Gaussian Approximation Method Research Articles

Quaternary DS-SSMA Communications Employing Generalized Detector over Rayleigh Fading Channels

This paper deals with an employment of the complex modulators and generalized receivers constructed based on the generalized approach to signal processing (GASP) in noise in quaternary direct-sequence spread-spectrum multiple-access (DS-SSMA) communication systems with complex signature sequences in flat Rayleigh fading. Owing to availability of large sets of complex spreading sequences possessing perfect correlation characteristics, the interest to use the complex spreading sequences in DS-SSMA communication systems has increased. The complex spreading sequences investigated in the present paper are based on the recently introduced orthogonal unified complex Hadamard transform (UCHN) sequences. In the present paper, the complex processing in modulators and generalized receivers is also employed with the purpose to take advantage of the correlation properties of complex signature sequences. We derive the average bit error rate (BER) for quarternary synchronous communications system based on the generalized approach to signal processing in noise first, and then the BER for quaternary asynchronous ones is evaluated using the characteristic function approach. We presented some results based on the Gaussian approximation method for asynchronous communication systems constructed on the basis of the generalized approach to signal processing in noise Computer modeling results demonstrate that the communication systems using UCHT spreading sequences perform generally better than the GOLD sequences and the 4-phase family A sequences. Comparative analysis between the asynchronous communication systems constructed on the basis of the generalized approach to signal processing in noise demonstrates superiority over the asynchronous communication systems employing the correlation receiver.

Global Visual and Semantic Observations for Outdoor Robot Localization

Most approaches to robot visual localization rely on local, global visual or semantic information as observation. In this paper, the combination of global visual and semantic information is used as landmark in the observation model of Bayesian filters. Introducing the improved Gaussian Process into observation models with visual information, The GP-Localize algorithm is extended to high dimensional data, which means that all the historical data with spatiotemporal correlation to achieve constant time and memory for persistent outdoor robot localization can be considered by the Bayesian filters. The other contribution of this paper is we combine the all above parts into a system for robot visual localization and apply it to two real-world outdoor datasets including unmanned ground vehicle (UGV) and unmanned aerial vehicle (UAV). According to the experimental results, it's no difficult to find there is a higher accuracy while using global vision and semantic results rather than just using single feature. By using the combined features and improved Gaussian process approximation method in Bayes filters, our system is more robust and practical than existing localization systems such as ORB-SLAM.

Optimisation design of systematic fountain codes on fading channels

The asymptotic performance and optimisation of systematic fountain codes are investigated on Rayleigh fading and Nakagami fading channels. Firstly, the closed-form bit error rates (BER) of systematic LT (SLT) codes and systematic Raptor (SR) codes are derived based on Gaussian approximation method, the results of which are close to that obtained by discretised density evolution. Secondly, a novel optimisation model combining linear programming and theoretical error probability is proposed to design the degree distributions of SLT/SR codes on fading channels. The simulation results show that the optimised codes provide better BER performance than the codes originally designed for binary erasure channel and additive white Gaussian noise channel. Moreover, the proposed method is easily extended to Rician fading channel and unfading channel.

Approximate Reliability Evaluation of Large-Scale Multistate Series-Parallel Systems

Multistate series-parallel system (MSSPS) is a widely used model for representing engineering systems, whose reliability has been extensively analyzed. Universal generating function (UGF) is an efficient method for evaluating the reliability of MSSPS. However, when facing the large-scale MSSPS, where the number of system components and possible states are enormous, calclating the exact system reliability can be rather time-consuming. To evaluate the reliability of large-scale MSSPS more efficiently, this paper proposes an approximation method, named continuization discretization approximation (CDA) method. The CDA approach consists of continuization and discretization processes. The continuization process applies Gaussian approximation method based on the central limit theory and the UGF technique to evaluate parallel subsystems. While the discretization process discretizes the continuous distribution to a discrete one, and proposes an algorithm to evaluate the series subsystems efficiently. The efficiency and accuracy performance of the CDA method can be adjusted by parameters according to the computational resource and the system scale. The newly proposed method is compared to the existing methods in evaluating the large-scale MSSPS. Numerical examples show that the CDA method has evident advantage in computational efficiency with satisfactory accuracy performance.

Gaussian Mixture Model for Millimeter-Wave Cellular Communication Networks

As compared to the microwave communication networks, the theoretical analyses of system performances such as the cell coverage and the cell average data rate are more difficult due to the unique propagation path loss model for mmWave cellular communication networks. In this paper, based on the unique transmission states of the distance-dependent piecewise propagation probability functions, the analytical six-state analytical mixture distribution of the propagation loss including the distance-dependent path loss, shadowing and small-scale fading is obtained. For each state, a novel Kullback–Leibler divergence based Gaussian approximation method is proposed to model the distribution of the propagation loss. The distribution of the propagation loss including the large-scale fading and small-scale fading is approximated via a six-state Gaussian mixture model, then the closed-form expression for the signal-to-noise ratio can be easily obtained. The cell coverage is expressed as the weighted sum of the error functions, and the cell average data rate is expressed as the weighted sum of the moments of the propagation loss for the six different states. Numerical results show that the cell coverage mainly depends on the none line-of-sight transmission and the cell average data rate mainly depends on the line-of-sight transmission.

Performance Analysis of LDPC-BICM System Based on Gaussian Approximation

In this paper, we propose a performance analysis algorithm of low density parity check-bit interleaved coded modulation (LDPC-BICM) system. First, we introduce the Gaussian mixture approximation method of the LLR messages output from the demodulator over the AWGN channel. Then, we analyze the density evolution based on these Gaussian mixture approximation LLR messages. During the analysis, the Gaussian approximation is applied to simplify the calculation. Some LDPC-BICM systems (which are adopted by ATSC3.0 standard) are used to evaluate the proposed algorithm. We also employ the actual performances and the thresholds obtained by the multi-edge type (MET) discretized density evolution algorithm as the references. The simulation results prove that our proposed algorithm can work well in most cases. Furthermore, the proposed algorithm is simpler than the MET algorithm because of the Gaussian or Gaussian mixture approximations.

Overall elastic properties of a material containing inhomogeneities of concave shape

In this paper, we consider materials containing superspherical inhomogeneities and compare effects produced by pores and rigid particles of this shape. The overall properties are expressed in terms of compliance contribution tensors calculated for inhomogeneities using Finite Element Method (FEM) and Gaussian Approximation (GA) method. Consistency of the results obtained by two numerical techniques is observed for most of the shapes (except of strongly concave inhomogeneities). Based on the numerical solution for octahedron and analytical results for sphere, contributions of a single inhomogeneity to the effective properties are approximated analytically with high accuracy. Effective properties of materials containing multiple superspherical pores or multiple superspherical rigid inhomogeneities are calculated using Non-Interaction Approximation (NIA) and Mori–Tanaka–Benveniste scheme (MTB) using results for compliance contribution tensors. Results of micromechanical predictions are compared against direct FEM simulations performed on artificial periodic representative volume elements containing parallel oriented pores and rigid particles with volume fraction up to 25%. It is shown that MTB scheme provides reasonably accurate approximations.

A new Gaussian mixture method with exactly exploiting the negative information for GMTI radar tracking in a low-observable environment

This paper investigates the problem of ground vehicle tracking with a Ground Moving Target Indicator (GMTI) radar. In practice, the movement of ground vehicles may involve several different maneuvering types (acceleration, deceleration, standstill, etc.). Consequently, the GMTI radar may lose measurements when the radial velocity of the ground vehicle is below a threshold when it stops, i.e. falling into the Doppler blind region. Besides, there will be false alarms in low-observable environments where there exist high noises interferences. In this paper, we develop a novel algorithm for the GMTI tracking in a low-observable environment with false alarms while exactly incorporating the ‘negative information’ (i.e., the target is likely to stop when no measurements are recorded) based on the Bayesian inference framework. For the Bayesian inference implementation, the Gaussian mixture approximation method is adopted to approximate related distributions, while different filtering algorithms (including both extended Kalman filter and its generalization for interval-censored measurements) are applied for updating the Gaussian mixture components. Target state estimation can be directly obtained through the Gaussian mixture model for the GMTI tracking at every time instance. We have compared the developed method with other state-of-the-art ones and the simulation results show that the proposed method substantially outperforms the existing methods for the GMTI tracking problem.

Accurate and Efficient P-value Calculation Via Gaussian Approximation: A Novel Monte-Carlo Method

ABSTRACTIt is of fundamental interest in statistics to test the significance of a set of covariates. For example, in genome-wide association studies, a joint null hypothesis of no genetic effect is tested for a set of multiple genetic variants. The minimum p-value method, higher criticism, and Berk–Jones tests are particularly effective when the covariates with nonzero effects are sparse. However, the correlations among covariates and the nonGaussian distribution of the response pose a great challenge toward the p-value calculation of the three tests. In practice, permutation is commonly used to obtain accurate p-values, but it is computationally very intensive, especially when we need to conduct a large amount of hypothesis testing. In this paper, we propose a Gaussian approximation method based on a Monte Carlo scheme, which is computationally more efficient than permutation while still achieving similar accuracy. We derive nonasymptotic approximation error bounds that could vanish in the limit even if the number of covariates is much larger than the sample size. Through real-genotype-based simulations and data analysis of a genome-wide association study of Crohn’s disease, we compare the accuracy and computation cost of our proposed method, of permutation, and of the method based on asymptotic distribution. Supplementary materials for this article are available online.

Generalized Multistream Spatial Modulation With Signal Constellations Based on Hurwitz Integers and Low-Complexity Detection

This letter proposes two contributions to improve the performance of transmission with generalized multistream spatial modulation (SM). In particular, a modified suboptimal detection algorithm based on the Gaussian approximation method is proposed. The proposed modifications reduce the complexity of the Gaussian approximation method and improve the performance for high signal-to-noise ratios. Furthermore, this letter introduces signal constellations based on Hurwitz integers, i.e., a 4-D lattice. Simulation results demonstrate that these signal constellations are beneficial for generalized SM with two active antennas.

Systematic Luby transform codes with modified grey‐mapped QAM constellation

Systematic Luby transform (LT) codes with grey-mapped QAM constellations over additive white Gaussian noise (AWGN) channels are investigated. For high-order modulations, it can be learnt that the traditional Gaussian approximation method developed for binary PSK (BPSK) is not accurate any more. To improve BER performance of systematic LT codes with grey-mapped QAM, therefore, presents a novel coded modulation scheme, which only extracts Gaussian alike log-likelihood ratios for decoding, based on the modified QAM constellation. More importantly, the proposed scheme allows to optimise degree distributions for QAM-modulated systematic LT codes as easily as for BPSK. Simulation results show that the degree distribution related to the proposed coded modulation scheme can provide outstanding BER performance for systematic LT codes over the AWGN channel.

Frozen Gaussian approximation for 3D seismic tomography

Three-dimensional (3D) wave-equation-based seismic tomography is computationally challenging in large scales and high-frequency regime. In this paper, we apply the frozen Gaussian approximation (FGA) method to compute 3D sensitivity kernels and seismic tomography of high-frequency. Rather than standard ray theory used in seismic inversion (e.g. Kirchhoff migration and Gaussian beam migration), FGA is used to compute the 3D high-frequency sensitivity kernels for travel-time or full waveform inversions. Specifically, we reformulate the equations of the forward and adjoint wavefields for the purpose of convenience to apply FGA, and with this reformulation, one can efficiently compute the Green’s functions whose convolutions with source time function produce wavefields needed for the construction of 3D kernels. Moreover, a fast summation method is proposed based on local fast Fourier transform which greatly improves the speed of reconstruction as the last step of FGA algorithm. We apply FGA to both the travel-time adjoint tomography and full waveform inversion (FWI) on synthetic crosswell seismic data with dominant frequencies as high as those of real crosswell data, and confirm again that FWI requires a more sophisticated initial velocity model for the convergence than travel-time adjoint tomography. We also numerically test the accuracy of applying FGA to local earthquake tomography. This study paves the way to directly apply wave-equation-based seismic tomography methods into real data around their dominant frequencies.

Physical model for multiple scattered space-borne lidar returns from clouds.

A practical model for determining the time-dependent lidar attenuated backscattering coefficient β was developed for application to global lidar data. An analytical expression for the high-order phase function was introduced to reduce computational cost for simulating the angular distribution of the multiple scattering irradiance. The decay rate of the multiple scattering backscattered irradiance was expressed by incorporating the dependence on the scattering angle and the scattering order based on the path integral approach. The estimated β over time and the actual range showed good agreement with Monte Carlo simulations for vertically homogeneous and inhomogeneous cloud profiles, resulting in about 15% mean relative error corresponding to 4 times improved accuracy against the Ornstein-Fürth Gaussian approximation method.

MOLECULAR ABSORPTION SPECTROSCOPY IN THE UV-VIS REGION FOR THE QUINOLINE-N-OXIDE, NICOTINAMIDE-N-OXIDE AND 2,2-DITHIOBISPYRIDINE-N-OXIDE LIGANDS

The purpose of this study was to analyze and quantify spectral parameters, the absorption bands, specifically in the uv-visible region of some N-oxide ligands. From the spectra, the area under the absorption band, the molar absorptivity, the integrated absorption coefficient and the oscillator strength by the Gaussian approximation method were calculated for each of them, using the proposed evaluation by Drago and Figgs. According to the obtained results, it can be concluded that the heterocyclic compounds studied absorb very well electromagnetic radiation in the ultraviolet region. For the ligands QUI-NO and NIC-NO it was observed that there are two types of bands, primary and secondary, being transitions of type π → π * and n → π*, respectively. For DITBIS-NO, there was only one primary band (transition 1) and two additional shoulders, which had the highest observed absorbance coefficient. These ligands are expected as potential electron donors in complex systems whose purpose is to change the energy levels of the electronic system in order to promote a better utilization of the absorbed energy and therefore a better efficiency.

Sparse Bayesian Learning-Based Kernel Poisson Regression.

In this paper, we introduce a closed-form sparse Bayesian kernel Poisson regression (SBKPR) model for count data regression problems based on the sparse Bayesian learning (SBL) approach. In Bayesian setting, a Gaussian prior is given to the model parameter, which is not the conjugate distribution of Poisson regression. Hence, the model parameters cannot be integrated analytically, which leads to the inference intractable problem. In this paper, the log-gamma Gaussian approximation method is proposed to solve this analytically intractable problem, which can give out the closed-form solutions. Furthermore, an individual Gaussian prior is given to the model parameters, which can enhance the flexibility of the proposed method. Finally, sparse solutions can be obtained by applying SBL, which can benefit the learning efficiency and reduce the computational time in practical applications. Experimental results demonstrate that the proposed SBKPR model can outperform some state-of-the-art count data regression models on both toy data and real-world data.

Proactive Monitoring Via Jamming for Rate Maximization Over MIMO Rayleigh Fading Channels

Legitimately monitoring suspicious wireless communications is important for national security. In this letter, we investigate average monitoring rate maximization problem for a legitimate monitoring system, which proactively monitors a suspicious wireless link via jamming over multiple-input-multiple-output Rayleigh fading channels. We propose to approximate mutual information rates by Gaussian distributions. Furthermore, we propose low-complexity eigenvalue-based methods to calculate the means and variances of mutual information rates. Simulation results demonstrate that our proposed Gaussian approximation methods perform almost the same with the method to employ true probability density functions of mutual information rates.

On the Exact Distribution of Mutual Information of Two-User MIMO MAC Based on Quotient Distribution of Wishart Matrices

We propose an exact calculation of the probability density function (PDF) and cumulative distribution function (CDF) of mutual information (MI) for a two-user multiple-input multiple-output (MIMO) multiple access channel (MAC) network over block Rayleigh fading channels. This scenario can be found in the uplink channel of MIMO non-orthogonal multiple access (NOMA) system, a promising multiple access technique for 5G networks. So far, the PDF and CDF have been numerically evaluated since MI depends on the quotient of two Wishart matrices, and no closed form for this quotient was available. We derive exact results for the PDF and CDF of extreme (the smallest/the largest) eigenvalues. Based on the results of quotient ensemble, the exact calculation for PDF and CDF of mutual information is presented via Laplace transform approach and by direct integration of joint PDF of quotient ensemble’s eigenvalues. Furthermore, our derivations also provide the parameters to apply the Gaussian approximation method, which is comparatively easier to implement. We show that approximation matches the exact results remarkably well for outage probability, i.e., CDF, above 10%. However, the approximation could also be used for 1% outage probability with a relatively small error. We apply the derived expressions to investigate the effects of adding antennas in the receiver and its ability to decode the weak user signal. By supposing no channel knowledge at transmitters and successive decoding at receiver, the capacity of the weak user increases and its outage probability decreases with the increment of extra antennas at the receiver end.

Direct method for Yau filtering system with nonlinear observations

ABSTRACTFor all known finite dimensional filters, one always assumes that the observation terms be degree one polynomials. However, in practice, the observation terms may be nonlinear, e.g. tracking problems. In this paper, we consider the Yau filtering system ( is constant for all i, j) with nonlinear observation terms and arbitrary initial condition. The novelty of the paper lies in (i) the real time computation of the solution of the Duncan-Mortensen-Zakai (DMZ) equation is reduced to the computation of Kolmogorov equation. Based on Gaussian approximation of the initial condition, the Kolmogorov equation can be solved in terms of ordinary differential equations; (ii) For a given probability density function, we give a new and original approach to do Gaussian approximation which is very effective and simple. The direct method developed here can be easily implemented in a real time and memoryless way. Besides, we do not need the controllability and observability assumption. Compared to the extended Kalman filter, our method is much stable and has theoretical proof. The numerical experiments show that the proposed Gaussian approximation method is very effective and our method can track the states very well.

A Novel Multiple-Access Correlation-Delay-Shift-Keying

In Correlation-Delay-Shift-Keying (CDSK), the reference signal and the information-bearing signal are added together during a certain time delay. Because the reference signal is not strictly orthogonal to the information-bearing signal, the cross-correlation between the adjacent chaotic signal (Intra-signal Interference, ISI) will be introduced into the demodulation at the receiver. Therefore, the Bit-Error Ratio (BER) of CDSK is higher than that of Differential-Chaos-Shift-Keying (DCSK). To avoid the ISI component and enhance the BER performance of CDSK in multiuser scenario, Multiple-Access CDSK with No Intra-signal Interference (MA-CDSK-NII) is proposed. By constructing the repeated chaotic generator and applying the Walsh code sequence to modulate the reference signal, in MA-CDSK-NII, the ISI component will be eliminated during the demodulation. Gaussian approximation method is adopted here to obtain the exact performance analysis of MA-CDSK-NII over additive white Gaussian noise (AWGN) channel and Rayleigh multipath fading channels. Results show that, due to no ISI component and lower transmitting power, the BER performance of MA-CDSK-NII can be better than that of multiple-access CDSK and Code-Shifted Differential-Chaos-Shift-Keying (CS-DCSK).

Tracking of group targets using multiple models GGIW-PHD algorithm based on best-fitting Gaussian approximation and strong tracking filter

Gamma Gaussian inverse Wishart probability hypothesis density (GGIW-PHD) filter algorithm is always used for tracking group targets with unknown number and variable measurement rates in the presence of cluttered measurements and missing detections. Aiming at the defect that the tracking error of GGIW-PHD filter algorithm will increase greatly in the maneuvering stage, a multiple model GGIW-PHD (MM-GGIW-PHD) algorithm is proposed in this paper based on the best-fitting Gaussian approximation and strong tracking filter. Firstly, on the basis of measurement set partition, the best-fitting Gaussian approximation method is proposed to implement the fusion of multiple models in the PHD predict stage. And a fading factor of strong tracking filter is proposed to correct the predicted covariance matrix of the GGIW component. Then, the estimation of kinematic state and extension state are deduced in the frame of multiple models. The probability of different tracking models is updated by the modified likelihood functions. The simulation results show that the MM-GGIW-PHD algorithm based on best-fitting Gaussian approximation and strong tracking filter can decrease the tracking error of group targets in the maneuvering stage and treated with the combination/spawning of group effectively.