Accurate evaluation of bit-error rates of optical communication systems using the Gram-Charlier series

The probability densities and cumulative distribution functions of decision statistics of optical communications systems are expanded as a Gram-Charlier (G-C) series, leading to arbitrarily accurate systematic evaluation of bit-error rates (BERs) and optimal decision thresholds of optical communication systems. The method displays negligible computational complexity and is applicable whenever the moment or cumulant generating functions of the decision statistics are analytically available. We applied the technique to a birth-and-death Markovian model of a direct-detection receiver with optical preamplifier in a two-level amplitude-shift keying system. The modal expansion series rapidly converged, whereas the alternative saddlepoint approximation method predicted a BER which deviated by 7% from the G-C result.     

A Gram-Charlier series method of calculating the probability of error in lightwave transmission systems

A Gram-Charlier series method has previously been applied to the calculation of the conditional probability of error, for a fixed data sequence, in the presence of intersymbol interference, detector multiplication noise, shot noise, and thermal noise. The probability of error is obtained by averaging the conditional probability of error over all possible data sequences. In this paper it is shown how the computational efficiency of the Gram-Charlier series method can be improved by calculating the probability of error without the need for an exhaustive averaging procedure.     

Inter-cell interference modeling for cellular networks

We develop and analyze several inter-cell interference modeling methods for various fading scenarios in wireless systems. The models can analyze multiple interfering signals under different fading scenarios. Incoherent addition of multiple interfering signals is assumed. In this paper, we present two approaches, i.e., the approximate and exact analysis methods to calculate the probability density function (PDF) of the power of the interference signals. We propose the use of the generalized Gram-Charlier Series to analyze the error of the reference model. Although the computational complexity of exact analysis is high, it can be used to ensure the accuracy of the approximate analysis method. Hermite polynomials are used to simplify the integration operation into the summation operation, thus reduces the computational complexity of the exact method dramatically. The approximate method is simple although it may lead to increased errors. The methods proposed are useful in designing and analyzing practical systems.     

Considerations on Error Probability in Correlated-Symbol Systems

An approach to evaluate the error probability in conventional PAM digital data transmission systems with correlated symbols in the presence of intersymbol interference and additive noise is formulated in general and it is applied to the Gram-Charlier series expansion method. It is shown that the technique of conditioning few symbols before and/or after the symbol to be detected increases substantially the range of signal-to-noise ratios with an acceptable increase of numerical work. This technique also improves existing bounds on error probability, as, e.g, Glave's bound.     

On Gram-Charlier Approximations

A Gram-Charlier series involves the expansion of one probability density function in terms of the derivatives of another density function. This paper generalizes the original series introduced by Gram, an expansion that minimizes a weighted square error. Two new Gram-Charlier expansions for the density of a finite variate are derived and recursion formulas for series coefficients are given.     

Generalized Gram-Charlier series with application to the sum of log-normal variates (Corresp.)

A generalized Gram-Charlier series, applicable to non-Gaussian problems, is developed. Expressions are given for the first six error coefficients. The high inherent accuracy of the series is demonstrated by development of the expansion for the sum of independent, identically distributed log-normal variates.     

非线性混叠信号的可分离性及分离方法研究

该文分析了非线性混叠信号的可分离性及分离条件,指出现阶段非线性混叠信号盲分离的局限性。将Edgeworth展开代入信息后向传输算法中,通过一种新的自适应累积量估计方法,克服了原算法指出的Edgeworth展开在盲信号分离中的缺限。计算机仿真结果表明了所提算法在特定非线性混叠模型信号分离的效果,我们还对不同的方法进行了分析对比,指出了累积量对不同算法的影响。     

Analysis of equal-gain diversity with partially coherent fadingsignals

An analytical technique based on Gram-Charlier series expansion is presented for the computation of the error probability of equal-gain combiner (EGC) with partially coherent fading signals. Imperfect carrier recovery is attributed to the random noise present in the carrier recovery loops. The resulting noisy phase references are assumed to satisfy Tikhonov distribution. The fades on the diversity branches are assumed to be slowly varying and statistically independent with Rayleigh-distributed envelopes. The error-rate performance of coherent and differentially coherent phase-shift keying (PSK) systems are compared and the phase precision requirement for a reliable coherent detection is computed. Detection loss caused by carrier phase errors is computed for several signal-to-noise ratio (SNR) reliability and bit error probability levels. It is demonstrated that the effect of carrier phase errors on the mean SNR is negligible compared to their effect on deep fades or small bit error probabilities. It is also shown that the carrier phase precision requirement can be reduced through signal combination     

An analytical method for approximate performance evaluation of binary linear block codes

An analytical method for approximate performance evaluation of binary linear block codes using an additive white Gaussian noise channel model with binary phase-shift keying modulation is presented. We focus on the probability density function of the bit log-likelihood ratio (LLR), which is expressed in terms of the Gram-Charlier series expansion. This expansion requires knowledge of the statistical moments of the bit LLR. We introduce an analytical method for calculating these moments. This is based on some recursive calculations involving certain weight enumerating functions of the code. It is proved that the approximation can be as accurate as desired, if we use enough terms in the Gram-Charlier series expansion. Numerical results are provided for some examples, which demonstrate close agreement with simulation results.     

A comprehensive performance analysis of relay-aided CDMA communications over dissimilar fading channels

In this paper, bit error probability (BEP), outage probability (OP) and channel capacity (CC) of direct-sequence code-division multiple access systems with amplify-and-forward relaying are presented for different fading scenarios. In the first scenario, the source-destination link is assumed to experience Rayleigh fading while it is subject to Nakagami-m fading in the second scenario. The source-relay and relay-destination channels are considered to have Nakagami-m fading conditions in two scenarios. First, analytical expressions for the end-to-end probability density function (PDF) are derived by using the convolution integral. Then, BEP, OP and CC are obtained based on these PDFs in terms of infinite series. Truncation error analyses are presented for different parameter values in order to show that truncation error arising from the infinite series is negligible. Simple and easy-to-compute asymptotic expressions are also introduced for BEP and OP in order to simplify the performance analysis in high signal-to-noise ratio region. Simulation results are provided to show the accuracy of the proposed approximate and asymptotic expressions.     

A New Approach to Bivariate Hoyt Distribution and its Application in Performance Analysis of Dual-Diversity Receivers

Novel infinite series based expressions for the bivariate Hoyt distribution are derived. More specifically, expressions for the joint probability density function (JPDF) and the joint cumulative distribution function (JCDF) of two Hoyt fading envelopes are derived, and proposed for use in performance analyses of dual-branch diversity receivers operating over correlated Hoyt fading channels. Using these reasonably simple and mathematically tractable expressions, we evaluate the performance of a dual-branch selection combining (SC) diversity receiver in terms of the outage probability (P _out ) and the average bit error probability (ABEP) criteria. The ABEP performance is evaluated for binary differential phase-shift-keying (BDPSK) and binary non-coherent frequency-shift keying (BNFSK) modulation schemes.     

An efficient reliability estimation method for CNTFET-based logic circuits

Carbon nanotube field-effect transistors (CNTFETs) have been widely studied as a promising technology to be included in post-complementary metal-oxide-semiconductor integrated circuits. Despite significant advantages in terms of delay and power dissipation, the fabrication process for CNTFETs is plagued by fault occurrences. Therefore, developing a fast and accurate method for estimating the reliability of CNTFET-based digital circuits was the main goal of this study. In the proposed method, effects related to faults that occur in a gate's transistors are first represented as a probability transfer matrix. Next, the target circuit's graph is traversed in topological order and the reliabilities of the circuit's gates are computed. The accuracy of this method (less than 3% reliability estimation error) was verified through various simulations on the ISCAS 85 benchmark circuits. The proposed method outperforms previous methods in terms of both accuracy and computational complexity.     

On outage and error rate analysis of the ordered V-BLAST

Outage and error rate performance of the ordered BLAST with more than 2 transmit antennas is evaluated for i.i.d. Rayleigh fading channels. A number of lower and upper bounds on the 1st step outage probability at any SNR are derived, which are further used to obtain accurate approximations to average block and total error rates. For m Tx antennas, the effect of the optimal ordering at the first step is an m-fold SNR gain. As m increases to infinity, the BLER decreases to zero, which is a manifestation of the space-time autocoding effect in the V-BLAST. While the sub-optimal ordering (based on the before-projection SNR) suffers a few dB SNR penalty compared to the optimal one, it has a lower computational complexity and a 3 dB SNR gain compared to the unordered V-BLAST and can be an attractive solution for low-complexity/low-energy systems. Uncoded D-BLAST exhibits the same outage and error rate performance as that of the V-BLAST. An SNR penalty of the linear receiver interfaces compared to the BLAST is also analytically evaluated.     

Unbiased Variance Estimates for System Reliability Estimate Using Block Decompositions

An unbiased estimator is proposed to calculate the variance of a system reliability estimate based on the estimated variance of component reliability estimates. The method does not require any parametric assumptions for component reliability or time-to-failure, and it allows Type-I and Type-II censored data. The approach can be applied to many situations as long as the system can be appropriately decomposed into series or parallel configurations. The new model is compared with existing methods using different reliability data and system structures. The empirical results show that the new model is generally superior in terms of computational efficiency, and estimation accuracy.      

Application of the Complementary Derivatives Method in the ADI-FDTD Solution of Maxwell's Equations

The alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is well suited for simulating structures with large aspect ratios or problems with large gradient fields where different grid sizes can be used to yield greater computational efficiency. However, using different grid sizes increases the truncation error at the interface between domains having different grid sizes. The truncation error is manifested as a spurious reflection from the grid boundary, thus decreasing the simulation accuracy. In this paper, we apply the complementary derivatives method (CDM) to reduce the spurious reflections arising from the use of different grid size domains when using the ADI-FDTD method. It is shown that, the CDM guarantees uniform second-order accuracy throughout the computational domain. When the CDM is implemented in the ADI-FDTD method, the implicit updating equations cannot be written in a tri-diagonal matrix and the computational efficiency of the ADI-FDTD method is not preserved. By employing the Sherman-Morrison formula, we retain the numerical efficiency of the conventional ADI-FDTD. A representative numerical example is presented to demonstrate the accuracy of CDM in the ADI-FDTD simulations.     

Accurate Evaluation of Bit-Error Rates of Optical Communication Systems Using the Gram–Charlier Series

Accurate Evaluation of Bit-Error Rates of Optical Communication Systems Using the Gram–Charlier Series The probability densities and cumulative distribution functions of decision statistics of optical communications systems are expanded as a Gram–Charlier series, leading to arbitrarily accurate systematic evaluation of bit-error rates and optimal decision thresholds of optical communication systems. The method displays negligible computational complexity, and is applicable whenever the moment or cumulant generating function of the decision statistics are analytically available. We applied the technique to a birth-and-death Markoffian model of a direct-detection receiver with optical preamplifier in a two-level amplitude-shift keying system. The modal expansion series rapidly converged, whereas the alternative saddlepoint approximation method predicted a bit-error rate which deviated by 7% from the Gram–Charlier result.     

基于累量的近场源快速定位算法

本文提出了一种基于累量的近场源参数快速估计方法。具体地,本文首先构造了一个累量矩阵,对其进行奇异值分解后,利用得到的右奇异向量和左奇异向量分别使用类Root-MUSIC方法得到了近场波达方向和距离估计的闭式解。该方法利用高阶累量矩阵,减少了阵列孔径损失,提高了能分辨的最大信源数,而且与其他基于高阶累积量的方法相比,该方法在近场的波达方向与距离的估计过程中只需要构造一个累量矩阵和进行一次奇异值分解,并且使用闭式解完全避免了峰值搜索,大大降低了运算量,同时还提高了估计的分辨概率和精度。此外,该方法在几乎没有增加额外计算量的情况下可以推广到混合场源的情况。仿真结果表明,该算法的分辨率和精度都有较大的优越性。      

Fiber Optics Receiver Error Rate Prediction Using the Gram-Charlier Series

This paper applies the Gram-Charlier series method to the caculation of error probabilties in digital optical receivers. This method allows the calculation of "exact" error probabilities including the effects of avalanche noise, thermal noise, and arbitrary posidetection processing filter. The predictions of this method are compared with those of a simple Gaussian approximation and with the Chernoff bounds. Finally, the effects of modal noise are included in the theory, and some specific cases are explored numerically.     

Outage Probability Analysis of Three-User Reed–Solomon Coded Cooperation Scheme for Wireless Slow Fading Channel

In a coded cooperation scheme, the relay must decode and re-encode data. This process needs to be completed rapidly. Therefore, a simple channel coding/decoding scheme that requires low computational loads is needed. Reed–Solomon (RS) codes are simple, forward error-correction codes with low decoding computational loads. This paper introduces a three-user RS coded cooperation scheme that aims to have simple encoding/decoding complexity as well as to increase diversity order. It also presents the mathematical derivations of outage probability and investigates the outage performance of the three-user RS coded cooperation scheme. The derived outage probability expressions prove that the three-user RS coded cooperation scheme can achieve full diversity. Numerical bit error rate comparisons show that the three-user RS coded cooperation scheme performs better than a two-user scheme under various inter-user and uplink channel conditions. Outage probability performance improves at approximately 5 dB for regions with low signal-to-noise ratio (SNR) and 10 dB for regions with high SNR under a slow-fading channel. The paper also presents the complete calculated numerical tables for outage probability terms (integral terms) that do not have closed-form solutions.     

Infinite series representations of the bivariate Rayleigh andNakagami-m distributions

Despite the usefulness of the bivariate (correlated) Nakagami-m cumulative distribution function (cdf) in communications systems analysis, an infinite series for the computation of this function is not known. In this letter, an infinite series representation of the bivariate cdf is derived. Bounds on the error resulting from truncation of the infinite series are also derived