Results on lattice vector quantization with dithering

Wide-sense stationary discrete-time random processes: Analyses in the discrete-Fresnel and discrete-frequency domains

A new method for representing and generating realizations of a wide-sense stationary non-Gaussian random process is described. The representation allows one to independently specify the power spectral density and the first-order probability density function of the random process. The only proviso is that the probability density function must be symmetric and infinitely divisible. The method proposed models the sinusoidal component frequencies as random variables, a key departure from the usual representation a of wide-sense stationary random process by the spectral theorem. Ergodicity in the mean and autocorrelation is also proven, under certain conditions. An example is given to illustrate its application to the K distribution, which is important in many physical modeling problems in radar and sonar.

Vandermonde-subspace frequency division multiplexing (VFDM) utilizes frequency-domain degrees of freedom (DoFs) to implement spectrum sharing. In this paper, a robust intra-tier precoder (ITP) is devised to suppress the interference for VFDM based small cell (SC) considering imperfect Gaussian distributed estimation error. We formulate the ITP design as a minimum mean square error (MMSE) optimization, where the total mean square error (MSE) is carefully derived. Considering the complexity of the solution, we then proposed an iterative algorithm to find the optimized robust ITP. Numerical results are presented to validate that the proposed algorithm can achieve lower mean square error (MSE) than the traditional one does.

In this paper, we study the asymptotic optimality of a low-complexity coding strategy for Gaussian vector sources. Specifically, we study the convergence speed of the rate of such a coding strategy when it is used to encode the most relevant vector sources, namely wide sense stationary (WSS), moving average (MA), and autoregressive (AR) vector sources. We also study how the coding strategy considered performs when it is used to encode perturbed versions of those relevant sources. More precisely, we give a sufficient condition for such perturbed versions so that the convergence speed of the rate remains unaltered.

Over the last decade it has become popular to analyze turbulent solar wind fluctuations with respect to a coordinate system aligned with the local mean magnetic field. This useful analysis technique has provided new information and new insights about the nature of solar wind fluctuations and provided some support for phenomenological theories of MHD turbulence based on the ideas of Goldreich and Sridhar. At the same time it has drawn criticism suggesting that the use of a scale‐dependent local mean field is somehow inconsistent or irreconcilable with traditional analysis techniques based on second‐order structure functions and power spectra that, for stationary time series, are defined with respect to the constant (scale‐independent) ensemble average magnetic field. Here it is shown that for fluctuations with power law spectra, such as those observed in solar wind turbulence, it is possible to define the local mean magnetic field in a special way such that the total mean square amplitude (trace amplitude) of turbulent fluctuations is approximately the same, scale by scale, as that obtained using traditional second‐order structure functions or power spectra. This fact should dispel criticism concerning the physical validity or practical usefulness of the local mean magnetic field in these applications.

Accurate estimation of precipitation from satellite precipitation products (PPs) over the complex topography and diverse climate of Pakistan with limited rain gauges (RGs) is an arduous task. In the current study, we assessed the performance of two PPs estimated from soil moisture (SM) using the SM2RAIN algorithm, SM2RAIN-CCI and SM2RAIN-ASCAT, on the daily scale across Pakistan during the periods 2000–2015 and 2007–2015, respectively. Several statistical metrics, i.e., Bias, unbiased root mean square error (ubRMSE), Theil’s U, and the modified Kling–Gupta efficiency (KGE) score, and four categorical metrics, i.e., probability of detection (POD), false alarm ratio (FAR), critical success index (CSI), and Bias score, were used to evaluate these two PPs against 102 RGs observations across four distinct climate regions, i.e., glacial, humid, arid and hyper-arid regions. Total mean square error (MSE) is decomposed into systematic (MSEs) and random (MSEr) error components. Moreover, the Tropical Rainfall Measurement Mission Multi-Satellite Precipitation Analysis (TRMM TMPA 3B42v7) was used to assess the performance of SM2RAIN-based products at 0.25° scale during 2007–2015. Results shows that SM2RAIN-based product highly underestimated precipitation in north-east and hydraulically developed areas of the humid region. Maximum underestimation for SM2RAIN-CCI and SM2RIAN-ASCAT were 58.04% and 42.36%, respectively. Precipitation was also underestimated in mountainous areas of glacial and humid regions with maximum underestimations of 43.16% and 34.60% for SM2RAIN-CCI. Precipitation was overestimated along the coast of Arabian Sea in the hyper-arid region with maximum overestimations for SM2RAIN-CCI (SM2RAIN-ASCAT) of 59.59% (52.35%). Higher ubRMSE was observed in the vicinity of hydraulically developed areas. Theil’s U depicted higher accuracy in the arid region with values of 0.23 (SM2RAIN-CCI) and 0.15 (SM2RAIN-ASCAT). Systematic error components have larger contribution than random error components. Overall, SM2RAIN-ASCAT dominates SM2RAIN-CCI across all climate regions, with average percentage improvements in bias (27.01% in humid, 5.94% in arid, and 6.05% in hyper-arid), ubRMSE (19.61% in humid, 20.16% in arid, and 25.56% in hyper-arid), Theil’s U (9.80% in humid, 28.80% in arid, and 26.83% in hyper-arid), MSEs (24.55% in humid, 13.83% in arid, and 8.22% in hyper-arid), MSEr (19.41% in humid, 29.20% in arid, and 24.14% in hyper-arid) and KGE score (5.26% in humid, 28.12% in arid, and 24.72% in hyper-arid). Higher uncertainties were depicted in heavy and intense precipitation seasons, i.e., monsoon and pre-monsoon. Average values of statistical metrics during monsoon season for SM2RAIN-CCI (SM2RAIN-ASCAT) were 20.90% (17.82%), 10.52 mm/day (8.61 mm/day), 0.47 (0.43), and 0.47 (0.55) for bias, ubRMSE, Theil’s U, and KGE score, respectively. TMPA outperformed SM2RAIN-based products across all climate regions. SM2RAIN-based datasets are recommended for agricultural water management, irrigation scheduling, flood simulation and early flood warning system (EFWS), drought monitoring, groundwater modeling, and rainwater harvesting, and vegetation and crop monitoring in plain areas of the arid region.

The Power Function distribution is one of the most suitable distributions for failure times modeling, especially of electric components and devices. The article proposes some new modified estimators for parameter estimation of the Power Function distribution. The proposed modified estimators are based on the mean and geometric mean of the distribution. The performance of these estimators is compared with existing traditional and modified estimators by means of Monte Carlo simulation and two real‐life examples. Total mean square error, total relative deviation, root mean square error and mean absolute error are used as performance criteria. The performance of the estimators is also compared on two real‐life data sets repressing the device failures times. From both, Monte Carlo simulation and real‐life applications, the results indicated that the proposed modified estimators perform better than the competing estimators and hence their use is recommended for parameter estimation of the Power Function probability model. The findings will help to get more precise parameter estimates for the distribution which is very much applied in different fields particularly in modelling failure times of electronic devices and components.

Studies the asymptotic characteristics of uniform scalar quantizers that are optimal with respect to mean-squared error (MSE). When a symmetric source density with infinite support is sufficiently well behaved, the optimal step size /spl Delta//sub N/ for symmetric uniform scalar quantization decreases as 2/spl sigma/N/sup -1/V~/sup -1/(1/6N/sup 2/), where N is the number of quantization levels, /spl sigma//sup 2/ is the source variance and V~/sup -1/(/spl middot/) is the inverse of V~(y)=y/sup -1/ /spl int//sub y//sup /spl infin// P(/spl sigma//sup -1/X>x) dx. Equivalently, the optimal support length N/spl Delta//sub N/ increases as 2/spl sigma/V~/sup -1/(1/6N/sup 2/). Granular distortion is asymptotically well approximated by /spl Delta//sub N//sup 2//12, and the ratio of overload to granular distortion converges to a function of the limit /spl tau//spl equiv/lim/sub y/spl rarr//spl infin//y/sup -1/E[X|X>y], provided, as usually happens, that /spl tau/ exists. When it does, its value is related to the number of finite moments of the source density, an asymptotic formula for the overall distortion D/sub N/ is obtained, and /spl tau/=1 is both necessary and sufficient for the overall distortion to be asymptotically well approximated by /spl Delta//sub N//sup 2//12. Applying these results to the class of two-sided densities of the form b|x|/sup /spl beta//e(-/spl alpha/|x|/sup /spl alpha//), which includes Gaussian, Laplacian, Gamma, and generalized Gaussian, it is found that /spl tau/=1, that /spl Delta//sub N/ decreases as (ln N)/sup 1//spl alpha///N, that D/sub N/ is asymptotically well approximated by /spl Delta//sub N//sup 2//12 and decreases as (ln N)/sup 2//spl alpha///N/sup 2/, and that more accurate approximations to /spl Delta//sub N/ are possible. The results also apply to densities with one-sided infinite support, such as Rayleigh and Weibull, and to densities whose tails are asymptotically similar to those previously mentioned.

As of late, the group of multi carrier direct sequence code division multiple access (MC-DS-CDMA) transmission technologies has drawn a considerable measure of consideration in giving broadband wireless communication services. It stands as a promising procedure to help multiple clients with secured high speed wireless communications. In any case, the limit of the MC-DS-CDMA is restricted via multiple access interference (MAI) as of different clients and furthermore it influences the CDMA frameworks performance. To beat such disadvantage, a proficient wireless transmission plot that mitigates the MAI for dual tree complex wavelet transform centered MC-DS-CDMA frameworks is proposed by this given paper. In the proposed conspire, total mean square error equalizer is utilized to presents the initial appraisal of clients’ data and the successive interference cancellation plot is after that utilized to regenerate and call off the MAI from the desired client. In this proposed scheme, MAI is revived; subsequently as of the signal that was received it is subtracted in time domain ahead of equalization. The proposed system successfully maintains a deliberate distance from the MAI and also enhances the limit is revealed in experimental outcomes.

A regressive logistic model for the analysis of data with dependent binary observations is constructed by successively conditioning on preceding observations. The properties of this model are investigated and compared to those of the ordinary logistic regression model in which the dependence is not considered, using computer simulation. Comparison criteria include the magnitude of the bias and the total mean square error (MSE) of the regression coefficient β and the significance level. The results suggest the regressive model significantly improves the estimation of the regression coefficient Keywords: Binary observationsMaximum likelihoodMonte CarloMultivariate analysisRobustness

In order to improve the level of coal mine safety inspection and ensure safety production, a dynamic perception model based on Internet of things is set up in view of uncertain areas and time of surrounding rock mass catastrophe. Observations from various types of different sensors are combined to provide a robust and complete description of surrounding rock mass in mine. Moreover, a multi-sensor data fusion algorithm based on the theory of support and adaptive weighted is proposed. Firstly, the consistency of data is checked and the outlier data is eliminated. Then, the mutual support degree is calculated and the low calculation data are replaced. Finally, the adaptive weighted algorithm is used to estimate the final parameters. Thus, the total mean square error of target parameter is minimum. The algorithm improves the accuracy of the fusion data free from any priori conditions. Experimental results verify the accuracy of the proposed algorithm and achieve the desired effects.

A Numerical Model with Finite Difference Schemes for Multi-Species Solute Transport in Porous Media

We present results concerning the parameter estimates obtained by prediction error methods in the case of input signals that are insufficiently rich, Such input signals are typical of industrial measurements where occasional stepwise reference changes occur, As is intuitively obvious, the data located around the input signal discontinuities carry most of the useful information, Using singular value decomposition (SVD) techniques, we show that in noise undermodeling situations, the remaining data may introduce large bias on the model parameters with a possible increase of their total mean square error, A data selection criterion is then proposed to discard such poorly informative data to increase the accuracy of the transfer function estimate.

The chapter contains elements of theory of random processes required for time series analysis and for understanding its results. The time series discussed in this book belong to the class of stationary random processes, which means that their statistical properties averaged over an ensemble of realizations of the process do not depend upon the time origin. If averaging over an ensemble of realizations is equivalent to averaging over time of any single realization, the process is ergodic. If a stationary process is Gaussian, it is also ergodic. In our research, we mostly have just one sample realization (one time series) of finite length and by extending the properties estimated from a single time series to the entire process under the study, we assume that the process is ergodic. The most important characteristics of any time series include the covariance function and spectral density, which describe the time series properties in the time and frequency domains, respectively. The two stationary discrete random processes typical for climatology and other disciplines are white noise and Markov chains. Examples of the true and estimated correlation functions and spectral densities including their sampling variability are briefly discussed for simulated time series of length \( N = 100 \).

A new threshold based Wavelet ECG data compression method is proposed. The proposed method uses linear phase Biorthogonal 9/7 discrete Wavelet transform. Wavelet coefficients are selected based on energy packing efficiency of each subband. Significant wavelet coefficients are quantized with uniform scalar zero zone quantizer (USZZQ). Significance map is created to store the indices of the significant coefficients and this map is encoded efficiently with less number of bits by applying Huffman coding on the differences between the indices. ECG records from the MIT-BIH arrhythmia and compression test database are selected as test data. For the record 117, the proposed method achieves a compression ratio of 17.641: 1 with lower percentage root mean square difference (PRD) compared to other threshold based methods. An average compression ratio of 20.8231:1 with an average PRD of 7.1641% is achieved for 19 records. The performance is better compared to the SPIHT and ASEC method for some selected records.