White Gaussian Noise Model Research Articles

A New Technique of Error-Rate Evaluation in a Wireless Environment With Arbitrary Interference and AWGN

In this paper, we present a new technique of the symbol error-rate evaluation for quadrature amplitude modulation in communication systems equipped with conventional detectors designed for additive white Gaussian noise (AWGN) model of interference, but operating over a fading environment with arbitrary interference and AWGN. In contrast to many reported methods, the given technique is applicable to arbitrary interference and fading models, and it can efficiently be implemented numerically. These facts make the derived result especially convenient for practical purposes.

Evaluation of ultra‐wideband in vivo radio channel and its effects on system performance

AbstractThis paper presents bit‐error‐rate (BER) performance analysis and improvement using equalizers for an in vivo radio channel at ultra‐wideband frequencies (3.1 GHz to 10.6 GHz). By conducting simulations using a bandwidth of 50 MHz, we observed that the in vivo radio channel is affected by small‐scale fading. This fading results in intersymbol interference affecting upcoming symbol transmission, causing delayed versions of the symbols to arrive at the receiver side and causes increase in BER. A 29‐taps channel was observed from the experimentally measured data using a human cadaver, and BER was calculated for the measured in vivo channel response along with the ideal additive white Gaussian noise and Rayleigh channel models. Linear and nonlinear adaptive equalizers, ie, decision feedback equalizer (DFE) and least mean square (LMS), were used to improve the BER performance of the in vivo radio channel. It is noticed that both the equalizers improve the BER but DFE has better BER compared to LMS and shows the 2‐dB and 4‐dB performance gains of DFE over the LMS at Eb/No = 12 dB and at Eb/No = 14 dB, respectively. The current findings will help guide future researchers and designers in enhancing systems performance of an ultra‐wideband in vivo wireless systems.

Low-cost implementation of M-QAM signal constellations

This paper aims to discuss ways of reducing hardware resource usage required for implementing vectorial coding and detection of a variable-order M-ary quadrature amplitude modulation (M-QAM) constellations in digital communication systems. In this regard, we introduce two techniques that are capable of mapping both square and cross M-QAM constellation symbols to bits and vice-versa, with distinct levels of hardware resource utilizations when M increases. These techniques are named Generic M-QAM and Extended Heuristic Decision Region (HDR). The latter technique modulates, demodulates, and detects M-QAM symbols with look-up tables and state machines, while the former technique performs the same tasks by using few logical elements and eliminating memory usage. Based on additive white Gaussian noise model assumption and hard decision rule, we show the bit error rate performances obtained with both techniques are equal to theoretical ones. Additionally, the attained results show the Generic M-QAM technique offers the lowest hardware resource utilization when M increases (M>256) in comparison with the Extended HDR one. Moreover, we point out that the Extended HDR technique has the flexibility to be easily implemented in any published standards, while the Generic M-QAM technique applies a Gray mapping function that might require adjustment to make it compatible to published standards.

Minimax linear estimation at a boundary point

This paper characterizes the minimax linear estimator of the value of an unknown function at a boundary point of its domain in a Gaussian white noise model under the restriction that the first-order derivative of the unknown function is Lipschitz continuous. The result is then applied to construct the minimax optimal estimator for the regression discontinuity design model, where the parameter of interest involves function values at boundary points.

PC-CC: An advancement in forward error correction using polar and convolutional codes for MIMO-OFDM system

Multiple-input multiple-output (MIMO) antennas integrated with orthogonal frequency division multiplexing (OFDM) gains high interest due to its potential reduction on interference as well as efficient data transmission. However, the rapid growth of voluminous data and their diverse characteristics necessitate the effectiveness of error correction schemes in the recent past. The conventional error correction schemes suffer from its compatibility over the diverse data. Despite the concatenated error correction schemes meet the requirements, the precision remains uncertain under data and image transmission. This paper intends to develop an error correction scheme with the combination of Polar Coding (PC), which is an advanced coding scheme, and the renowned Convolution coding (CC). The competiveness of the proposed error correction scheme is experimented under extensive simulation constraints. Accordingly, this paper simulates MIMO-OFDM system with three antenna configurations (2 × 2), (2 × 4) and (4 × 4), which are subjected to experimentation under three modulation schemes such as Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), Quadrature Amplitude Modulation (QAM)-16 and QAM-64. Three practical channel models such as Additive White Gaussian Noise (AWGN), Rayleigh and Rician channel models are used in the proposed study. The performance of the proposed coding scheme is compared against the traditional error correction schemes such as CC, Reed Solomon Code (RSC)-CC, Low-Density Parity Check (LDPC)-CC and turbo-CC. The study is also extended by transmitting the data as well as image to ensure the fairness on diversity of the data characteristics. The study discloses the effectiveness of the proposed error correction scheme over the conventional error correction schemes in terms of BER (Bit Error Rate) and PSNR (Peak Signal to Noise Ratio), when data and images are transmitted, respectively. The proposed method is compared with the conventional techniques and the results have shown that the PSNR performance of the proposed PC-CC method is 37.95% better than CC, 31.73% better than RSC-CC, 24.52% better than LDPC-CC and 14.12% better than turbo-CC method.

Adaptive Bernstein–von Mises theorems in Gaussian white noise

We investigate Bernstein-von Mises theorems for adaptive nonparametric Bayesian procedures in the canonical Gaussian white noise model. We consider both a Hilbert space and multiscale setting with applications in $L^2$ and $L^\infty$ respectively. This provides a theoretical justification for plug-in procedures, for example the use of certain credible sets for sufficiently smooth linear functionals. We use this general approach to construct optimal frequentist confidence sets based on the posterior distribution. We also provide simulations to numerically illustrate our approach and obtain a visual representation of the geometries involved.

Blind Detection for SPAD-Based Underwater VLC System Under P–G Mixed Noise Model

There is Poisson slot noise generated by the single photon avalanche diode (SPAD) and Gaussian thermal noise generated by the transimpedance amplifier, respectively, if an analog SPAD detector is applied in the visible light communication (VLC) system. In this letter, for the long distance SPAD-based underwater VLC system, a fast blind multiple-symbol detection (MSD) algorithm is developed under the pure Poisson noise model. And then, a blind MSD algorithm based on generalized maximum-likelihood rule under the Poisson-Gaussian (P-G) mixed noise model is proposed. A generalized Anscombe transform (GAT) is employed to make the P-G mixed noise model as an equivalent additive white Gaussian noise model, then an equivalent minimum Euclidean distance criterion is presented to formulate the optimization problem. Simulation results show that our blind MSD scheme can be identical to the performance under a GAT-based detector with perfect channel state information.

A Robust Algorithm for Segmentation of Phonocardiography Signal Using Tunable Quality Wavelet Transform

Segmentation of the phonocardiography (PCG) signal is of importance for diagnosis of heart health and the same is recently reported to be done with tunable quality Wavelet transform (TQWT). In the reported method, parameters of TQWT are tuned to vary the frequency range of the approximation level such that its kurtosis gets maximized. Kurtosis will be larger for the fundamental heart sounds (FHS) as compared to the murmur because probability distribution of FHS is super-Gaussian and murmur is sub-Gaussian. However, this is observed in some pathological cases with sharp peak murmurs, murmur and FHS are indistinguishable using kurtosis. Since Fano factor gives a measure of relative variability, we propose to use Fano-factor for selection of the sub-band, in place of Kurtosis. The proposed method decomposes the signal up to twenty levels only once as compared to approximately 55 times in the reported method and then selects a sub-band considering the detailed levels only. This result into 25 times reduction in computational cost. Moreover, exclusion of the approximation level also helps in reduction of the real-life noise. Another contribution of the paper is the adaptive thresholding method used to suppress the noise level from the selected level that improves the segmentation accuracy in the presence of noise. Experiments are performed on PCG signals of various normal and pathological cases, with and without simulated noise using white Gaussian, pink, and red noise models, separately. The obtained results show the efficiency of the proposed method to segment the PCG signal in the presence of noise, murmurs, and both.

Single particle Brownian motion with solid friction.

We study the Brownian dynamics of a solid particle on a vibrating solid surface. Phenomenologically, the interaction between the two solid surfaces is modeled by solid friction, and the Gaussian white noise models the vibration of the solid surface. The solid friction force is proportional to the sign of relative velocity. We derive the Fokker-Planck (FP) equation for the time-dependent probability distribution to find the particle at a given location. We calculate analytically the steady state velocity distribution function, mean-square velocity and diffusion coefficient in d-dimensions. We present a generic method of calculating the autocorrelations in d-dimensions. This results in one dimension in an exact evaluation of the steady state velocity autocorrelation. In higher dimensions our exact general expression enables the analytic evaluation of the autocorrelation to any required approximation. We present approximate analytic expressions in two and three dimensions. Next, we numerically calculate the mean-square velocity and steady state velocity autocorrelation function up to d = 3 . Our numerical results are in good agreement with the analytically obtained results.

Minimax optimal procedures for testing the structure of multidimensional functions

We present a novel method for detecting some structural characteristics of multidimen-sional functions. We consider the multidimensional Gaussian white noise model with an anisotropic estimand. Using the relation between the Sobol decomposition and the geometry of multidimensional wavelet basis we can build test statistics for any of the Sobol functional components. We assess the asymptotical minimax optimality of these test statistics and show that they are optimal in presence of anisotropy with respect to the newly determined minimax rates of separation. An appropriate combination of these test statistics allows to test some general structural characteristics such as the atomic dimension or the presence of some variables. Numerical experiments show the potential of our method for studying spatio-temporal processes.

Closed-Form BER Expressions for HSV-Based ${M}$ PSK-CSK Systems

The analysis of hybrid phase shift keying-color shift keying ( ${M}$ PSK-CSK) systems under the additive white Gaussian noise model is presented. ${M}$ PSK-CSK systems are formed by mapping phase shift keying symbols to color shift keying using hue-saturation-value color space. Analytical expressions of bit error rate are given for ${M} =2$ , 4, 8, and 16, to validate the simulation results published previously.

A Coherent Optical OFDM Communication System with Nonlinear Distortion Compensation in the Channel and Receiver

AbstractA simple and low-cost scheme is proposed for reducing the distortions in the coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system. The total wireless channel noise and the distortions in the receiver can be considered as an additive white Gaussian noise model and all distortions can be reduced using maximum likelihood sequence estimation (MLSE) equalizers. The performance of the CO-OFDM is analyzed for different fiber lengths and laser powers. Results show that the MLSE-equalized system can outperform with a higher

Minimax Linear Estimation at a Boundary Point

This paper characterizes the minimax linear estimator of the value of an unknown function at a boundary point of its domain in a Gaussian white noise model under the restriction that the first-order derivative of the unknown function is Lipschitz continuous (the second-order Holder class). The result is then applied to construct the minimax optimal estimator for the regression discontinuity design model, where the parameter of interest involves function values at boundary points.

Adaptive variable selection in nonparametric sparse additive models

We consider the problem of recovery of an unknown multivariate signal $f$ observed in a $d$-dimensional Gaussian white noise model of intensity $\varepsilon $. We assume that $f$ belongs to a class of smooth functions in $L_{2}([0,1]^{d})$ and has an additive sparse structure determined by the parameter $s$, the number of non-zero univariate components contributing to $f$. We are interested in the case when $d=d_{\varepsilon }\to \infty $ as $\varepsilon \to 0$ and the parameter $s$ stays “small” relative to $d$. With these assumptions, the recovery problem in hand becomes that of determining which sparse additive components are non-zero. Attempting to reconstruct most, but not all, non-zero components of $f$, we arrive at the problem of almost full variable selection in high-dimensional regression. For two different choices of a class of smooth functions, we establish conditions under which almost full variable selection is possible, and provide a procedure that achieves this goal. Our procedure is the best possible (in the asymptotically minimax sense) for selecting most non-zero components of $f$. Moreover, it is adaptive in the parameter $s$. In addition to that, we complement the findings of [17] by obtaining an adaptive exact selector for the class of infinitely-smooth functions. Our theoretical results are illustrated with numerical experiments.

Nonlocal Means and Optimal Weights for Noise Removal

In this paper, a new denoising algorithm to deal with the additive white Gaussian noise model is described. Following the nonlocal (NL) means approach, we propose an adaptive estimator based on the weighted average of observations taken in a neighborhood with weights depending on the similarity of local patches. The idea is to compute adaptive weights that best minimize an upper bound of the pointwise $L_2$ risk. In the framework of adaptive estimation, we show that the “oracle” weights are optimal if we consider triangular kernels instead of the commonly used Gaussian kernel. Furthermore, we propose a way to automatically choose the spatially varying smoothing parameter for adaptive denoising. Under conventional minimal regularity conditions, the obtained estimator converges at the usual optimal rate. The implementation of the proposed algorithm is also straightforward and the simulations show that our algorithm significantly improves the classical NL means and is competitive when compared to the more so...

An improved correlation method for amplitude estimation of gravitational background signal with time-varying frequency.

In the measurement of the gravitational constant G with angular acceleration method, the accurate estimation of the amplitude of the useful angular acceleration generated by source masses depends on the effective subtraction of the spurious gravitational signal caused by room fixed background masses. The gravitational background signal is of time-varying frequency, and mainly consists of the prominent fundamental frequency and second harmonic components. We propose an improved correlation method to estimate the amplitudes of the prominent components of the gravitational background signal with high precision. The improved correlation method converts a sinusoidal signal with time-varying frequency into a standard sinusoidal signal by means of the stretch processing of time. Based on Gaussian white noise model, the theoretical result shows the uncertainty of the estimated amplitude is proportional to σNT, where σ and N are the standard deviation of noise and the number of the useful signal period T, respectively.

A Novel Approach of Despeckling SAR Images Using Nonlocal Means Filtering

Synthetic aperture radar (SAR) is a day and night, all weather satellite imaging technology. Inherent property of SAR image is speckle noise which produces granular patterns in the image. Speckle noise occurs due to the interference of backscattered echo from earth’s rough surface. There are various speckle reduction techniques in spatial domain and transform domain. Non local means filtering (NLMF) is the technique used for denoising which uses Gaussian weights. In NLMF algorithm, the filtering is performed by taking the weighted mean of all the pixels in a selected search area. The weight given to the pixel is based on the similarity measure calculated as the weighted Euclidean distance over the two windows. Non local means filtering smoothes out homogeneous areas but edges are not preserved. So a discontinuity adaptive weight is used in order to preserve heterogeneous areas like edges. This technique is called as discontinuity adaptive non local means filtering and is well-adapted and robust in the case of Additive White Gaussian Noise (AWGN) model. But speckle is a multiplicative random noise and hence Euclidean distance is not a good choice. This paper presents evaluation results of using different distance measures for improving the accuracy of the Non local means filtering technique. The results are verified using real and synthetic images and from the results it can be concluded that the usage of Manhattan distance improves the accuracy of NLMF technique. Non local approach is used as a preprocessing or post processing technique for many denoising algorithms. So improving NLMF technique would help improving many of the existing denoising techniques.

On adaptive posterior concentration rates

We investigate the problem of deriving posterior concentration rates under different loss functions in nonparametric Bayes. We first provide a lower bound on posterior coverages of shrinking neighbourhoods that relates the metric or loss under which the shrinking neighbourhood is considered, and an intrinsic pre-metric linked to frequentist separation rates. In the Gaussian white noise model, we construct feasible priors based on a spike and slab procedure reminiscent of wavelet thresholding that achieve adaptive rates of contraction under $L^2$ or $L^{\infty}$ metrics when the underlying parameter belongs to a collection of H\"{o}lder balls and that moreover achieve our lower bound. We analyse the consequences in terms of asymptotic behaviour of posterior credible balls as well as frequentist minimax adaptive estimation. Our results are appended with an upper bound for the contraction rate under an arbitrary loss in a generic regular experiment. The upper bound is attained for certain sieve priors and enables to extend our results to density estimation.

A novel hybrid prediction algorithm to network traffic

Network traffic describes the characteristics and users’ behaviors of communication networks. It is a crucial input parameter of network management and network traffic engineering. This paper proposes a new prediction algorithm to network traffic in the large-scale communication network. First, we use signal analysis theory to transform network traffic from time domain to time-frequency domain. In the time-frequency domain, the network traffic signal is decomposed into the low-frequency and high-frequency components. Second, the gray model is exploited to model the low-frequency component of network traffic. The white Gaussian noise model is utilized to describe its high-frequency component. This is reasonable because the low-frequency and high-frequency components, respectively, represent the trend and fluctuation properties of network traffic, while the gray model and white Gaussian noise model can well capture the characteristics. Third, the prediction models of low-frequency and high-frequency components are built. The hybrid prediction algorithm is proposed to overcome the problem of network traffic prediction in the communication network. Finally, network traffic data from the real network is used to validate our approach. Simulation results indicate that our algorithm holds much lower prediction error than previous methods.

Adaptive estimation over anisotropic functional classes via oracle approach

We address the problem of adaptive minimax estimation in white gaussian noise model under Lp-loss, 1 � p � 1, on the anisotropic Nikolskii classes. We present the es- timation procedure based on a new data-driven selection scheme from the family of kernel estimators with varying bandwidths. For proposed estimator we establish so-called Lp-norm oracle inequality and use it for deriving minimax adaptive results. We prove the existence of rate-adaptive estimators and fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm indexes in definitions of the functional class and of the risk. In particular some new asymptotics of the minimax risk are discovered including necessary and sufficient conditions for existencea uniformly consistent estimator. We provide also with detailed overview of existing methods and results and formulate open problems in adaptive minimax estimation.