Gaussian Approximation Technique Research Articles

Reducing Delay and Packets Loss in IoT-Cloud Based ECG Monitoring by Gaussian Modeling

Abstract— Health monitoring based on the internet of things (IoT) and cloud computing is regarded as a hot topic to research. However, such systems often face issues with delay and throughput due to the large amount of data that must be transmitted from sensors to the cloud. One important type of data for health monitoring is Electrocardiogram (ECG) signals, which generate a large amount of data to be transmitted. This research treats this problem by modelling these signals in order to reduce their size using Gaussian approximation. The cloud server is an MQTT broker to which the sensors publish their data via a gateway. The Gaussian parameters are calculated in the gateway, which act as a Fog layer, before published to the broker. The monitoring devices can subscribe to the broker and access the transmitted data. Our experiments were conducted using the MIT–BIH dataset and a real broker (HiveMQ). The results showed that the system was able to significantly reduce delay in transmitting data and prevent loss of information. Without using the Gaussian approximation technique, the system was only able to monitor a limited number of patients (17 for Qos1 and 23 for Qos0) without losing information. However, when using the Gaussian approximation model with five functions, the system was able to monitor many more patients (78 for Qos1 and 100 or more for Qos0) without losing any data.

Performance analysis of optical spectral amplitude CDMA system unipolar codes with double weight construction design

Abstract Optical Codes Division Multiple Access is a multiplexing approach in which the transmitter a distinguishable optical code is assigned to each user in the communication channel. OCDMA is designed for radio frequency (RF) communication systems and it is a variation of the CDMA system. Subsequently, to develop all OCDMA communication systems, the success of CDMA in wireless networks, as well as the full benefits of fibre optics, such as good security, extremely high bandwidth, low attenuation, and long-haul transmission. In this research Spectral Amplitude Coding-Optical Code Division Multiple Access is proposed. Initially, Modified Double Weight and Zero Cross-Correlation (MDW-ZCC) is proposed in this research to construct the code design of SAC-OCDMA, it produces the best possible autocorrelation and cross-correlation values. Subsequently, a combined Single Photodiode (SPD) and Direct detection technique is introduced to decode the transmitter information and it reduces the noise. Accordingly, a Gaussian approximation technique is presented to estimate the Bit error rate from the eye diagram of BER and Q-factor. Accordingly, the proposed method is simulated using Python software. The performance metrics are Q-factor, and bit error rate and the proposed method is compared with the existing Three-Dimensional Single Weight Zero Cross-Correlation (3D-SWZCC) Code, Two Dimensional Spectral/Spatial Cyclic Shift (2D-SSCS), and Permutation Matrix Zero Cross-Correlation (PM-ZCC) Code. Subsequently, these results exhibit that the proposed method produces the best performance than the other methods and it estimates the BER. Consequently, future work is based on the study of 3D codes with m-sequence code in the spectral/time/spatial OCDMA domain. The approach has elegantly integrated the design of an encoder and a decoder, allowing the system to efficiently create code in 3D bipolar mode, respectively.

Improved statistical fluctuation analysis for measurement-device-independent quantum key distribution

Measurement-device-independent quantum key distribution (MDI-QKD) is a promising protocol for realizing long-distance secret keys sharing. However, its key rate is relatively low when the finite-size effect is taken into account. In this paper, we consider statistical fluctuation analysis for the three-intensity decoy-state MDI-QKD system based on the recent work (Zhang et al. in Phys Rev A 95:012333, 2017) and further compare its performance with that of applying the Gaussian approximation technique and the Chernoff bound method. The numerical simulations demonstrate that the new method has apparent enhancement both in key generation rate and transmission distance than using Chernoff bound method. Meanwhile, the present work still shows much higher security than Gaussian approximation analysis.

Uncertainty Quantification for History-Matching Problems

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 181611, “Uncertainty Quantification for History-Matching Problems With Multiple Best Matches Using a Distributed Gauss-Newton Method,” by Guohua Gao, SPE, Jeroen C. Vink, SPE, Chaohui Chen, SPE, Mohammadali Tarrahi, SPE, and Yaakoub El Khamra, Shell, prepared for the 2016 SPE Annual Technical Conference and Exhibition, Dubai, 26–28 September. The paper has not been peer reviewed. It is critically important for decision making and an extremely challenging task to quantify the uncertainty of model parameters and production forecasts properly after conditioning to production data. This paper presents a novel approach to generate approximate conditional realizations using the distributed Gauss-Newton (DGN) method together with a multiple local Gaussian approximation technique. Results are compared with those obtained from other approaches, such as randomized maximum likelihood (RML), ensemble Kalman filter (EnKF), and Markov-chain Monte Carlo (MCMC). Introduction It is well-known that oil- and gasfield development is a high-risk venture. Uncertainties originating from geological models (e.g., structure, stratigraphy, channels, and geobodies) are coupled with uncertainties of reservoir models (e.g., distribution of permeability and porosity in the reservoir) and uncertainties of economic parameters (e.g., oil and gas prices and costs associated with drilling and other operations). It is critically important to properly quantify the uncertainty of such parameters and their effect on production forecasts and economic evaluations. Recently, multiobjective-optimization techniques have been developed to maximize expectations of some economic indicators (e.g., net present value) and, at the same time, to minimize associated uncertainty or risk. Because of limited access to the subsurface reservoir (e.g., it is impossible to measure the permeability and porosity at the location of each gridblock of a simulation model), reservoir properties have quite large uncertainties. In a greenfield, before starting production, available data are limited to static data or hard data such as core data, well-log data, well-testing data, and sometimes seismic data. Hence, it is necessary to generate multiple realizations of structural and petrophysical models with limited information, on the basis of prior estimates of the relative probability of each realization. Then, uncertainty in reservoir performance or production forecasting can be quantified (e.g., with design of experiment or with other techniques). Generally, production profiles generated by running reservoir-simulation models with these prior realizations or unconditional realizations do not honor production data. Uncertain model parameters, such as permeability and porosity, potentially in each gridblock, have to be tuned so that the modified reservoir models are able to generate production profiles that are compatible with production data (e.g., by use of assisted history matching).

Improved key-rate bounds for practical decoy-state quantum-key-distribution systems

The decoy-state scheme is the most widely implemented quantum key distribution protocol in practice. In order to account for the finite-size key effects on the achievable secret key generation rate, a rigorous statistical fluctuation analysis is required. Originally, a heuristic Gaussian-approximation technique was used for this purpose, which, despite of its analytical convenience, was not sufficiently rigorous. The fluctuation analysis has recently been made rigorous by using the Chernoff bound. There is a considerable gap, however, between the key rate bounds obtained from these new techniques and that obtained from the Gaussian assumption. Here, we develop a tighter bound for the decoy-state method, which yields a smaller failure probability. This improvement results in a higher key rate and increases the maximum distance over which secure key exchange is possible. By optimizing the system parameters, our simulation results show that our new method almost closes the gap between the two previously proposed techniques and achieves a similar performance to that of conventional Gaussian approximations.

Performance Analysis of IEEE 802.15.4 RF Zigbee Transceiver in an Indoor and Outdoor Environment

Objective: This paper focuses on the Bit Error Rate (BER) performance of IEEE 802.15.4 RF Zigbee transceiver compliant WSN in an interference environment. This includes 1. Studying of effect of various building materials and partitions in an indoor environment and 2. Effect of interference that coexist in an outdoor environment. Methods/Statistical Analysis: In an indoor environment, building materials such as hard board, concrete wall and the partitions of two floors are considered for the analysis. Path loss due to those materials in an indoor environment is calculated by log-distance model. Improved Gaussian Approximation (IGA) technique is used to derive the closed form expression for BER considering less number of interferers in a Rayleigh fading outdoor environment. BER are analysed by varying the IEEE 802.15.4 standard specific physical layer parameters, such as number of bits in a Zigbee symbol, number of modulation levels used in an OQPSK modulator and spreading length of PN sequence. Findings: The analysis in an indoor environment points out that, path-loss provided by hard board and concrete wall to the signal is equal. In case of floors, path-loss value get increased as number of floors increases between transmitter and receiver. In outdoor environment, it is analysed that BER performance of Zigbee transceiver shows better performance when lower number of bits in a Zigbee symbol and lower level of modulation scheme in OQPSK modulator. Application/Improvements: The performance can be improved by using chaotic sequence for spreading in place of PN sequence and can be implemented for IoT based applications.

Some Asymptotic Results of Kernel Density Estimators Under Random Left-Truncation and Dependent Data

Problems with truncated data arise frequently in survival analyses and reliability applications. The estimation of the density function of the lifetimes is often of interest. In this article, the estimation of density function by the kernel method is considered, when truncated data are showing some kind of dependence. We apply the strong Gaussian approximation technique to study the strong uniform consistency for kernel estimators of the density function under a truncated dependent model. We also apply the strong approximation results to study the integrated square error properties of the kernel density estimators under the truncated dependent scheme.

Theoretical Analysis on Bit Error Rate of VSG CDMA in Nakagami Fading

In this paper, an efficient analytical technique for bit error rate (BER) of variable spreading gain code division multiple access (VSG CDMA) in Nakagami fading is introduced. Based on the accurate improve Gaussian approximation (IGA) technique, a new BER expression is derived in a closed form. Validated by Monte Carlo simulation, the proposed expression is used to accurately investigate the impacts of channel's conditions, power allocation and random users' distributions on the BER performance.

Asymptotic behaviors of the Lorenz curve and Gini index in sampling from a length-biased distribution

In this work, we consider the nonparametric estimators of the Lorenz curve and Gini index based on a sample from the corresponding length-biased distribution. We show that this estimators are strongly consistent for the associated Lorenz curve and Gini index. Strong Gaussian approximations for the associated Lorenz process are established under appropriate assumptions. We apply the strong Gaussian approximation technique to obtain a functional law for the iterated logarithm for the Lorenz curve. Also, we obtain an asymptotic normality for the corresponding Gini index.

Bit Error Rate Performance for Multicarrier Code Division Multiple Access over Generalized η-μ Fading Environment

The multicarrier code division multiple access (MC-CDMA) system has received a considerable attention from researchers owing to its great potential in achieving high data rates transmission in wireless communications. Due to the detrimental effects of multipath fading the performance of the system degrades. Similarly, the impact of non-orthogonality of spreading codes can exist and cause interference. This paper addresses the performance of multicarrier code division multiple access system under the influence of frequency selective generalized η-µ fading channel and multiple access interference caused by other active users to the desired one. We apply Gaussian approximation technique to analyse the performance of the system. The avearge bit error rate is derived and expressed in Gauss hypergeometic functions. Maximal ratio combining diversity technique is utilized to alleviate the deleterious effect of multipath fading. We observed that the system performance improves when the parameter η increase or decreasse in format 1 or format 2 conditions respectively.

Exact BER performance of asynchronous MC-DS-CDMA over fading channels [Transactions Letters

In this contribution an accurate average Bit Error Rate (BER) formula is derived for MC-DS-CDMA in the context of asynchronous transmissions and random spreading sequences. We consider a flat Nakagami-m fading channel for each subcarrier. Our analysis is based on the Characteristic Function (CF) and does not rely on any assumption concerning the statistical behavior of the interference. We develop a new closed-form expression for the conditional CF of the inter-carrier interference and provide a procedure for calculating the exact BER expressed in the form of a single numerical integration. The accuracy of the Standard Gaussian Approximation (SGA) technique is also evaluated. Link-level results confirm the accuracy of the SGA for most practical conditions.

BER Analysis of OFDM Systems Impaired by Phase Noise in Frequency-Selective Fading Channels

In this paper, we study the effect of finite-power, phase-locked loop based phase noise on the bit-error-rate (BER) performance of orthogonal frequency division multiplexing (OFDM) systems in frequency-selective fading channels. It is well known the impact of phase noise on the performance of an OFDM system can be divided into a multiplicative term called common phase error (CPE) and an additive term called intercarrier interference (ICI). Based on the conditional Gaussian approximation technique, we first derive the BER formulas for BPSK, QPSK, 16-QAM, and 64-QAM modulated OFDM signals in frequency-selective Rayleigh fading channels. To further quantify the individual influence of the CPE and the ICI on system performance for different phase noise spectra, we derive the BER expressions for perfect CPE compensation cases. The analytical results obtained for frequency-selective Rayleigh fading channels are then generalized to frequency-selective Rician fading channels. Simulation results not only validate the accuracy of our analysis but also show the dependency of BERs on the shapes of phase noise spectra.

Strong uniform consistency of kernel density estimators under a censored dependent model

Problems with censored data arise frequently in survival analyses and reliability applications. The estimation of the density function of the lifetimes is often of interest. In this paper, the estimation of the density function by the kernel method is considered, when censored data show some kind of dependence. We apply the strong Gaussian approximation technique for studying the strong uniform consistency for kernel estimators of the density function under a censored dependent model.

Hybrid optical/RF channels: characterization and performance study using low density parity check codes

A hybrid channel, consisting of a free space optical (FSO) link and a parallel radio frequency (RF) link, is considered. The FSO link carries most of the transmitted data while leaving only a small fraction of the data to be carried by the RF link. It is first shown that the capacity of the proposed hybrid structure is much higher than the capacity of a single FSO link. Next the performance of the hybrid channel is studied using a low density parity check code. A density evolution strategy for the hybrid channel is derived and a Gaussian approximation technique is presented. Using these techniques, the conditions for the convergence of the message passing algorithm in terms of minimum data carrying rate through the RF link are derived. Finally, numerical results showing the benefits of the hybrid channel under various channel conditions are presented.

Precise asymptotics in the law of logarithm under dependence assumptions

In a recent paper by Spătaru [Precise asymptotics for a series of T.L. Lai, Proc. Amer. Math. Soc. 132 (11) (2004) 3387–3395] a precise asymptotics in the law of the logarithm for sequence of i.i.d. random variables has been established. In this paper we show that there is an analogous result for strictly stationary φ -mixing sequence. To prove this result, we have to use a different method. One of our main tools is the Gaussian approximation technique.

A Linear Programming Approach to Cross-Layer Optimization in Multiclass VSG-CDMA Over Rayleigh Fading

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents a new linear programming approach for throughput maximization on the uplink of a multiclass variable spreading gain code-division multiple-access (CDMA) multicellular system in Rayleigh fading for both binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) modulations. Based on the improved Gaussian approximation technique, we derive exact closed-form expressions of the outage probability, which are used as a physical (PHY) layer constraint of the maximization problem. We show that it is possible to transform the nonlinear constraint into a set of equivalent linear expressions. This facilitates the formulation of a new linear throughput maximization that noticeably requires less computational complexity than the known nonlinear approaches. Furthermore, due to the simplicity of the linear approach, we can include the constraints of such higher layers, i.e., media access control (MAC) and call admission control (CAC) layers, into the proposed formula. Accordingly, we introduce two linear programming optimization formulas. One is for MAC-PHY optimization, and another is for cross-layer optimal CAC policy. In the case of MAC-PHY optimization, the throughput is maximized, at low background noise level, when every user retains the same bit energy, particularly in the case where the difference in data rates is high. Nonetheless, at high levels of background noise, the throughput would be maximized when a larger amount of bit energy is allocated to the high-rate users. For the joint optimal policy, the throughput and the blocking probability are optimized and improved up to 50% in comparison to those of the conventional CAC policy, which is known as the <emphasis emphasistype="boldital">complete sharing</emphasis> policy. </para>

Near Optimum and Highly Efficient Decision-Feedback Receivers for Direct Sequence Ultra-Wideband Radio

This paper investigates three decision- feedback receivers for Direct-Sequence Ultra-Wideband Radio (DS-UWB) based on two-channel BPSK modulation with ternary spreading code. A compact and insightful vector-matrix signal model is built up for receiver design under UWB channel dispersion over many consecutive symbols. First, we consider the design of a RAKE with Decision Feedback (RAKE-DF) receiver. Using the Gaussian approximation technique, we derive its analytic performance under no error propagation. It is shown that the RAKE-DF receiver suffers from a significant error floor due to the uncancelled pre-cursor ISI (or pre-ISI abbreviated). Next, we design the MMSE-DF receiver to achieve a better performance by suppressing the pre-ISI, too. However, the MMSE receiver requires costly matrix inversion. Then a new receiver is investigated as the third one, which is called the RAKE with Bi-Directional Decision Feedback (RAKE-BDDF) receiver, for efficiently canceling both the post-(cursor) ISI and pre-ISI at symbol rate. It cannot only attain the matched filter bound approximately, but also maintain a similar complexity as that of the RAKE-DF receiver. Simulation and semi-analytic BER curves are included for performance comparison of the three receivers in the presence of the CM2 and CM4 UWB channels.

Efficient and robust decision delays selection scheme for multiuser MIMO DFE in power imbalance situation

Recently, it has been shown that the selection of decision delays has a crucial effect on the performance of finite-length multiple-input multiple-output decision-feedback equalization (MIMO-DFE) receiver for multiuser time division multiple access (TDMA) system. With the minimum joint-BER (MJB) criterion, choosing the optimum different decision delays for individual uplink users would require multi- dimensional searching, which is too costly for real-time applications. In this paper, we propose an efficient power-ratio-based (PRB) scheme to solve the multiuser decision delay problem in practice. First, it employs the MIMO channel responses to calculate the received power ratios among uplink users. The ratios are then compared to a set of preset thresholds to determine the decision delays. To optimize the thresholds, Gaussian approximation (GA) technique is used for speeding up the off-line searching process. Under power imbalance situation, we note that the decision delays must be carefully selected on a burst-by-burst basis, or else the performance loss for the weaker users would be very significant. Hence, both the MJB and PRB methods can resist the near-far effect. Finally, simulation results show that the proposed PRB scheme has an approximate BER performance, but with much reduced computational complexity, as compared to the optimal MJB one.

Raptor codes on binary memoryless symmetric channels

In this paper, we will investigate the performance of Raptor codes on arbitrary binary input memoryless symmetric channels (BIMSCs). In doing so, we generalize some of the results that were proved before for the erasure channel. We will generalize the stability condition to the class of Raptor codes. This generalization gives a lower bound on the fraction of output nodes of degree 2 of a Raptor code if the error probability of the belief-propagation decoder converges to zero. Using information-theoretic arguments, we will show that if a sequence of output degree distributions is to achieve the capacity of the underlying channel, then the fraction of nodes of degree 2 in these degree distributions has to converge to a certain quantity depending on the channel. For the class of erasure channels this quantity is independent of the erasure probability of the channel, but for many other classes of BIMSCs, this fraction depends on the particular channel chosen. This result has implications on the "universality" of Raptor codes for classes other than the class of erasure channels, in a sense that will be made more precise in the paper. We will also investigate the performance of specific Raptor codes which are optimized using a more exact version of the Gaussian approximation technique.

Statistical characterization and bit-error rate analysis of lightwave systems with optical amplification using two-photon-absorption receiver structures

In this paper, the authors study the performance of a two-photon absorption (TPA) receiver in a typical communication system employing an optical amplifier. For the study, the authors develop a comprehensive performance analysis, taking into account noises due to an optical amplifier, shot noise, and thermal noise, using Gaussian approximation technique. In evaluating the performance of the system using this technique, the mean and the variance of the received signal will be derived. Comparing the results of receivers using the TPA process with that of a typical single-photon absorption (SPA) structure leads the authors to conclude that TPA receivers can be used when the speed of the electronic parts of the receiver structures is not too high, as expected