Group-Based Successive Interference Cancellation for Multi-Antenna NOMA System with Error Propagation

Non-orthogonal multiple access(NOMA)is viewed as a key technique to improve the spectrum efficiency and solve the issue of massive connectivity.However,for power domain NOMA,the required overall transmit power should be increased rapidly with the increasing number of users in order to ensure that the signal-to-interference-plus-noise ratio reaches a predefined threshold.In addition,since the successive interference cancellation(SIC)is adopted,the error propagation would become more serious as the order of SIC increases.Aiming at minimizing the total transmit power and satisfying each user’s service requirement,this paper proposes a novel framework with group-based SIC for the deep integration between power domain NOMA and multi-antenna technology.Based on the proposed framework,a joint optimization of power control and equalizer design is investigated to minimize transmit power consumption for uplink multi-antenna NOMA system with error propagations.Based on the relationship between the equalizer and the transmit power coefficients,the original problem is transformed to a transmit power optimization problem,which is further addressed by a parallel iteration algorithm.It is shown by simulations that,in terms of the total power consumption,the proposed scheme outperforms the conventional OMA and the existing cluster-based NOMA schemes.

Handling Error Propagation in Sequential Data Assimilation Using an Evolutionary Strategy

An evolutionary strategy-based error parameterization method that searches for the most ideal error adjustment factors was developed to obtain better assimilation results. Numerical experiments were designed using some classical nonlinear models （i.e., the Lorenz-63 model and the Lorenz-96 model）. Crossover and mutation error adjustment factors of evolutionary strategy were investigated in four aspects： the initial conditions of the Lorenz model, ensemble sizes, observation covarianee, and the observation intervals. The search for error adjustment factors is usually performed using trial-and-error methods. To solve this difficult problem, a new data assimilation system coupled with genetic algorithms was developed. The method was tested in some simplified model frameworks, and the results are encouraging. The evolutionary strategy- based error handling methods performed robustly under both perfect and imperfect model scenarios in the Lorenz-96 model. However, the application of the methodology to more complex atmospheric or land surface models remains to be tested.

Total Sensitivity Index Calculation of Tool Requirement Model via Error Propagation Equation

A new and convenient method is presented to calculate the total sensitivity indices defined by variance-based sensitivity analysis. By decomposing the output variance using error propagation equations, this method can transform the ＂double-loop＂ sampling procedure into ＂single-loop＂ one and obviously reduce the computation cost of analysis. In contrast with Sobors and Fourier amplitude sensitivity test （FAST） method, which is limited in non-correlated variables, the new approach is suitable for correlated input variables. An application in semiconductor assembling and test manufacturing （ATM） factory indicates that this approach has a good performance in additive model and simple non-additive model.

Extensions of nonlinear error propagation analysis for explicit pseudodynamic testing

Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm （Chang, 2003） are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom （SDOF） system, can be applied to a nonlinear multiple degree of freedom （MDOF） system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing.

Error Propagation in Geochemical Calculations of Groundwater-Mineral Interactions:A Case Study from the Pingdingshan Coalfield,Henan

The WATEQ4F-based “multiple step method”, or the method of running WATEQ4F repeatedly, was used to evaluate the error propagation in computations of water-mineral interactions under the circumstances of constant and varied temperatures due to the uncertainties of input variables. The results show the following: the errors of water chemistry analysis can strongly affect the modelling results of water-mineral reactions; different input variables (errors) have different effects on the saturation indices (S.I.) of different minerals; in many cases, the S.I. errors of minerals change with temperatures.

A SCR method for uncertainty estimation in geodesy non-linear error propagation: Comparisons and applications

We review three derivative-free methods developed for uncertainty estimation of non-linear error propagation, namely, MC(Monte Carlo), SUT(scaled unscented transformation), and SI(sterling interpolation). In order to avoid preset parameters like as these three methods need, we introduce a new method to uncertainty estimation for the first time, namely, SCR(spherical cubature rule), which is no need for setting parameters. By theoretical derivation, we prove that the precision of uncertainty obtained by SCR can reach second-order. We conduct four synthetic experiments, for the first two experiments, the results obtained by SCR are consistent with the other three methods with optimal setting parameters, but SCR is easier to operate than other three methods, which verifies the superiority of SCR in calculating the uncertainty. For the third experiment, real-time calculation is required, so the MC is hardly feasible. For the forth experiment, the SCR is applied to the inversion of seismic fault parameter which is a common problem in geophysics, and we study the sensitivity of surface displacements to fault parameters with errors. Our results show that the uncertainty of the surface displacements is the magnitude of ±10 mm when the fault length contains a variance of 0.01 km^(2).

Misclassification error propagation in land cover change categorization

It is important to describe misclassification errors in land cover maps and to quantify their propagation through geo-processing to resultant information products,such as land cover change maps.Geostatistical simulation is widely used in error modeling,as it can generate equal-probable realizations of the fields being considered,which can be summarized to facilitate error propagation analysis.To fix noninvariance in indicator simulation,discriminant space-based methods were proposed to enhance consistency in area-class mapping and replicability in uncertainty modeling,as the former is achieved by imposing means while the latter is ensured by projecting spatio-temporal correlated residuals in discriminant space to geographic space through a mapping process.This paper explores discriminant models for error propagation in land cover change detection,followed by experiments based on bi-temporal remote sensing images.It was found that misclassification error propagation is effectively characterized with discriminant covariate-based stochastic simulation,where spatio-temporal interdependence is taken into account.

Locating Error Considering Dimensional Errors Modeling for Multistation Manufacturing System

Multistation machining process is widely applied in contemporary manufacturing environment. Modeling of variation propagation in multistation machining process is one of the most important research scenarios. Due to the existence of multiple variation streams, it is challenging to model and analyze variation propagation in a multi-station system. Current approaches to error modeling for multistation machining process are not explicit enough for error control and ensuring final product quality. In this paper, a mathematic model to depict the part dimensional variation of the complex multistation manufacturing process is formulated. A linear state space dimensional error propagation equation is established through kinematics analysis of the influence of locating parameter variations and locating datum variations on dimensional errors, so the dimensional error accumulation and transformation within the multistation process are quantitatively described. A systematic procedure to build the model is presented, which enhances the way to determine the variation sources in complex machining systems. A simple two-dimensional example is used to illustrate the proposed procedures. Finally, an industrial case of multistation machining part in a manufacturing shop is given to testify the validation and practicability of the method. The proposed analytical model is essential to quality control and improvement for multistation systems in machining quality forecasting and design optimization.

Altimetric Algorithm and Errors of Ocean Altimetry Using GNSS Reflection Signals

As a new remote sensing technology, the global navigation satellite system（GNSS） reflection signals can be used to collect the information of ocean surface wind, surface roughness and sea surface height. Ocean altimetry based on GNSS reflection technique is of low cost and it is easy to obtain large amounts of data thanks to the global navigation satellite constellation. We can estimate the sea surface height as well as the position of the specular reflection point. This paper focuses on the study of the algorithm to determine the specular reflection point and altimetry equations to estimate the sea surface height over the reflection region. We derive the error equation of sea surface height based on the error propagation theory. Effects of the Doppler shift and the size of the glistening zone on the altimetry are discussed and analyzed at the same time. Finally, we calculate the sea surface height based on the simulated GNSS data within the whole day and verify the sea surface height errors according to the satellite elevation angles. The results show that the sea surface height can reach the precision of 6 cm for elevation angles of 55° to 90°, and the theoretical error and the calculated error are in good agreement.

Analytical exploration of γ-function explicit method for pseudodynamic testing of nonlinear systems

It has been well studied that the γ-function explicit method can be effective in providing favorable numerical dissipation for linear elastic systems. However, its performance for nonlinear systems is unclear due to a lack of analytical evaluation techniques. Thus, a novel technique is proposed herein to evaluate its efficiency for application to nonlinear systems by introducing two parameters to describe the stiffness change. As a result, the numerical properties and error propagation characteristics of the γ-function explicit method for the pseudodynamic testing of a nonlinear system are analytically assessed. It is found that the upper stability limit decreases as the step degree of nonlinearity increases; and it increases as the current degree of nonlinearity increases. It is also shown that this integration method provides favorable numerical dissipation not only for linear elastic systems but also for nonlinear systems. Furthermore, error propagation analysis reveals that the numerical dissipation can effectively suppress the severe error propagation of high frequency modes while the low frequency responses are almost unaffected for both linear elastic and nonlinear systems.

New SST correction method from multi-satellite based on the coefficient of variation

In remote sensing sea surface temperature （SST）, the traditional fusion method is used to compute the dot product of a subjective weight vector with a satellite measurement vector, while the result requires validation by field measurement. However, field measurement that relative to the satellite measurement is very sparse, many information may not be verified. A relative objective weight vector is constructed by using the limited field measurement, which is based on coefficient of variation method. And then it make an application of the data fusion by the weighted average method in the SST data. fuse SST data with the weighted average method. In this way, some posteriori information can be added to the fusion process. The model reduces the dependence on verification, and some of the satellite measurement can be handled without corresponding to the field measurement, and the fusion result matches transfer errors theory.

Dual-threshold symbol selective relaying in cooperative networks

In order to efficiently mitigate error propagation and reduce computational complexity, this paper proposes a scheme for traditional cooperative networks, named as dual-threshold symbol selective demodulate-and-forward. In the scheme, two log likelihood ratio(LLR)-based thresholds are devised to measure the reliability of received signals for the relay and the destination, respectively. One of the threshold guarantees that the relay only forwards reliable symbols, thus less error will be propagated to the destination. The other threshold is used at the destination for determining the reliability of symbols received from the source.The destination will directly demodulate reliable symbols received from the source. Otherwise, when the symbols received from the source are not reliable, the maximum ratio combiner(MRC) is used to combine symbols received from the source and the relay.Closed-form expression of the bit error probability(BEP) of the proposed scheme is derived and analyzed under binary phase shift keying(BPSK) modulation. Then, the relationship and closed-form solutions of two LLR-based thresholds are derived. Simulation results prove that the theoretical BEP of the proposed scheme closely matches the simulated ones. The proposed scheme can achieve high performance with low computational complexity compared to existing schemes.

Selection of time step for pseudodynamic testing

Although the step degree of nonlinearity has been introduced to conduct basic analysis and error propagation analysis for the pseudodynamic testing of nonlinear systems, it cannot be reliably used to select an appropriate time step before performing a pseudodynamic test. Therefore, a novel parameter of instantaneous degree of nonlinearity is introduced to monitor the stiffness change at the end of a time step, and can thus be used to evaluate numerical and error propagation properties for nonlinear systems. Based on these properties, it is possible to select an appropriate time step to conduct a pseudodynamic test in advance. This possibility is very important in pseudodynamic testing, since the use of an arbitrary time step might lead to unreliable results or even destroy the test specimen. In this paper, guidelines are proposed for choosing an appropriate time step for accurate integration of nonlinear systems. These guidelines require estimation of the maximum instantaneous degree of nonlinearity and the solution of the initial natural frequency. The Newmark explicit method is chosen for this study. All the analytical results and the guidelines proposed are thoroughly confirmed with numerical examples.

Computing mean fields with known Reynolds stresses at steady state

With the rising of modern data science,data-driven turbulence modeling with the aid of machine learning algorithms is becoming a new promising field.Many approaches are able to achieve better Reynolds stress prediction,with much lower modeling error(∈_(M)),than traditional Reynolds-averaged Navier-Stokes(RANS)models,but they still suffer from numerical error and stability issues when the mean velocity fields are estimated by solving RANS equations with the predicted Reynolds stresses.This fact illustrates that the error of solving the RANS equations(∈_(P))is also very important for a RANS simulation.In the present work,the error∈_(P)is studied separately by using the Reynolds stresses obtained from direct numerical simulation(DNS)/highly resolved large-eddy simulation to minimize the modeling error∈_(M),and the sources of∈_(P)are derived mathematically.For the implementations with known Reynolds stresses solely,we suggest to run an auxiliary RANS simulation to make a first guess onν_(t)^(*)and S_(ij)^(0).With around 10 iterations,the error of the streamwise velocity component could be reduced by about one-order of magnitude in flow over periodic hills.The present work is not to develop a new RANS model,but to clarify the facts that obtaining mean field with known Reynolds stresses is nontrivial and that the nonlinear part of the Reynolds stresses is very important in flow problems with separations.The proposed approach to reduce∈_(P)may be very useful for the a posteriori applications of the data-driven turbulence models.

Estimation and Prediction of Gas Chromatography Retention Indices of Hydrocarbons in Straight-run Gasoline by Using Artificial Neural Network and Structural Coding Method

The molecular structures of hydrocarbons in straight run gasoline were numerically coded. The nonlinear quantitative relationship(QSRR) between gas chromatography(GC) retention indices of the hydrocarbons and their molecular structures were established by using an error back propagation(BP) algorithm. The GC retention indices of 150 hydrocarbons were then predicted by removing 15 compounds(as a test set) and using the 135 remained molecules as a calibration set. Through this procedure, all the compounds in the whole data set were then predicted in groups of 15 compounds. The results obtained by BP with the correlation coefficient and the standard deviation 0 993 4 and 16 54, are satisfied.

Spatial Propagation of Different Scale Errors in Meiyu Frontal Rainfall Systems

The spatial propagation of meso-and small-scale errors in a Meiyu frontal heavy rainfall event,which occurred in eastern China during 4-6 July 2003,is investigated by using the mesoscale numerical model MM5.In general,the spatial propagation of simulated errors depends on their horizontal scales.Small-scale（L 〈 100 km） initial error may spread rapidly as an isotropic circle through the sound wave.Then,many scattered convection-scale errors are triggered in moist convection zone that will spread abroad through the isotropic,round-shaped sound wave further more.Corresponding to the evolution of the rainfall system,several new convection-scale errors may be generated continuously by moist convection within the propagated round-shaped errors.Through the above circular process,the small-scale error increases in amplitude and grows in scale rapidly.Mesoscale（100 km 〈 L 〈 1000 km） initial error propagates up-and down-stream wavelike through the gravity wave,meanwhile migrating down-stream slowly along with the rainfall system by the mean flow.The up-stream propagation of the mesoscale error is very important to the error growth because it can accumulate error energy locally at a place where there is no moist convection and far upstream from the initial perturbation source.Although moist convection plays an important role in the rapid growth of errors,it has no impact on the propagation of meso-and small-scale errors.The diabatic heating could trigger,strengthen,and promote upscaling of small-scale errors successively,and provide ＂error source＂ to error growth and propagation.The rapid growth of simulated errors results from both intense moist convection and appropriate spatial propagation of the errors.

An error analysis and optimization method for combined measurement with binocular vision

The accurate measurement of surfaces of large aviation components is vital for the assessment of manufacturing and assembly quality of such components.To satisfy the measurement requirement of large-size components,most current researches pay more attention to combined measurement methods utilizing different measuring instruments,but the related researches on error analysis and optimization methods are not taken enough attention.This paper proposes a combined laser-assisted measurement method with feature enhancement techniques,and it also develops an error propagation model of the main factors affecting the overall measurement error in detail.Firstly,the surface of a large-size component is measured by the measurement system at multiple stations.Secondly,a control point coordinate system is established as a bridge to unify all local measurement data into the global coordinate system.To improve the overall measurement accuracy,the pixel extraction error as a key factor causing the overall measurement error is analyzed in detail.Next,the error propagation model is established,and some optimization strategies of layout for minimizing measurement error and transformation error are researched.Finally,experiments are carried out to verify the effectiveness of the proposed method.The results show that the measurement error of the proposed method reaches 0.073%and 0.14%with a 1 D standard ruler and a flat plate,respectively.

MLSE-assisted decision feedback equalizer for error-propagation suppression in high-speed IM-DD transmission systems

We propose a trellis-compressed maximum likelihood sequence estimation(TC-MLSE)-assisted sliding-block decision feedback equalizer(DFE)to suppress the error propagation resulting from the DFE in high-speed systems.We use an out-ofrange detector to detect the end of burst errors from the DFE and activate the optional TC-MLSE to correct burst errors.We conduct experiments to transmit a 201-Gbit/s PAM-8 signal.The results show that the proposed method achieves a bit error rate of 3.65×10^(-3),which is close to that of MLSE.The optional MLSE is only activated when needed and processes 11.4%of the total symbols.Moreover,the proposed method compresses the maximum length of burst errors from 19 to 5.

A tip clearance prediction model for multistage rotors and stators in aero-engines

Tip clearances of multistage rotors and stators greatly affect aero-engines’ aerodynamic efficiency, stability and safety. The inevitable machining and assembly errors, as well as the complicated error propagation mechanism, cause overproof or non-uniform tip clearances. However, it is generally accepted that tip clearances are difficult to predict, even under assembly state. In this paper, a tip clearance prediction model is proposed based on measured error data. Some 3 D error propagation sub-models, regarding rotors, supports and casings, are built and combined. The complex error coupling relationship is uncovered using mathematical methods. Rotor and stator tip clearances are predicted and analyzed in different phase angles. The maximum, minimum and average tip clearances can be calculated. The proposed model is implemented by a computer program,and a case study illustrates its performance and verifies its feasibility. The results can be referred by engineers in assembly quality judgement and decision-making.

Transmit correlation effect on SIC-ZF receiver for V-BLAST system

It has been shown that transmit correlation causes a signal-to-noise ratio （SNR） loss in the zero forcing （ZF） receiver for V-BLAST （Vertical Bell LAbs LAyered Space-Time） system. In this paper, we investigate the transmit correlation effect on the ZF receiver with successive interference cancellation （SIC）. We show that such an unfavorable condition leads to twofold effects on the performance degradation. In addition to the immediate SNR loss, the transmit correlation can increase the propagation factor to spread decision error significantly. These two effects are evaluated analytically. We derive the probability density function （pdf） of the effective SNR at each decoded stream, and hence accurately quantify the SNR loss. We also calculate the decision error propagation factor in terms of its second moment. In particular, we show that transmit correlation can cause a stable component of error propagation which does not decline during the SIC procedure. Finally, we conduct the simulation to verify the analytical results.