under the same conditions, the proposed event detection method is comparable to likelihood ratio-based detection method and that it significantly outperforms energy detection method in terms of detection performance. Moreover, the proposed method does not require perfect knowledge of noise variance to set up a decision threshold in terms of a false alarm probability as the likelihood ratio based detection and the energy detection do.

Spectrum sensing in cognitive radio networks with known and unknown noise levels

In this study, the authors consider the problem of signal detection in cognitive radio under the cases of known and unknown noise levels. The analysis is focused on maximum eigenvalue-based method which requires the knowledge of noise variance and the ratio of maximum eigenvalue to the trace of covariance matrix. The analytical formulas are derived for threshold calculation and probability of detection for the considered methods. Performance of the considered methods is measured through simulation analysis. The performance comparison between the considered methods and other existing methods is provided. Simulations based on independent and identically distributed signals and wireless microphone signals are presented to verify the various sensing methods.

Eigenvalue-Based Sensing and SNR Estimation for Cognitive Radio in Presence of Noise Correlation

Herein, we present a detailed analysis of an eigenvalue-based sensing technique in the presence of correlated noise in the context of a cognitive radio (CR). We use standard-condition-number (SCN)-based decision statistics based on asymptotic random matrix theory (RMT) for the decision process. First, the effect of noise correlation on eigenvalue-based spectrum sensing (SS) is analytically studied under both the noise-only and signal-plus-noise hypotheses. Second, new bounds for the SCN are proposed to achieve improved sensing in correlated noise scenarios. Third, the performance of fractional-sampling (FS)-based SS is studied, and a method to determine the operating point for the FS rate in terms of sensing performance and complexity is suggested. Finally, a signal-to-noise ratio (SNR) estimation technique based on the maximum eigenvalue of the covariance matrix of the received signal is proposed. It is shown that the proposed SCN-based threshold improves sensing performance in correlated noise scenarios, and SNRs up to 0 dB can be reliably estimated with a normalized mean square error (MSE) of less than <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hbox{1}\%$</tex></formula> in the presence of correlated noise without the knowledge of noise variance.

An investigation into the noise variance and the SNR estimators in imperfectly-synchronized OFDM systems

Orthogonal frequency division multiplexing (OFDM) systems require the knowledge of signal-to-noise ratio (SNR) at the receiver in order to optimize the system performance. In general, the noise variance is required by the SNR estimator and the knowledge of noise variance also improves the performance of carrier frequency offset (CFO) and channel state estimations. This paper commences by investigating the maximum likelihood noise variance estimator (ML-NVE) in OFDM systems with imperfect synchronization. Theoretical derivations show that both the mean and the variance of the ML-NVE are functions of the CFO and the advanced timing offset (ATO). In particular, it is demonstrated that the mean of the ML-NVE converges to a CFO-independent value as the ATO increases, while the variance converges to a CFO-dependent value. By exploiting the analytical results of the ML-NVE, we further investigate the SNR estimator. It is mathematically demonstrated that the SNR estimate is biased in the presence of CFO and ATO. Finally, the validity of the theoretical observations is confirmed by simulation experiments.