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.     

Detection in weibull and log-normal noises

The discrete-time detection of narrowband coherent and incoherent pulse train signals in narrowband non-Gaussian noise is investigated. The locally optimum (LO) detector structures are developed and found to be in the form of incorporating a locally optimum zero-memory nonlinearity (LOZNL) into the Neyman-Pearson optimum detector for narrowband Gaussian noise. Many practical detectors belong in the same class of structures with the LO detector. The expressions for the efficacies of the detectors are derived. In particular, Weibull and log-normal noise models are considered. The LOZNL’s, and the efficacies of the detectors are given, and numerical results are graphically presented. It is shown that, in the sense of the Pitman asymptotic relative efficiency (ARE), the asymptotic performance of many detectors whose nonlinearity can more effectively suppress the tail of the noise envelope distribution is apparently better than that of the Neyman-Pearson optimum detector for narrowband Gaussian noise.     

威伯尔和对数正态噪声中的检测问题

本文研究窄带非高斯(non-Gaussian)噪声中窄带相参和非相参脉冲串信号的离散时间检测。导出了局部最佳(LO)检测器结构,它具有在窄带高斯噪声中的尼曼-皮尔逊(Neyman-Pearson)最佳检测器里引入局部最佳零记忆非线性(LOZNL)的形式。许多实用检测器属于与LO检测器相同类型的结构,导出了这些检测器功效的表达式,特别研究了威伯尔(Weibull)和对数正态噪声模型。导出了LOZNL和检测器功效,并用曲线给出了数值结果。说明在皮特曼(Pitman)的渐近相对效率(ARE)意义上,许多具有能更多抑制噪声包络分布尾部的非线性的检测器,其渐近性能明显优于窄带高斯噪声中的尼曼-皮尔逊最佳检测器。     

An investigation of Gaussian tail and Rayleigh tail densityfunctions for importance sampling digital communication systemsimulation

The gains achieved by the use of importance sampling in communication system simulation are strongly influenced by the choice of the biased input noise distribution. The Rayleigh tail and the Gaussian tail distributions are investigated for use as biased distributions in importance sampling. The robustness of these schemes with respect to the estimate of the unknown error probability is examined. It is shown that the Gaussian tail distribution previously considered to be theoretically optimum is not optimum in this regard. Methods of generating the biased random variates are presented     

Dual diversity over correlated log-normal fading channels

A great deal of attention has been devoted in the literature to studying the bit error rate (BER) performance of diversity combining systems in the presence of Rayleigh, Rice, and Nagakami-m fading. By comparison, the literature is relatively sparse in comparable analyses over log-normal channels which typically characterize shadowing from indoor obstacles and moving human bodies. One reason for this disparity stems from the difficulty in evaluating the exact average BER when log-normal variates are involved, using, for example, the moment-generating function (MGF) approach, due to the inability of expressing the MGF itself in a simple closed form. Since it is possible to evaluate the marginal and joint statistical moments as well as the cumulative distribution function (CDF) associated with a log-normal distribution in closed form, we rather focus here on other performance measures, namely, average combined output signal-to-noise ratio, amount of fading, and outage probability. The first two performance measures depend only on the moments, whereas the outage probability depends solely on the cdf. Closed-form expressions (in terms of known functions), single-integral representations, or upper and lower bounds are obtained for these measures corresponding to maximal-ratio combining, selection combining, and switch-and-stay combining schemes, allowing for the possibility of correlation between the two branches. Numerical evaluations of these expressions illustrating the performances of each individual diversity type as well as comparisons among them are also presented.     

Asymptotic Distribution of Bayes Estimators in Censored Type-I Samples From A Mixed Exponential Population

Bayes estimators in censored type-I samples, from a mixed exponential population are considered. Their large sample properties are examined by simulation. A log-normal distribution can explain adequately the asymptotic behaviour of Bayes estimators of the parameters.     

Efficient Nakagami-m fading channel Simulation

An efficient method for generating correlated Nakagami-m fading envelope samples is presented; this method is applicable for arbitrary values of the fading parameter m. The new method is compared to other methods used to generate Nakagami-m random variates. An accurate approximation to the inverse Nakagami-m cumulative distribution function, valid for all values of m, is derived. Uncertainties regarding the autocorrelation of the Nakagami-m fading process are discussed. The fading envelope autocorrelation is determined by simulation and asymptotic analysis.     

Sum and difference of two squared correlated Nakagami variates in connection with the McKay distribution

General formulas for the probability density function of the sum and the difference of two correlated, not necessarily identically distributed, squared Nakagami variates (or equivalently, gamma variates) are derived. These expressions are shown to be in the form of the McKay "Bessel function" distributions. In addition, formulas for the moments of these distributions, in terms of the Gauss hypergeometric function, are provided. An application of these new results relevant to the calculation of outage probability in the presence of self-interference is discussed.     

Tail probabilities with statistical multiplexing and effective bandwidths in multi-class queues

Our primary purpose in this paper is to contribute to the design of admission control schemes for multi-class service systems. We are motivated by emerging highspeed networks exploiting asynchronous transfer mode (ATM) technology, but there may be other applications. We develop a simple criterion for feasibility of a set of sources in terms of effective bandwidths. These effective bandwidths are based on asymptotic decay rates of steady-state distributions in queueing models. We show how to compute asymptotic decay rates of steady-state queue length and workload tail probabilities in general infinite-capacity multi-channel queues. The model hasm independent heterogeneous servers that are independent of an arrival process which is a superposition ofn independent general arrival processes. The contribution of each component arrival process to the overall asymptotic decay rates can be determined from the asymptotic decay rates produced by this arrival process alone in a G/D/1 queue (as a function of the arrival rate). Similarly, the contribution of each service process to the overall asymptotic decay rates can be determined from the asymptotic decay rates produced by this service process alone in a D/G/1 queue. These contributions are characterized in terms of single-channel asymptotic decay-rate functions, which can be estimated from data or determined analytically from models. The asymptotic decay-rate functions map potential decay rates of the queue length into associated decay rates of the workload. Combining these relationships for the arrival and service channels determines the asymptotic decay rates themselves. The asymptotic decay-rate functions are the time-average limits of logarithmic moment generating functions. We give analytical formulas for the asymptotic decay-rate functions of a large class of stochastic point processes, including batch Markovian arrival processes. The Markov modulated Poisson process is a special case. Finally, we try to put our work in perspective with the related literature.     

A central-limit-theorem-based approach for analyzing queue behaviorin high-speed networks

In this paper, we study P(𝒬>x), the tail of the steady-state queue length distribution at a high-speed multiplexer. In particular, we focus on the case when the aggregate traffic to the multiplexer can be characterized by a stationary Gaussian process. We provide two asymptotic upper bounds for the tail probability and an asymptotic result that emphasizes the importance of the dominant time scale and the maximum variance. One of our bounds is in a single-exponential form and can be used to calculate an upper bound to the asymptotic constant. However, we show that this bound, being of a single-exponential form, may not accurately capture the tail probability. Our asymptotic result on the importance of the maximum variance and our extensive numerical study on a known lower bound motivate the development of our second asymptotic upper bound. This bound is expressed in terms of the maximum variance of a Gaussian process, and enables the accurate estimation of the tail probability over a wide range of queue lengths. We apply our results to Gaussian as well as multiplexed non-Gaussian input sources, and validate their performance via simulations. Wherever possible, we have conducted our simulation study using importance sampling in order to improve its reliability and to effectively capture rare events. Our analytical study is based on extreme value theory, and therefore different from the approaches using traditional Markovian and large deviations techniques     

Asymptotic sampling distribution of inversecoefficient-of-variation and its applications

This paper develops the asymptotic sampling distribution of the inverse of the coefficient of variation (InvCV). This distribution is used for making statistical inference about the population CV (coefficient of variation) or InvCV without making an assumption about the population distribution. It applies to making inferences (point and interval estimation, and hypothesis-testing) about the shape parameter of some popular lifetime distributions like the Gamma, Weibull, and log-normal, when the scale parameter is unknown. The test procedure is used to test exponentiality against a Gamma or a Weibull alternative. The results are compared with those in the literature     

Capacity Bounds for MIMO Nakagami- $m$ Fading Channels

This paper studies the ergodic capacity limits of multiple-input multiple-output (MIMO) antenna systems with arbitrary finite number of antennas operating on general fading environments. Through the use of majorization theory, we first investigate in detail the ergodic capacity of Nakagami- $m$ fading channels, for which we derive several ergodic capacity upper and lower bounds. We then show that a simple expression for the capacity upper bound is possible for high signal-to-noise ratio (SNR), which permits to analyze the impact of the channel fading parameter $m$ on the ergodic capacity. The asymptotic behavior of the capacity in the large-system limit in which the number of antennas at one or both side(s) goes to infinity, is also addressed. Results demonstrate that the capacity scaling laws for Nakagami-$m$ and Rayleigh-fading MIMO channels are identical. Finally, we employ the same technique to distributed MIMO (D-MIMO) systems undergoing composite log-normal and Nakagami fading, where we derive similar ergodic capacity upper and lower bounds. Monte Carlo simulation results are provided to verify the tightness of the proposed bounds.      

Tradeoff analysis of throughput and fairness on CDMA packet downlinks with location-dependent QoS

This work presents the quantitative tradeoff relation between system throughput and fairness on multirate code-division multiple-access (CDMA) downlinks. We develop and use an analytical model and a method for performance evaluation. The proposed model and method reflect the effects of multiplexing scheme, a limited data-rate set, log-normal shadowing, the best base station selection, and self-interference. System performance measures include asymptotic throughput, fairness performance factors, and outage probability . The performance of packet channels for delay-tolerant service is evaluated based on 3GPP wide-band code-division multiple-access (WCDMA) system model. Using the method developed, various algorithms for time resource assignment are applied and the system performance measures are derived and compared. We have derived the tradeoff between asymptotic throughput and fairness performance factors caused by the location-dependent carrier-to-interference ratio. The results show that we can control the tradeoff by applying various time resource-assignment schemes. It is also shown that the tradeoff in the system with the limited data-rate set can be improved by setting the number of simultaneous users properly.     

On the generation of Tikhonov variates

A novel, simple and efficient method for the generation of Tikhonov (a.k.a. von Mises) random variates is proposed. In the proposed method, circular variates of a prescribed Tikhonov distribution p_T(x;alpha,xi) are generated via the transformation of variates selected randomly, on a one-for-one basis, from a bank of K distinct Cauchy and Gaussian generators. The mutually exclusive probabilities of sampling from each of the Cauchy or Gaussian generators, as well as the variance and half-width parameters that specify the latter, are derived directly from the Cauchy, Gaussian and Tikhonov characteristic functions, all of which are either known or given in closed form. The proposed random mixture technique is extremely efficient in that a single pair of uniform random numbers is consumed in the generation of each Tikhonov (or von Mises) sample, regardless of the prescribed concentration and centrality parameters (alpha, xi), all requiring neither the rejection of samples, nor the repetitive evaluation of computationally demanding functions. Additional attractive features of the method are as follows. By construction, the first (dominant) N circular moments of Tikhonov variates generated with the proposed random mixture technique are the ones that best approximate their corresponding theoretical values, with errors measured exactly. The exact distribution of generated Tikhonov variates is determined analytically, and its (Kullback-Leibler) divergence to the exact Tikhonov PDF is shown also analytically to be negligible. Finally, the technique establishes a connection between Tikhonov and Gaussian variates which can be exploited, e.g., in the generation of piecewise-continuous pseudo-random functions with Tikhonov-distributed outcomes.     

Estimating the Ergodic Capacity of Log-Normal Channels

In this paper, we first provide a very accurate estimation of the capacity of a single-input single-output system operating in a log-normal environment. Then, hinging on the fact that the sum of log-normal Random Variables (RV) is well approximated by another log-normal RV, we apply the obtained results to find the capacity of Maximum Ratio Combining and Equal Gain Combining in a log-normal environment. The capacity in an interference-limited environment is also investigated in this paper. The analytical expressions obtained match perfectly the capacity given by simulations.     

Asymptotic mean integrated squared errors of some nonparametric density estimators (Corresp.)

For estimation of a probability density functionfby an empirical functionf_{n},, based on a sample of sizenfromf, a widely used performance measure is the mean integrated squared error. For the wellknowndelta-function type off_{n}, the asymptotic behavior of this measure is shown to be essentially unchanged iff_{n}is replaced by a recursive version. Also, this asymptotic behavior is characterized under somewhat milder smoothness restrictions but stronger tail restrictions than previously considered in the literature.     

Capture and retransmission control in mobile radio

We consider the slotted ALOHA protocol with capture, in a mobile communication environment, in the presence of Rayleigh fading and log-normal shadowing. The capture probabilities and their asymptotic value, as the number of colliding packets tends to infinity, are computed. A sufficient condition, under which this limit is positive, is identified and expressed in terms of the spatial distribution of the users. Also, various models for this latter distribution are discussed. These results help identify the region in which the system may achieve a positive stable throughput. Finally, a retransmission control scheme, that enhances the throughput, is considered, and the stability of the system is rigorously proven. We also show that the use of retransmission control is unavoidable if the network performance predicted in some recent literature is to be achieved     

Effects of Rician faded and log-normal shadowed signals on spectrumefficiency in microcellular radio

An assessment of spectrum efficiency for a microcellular land mobile radio system is presented by considering the desired signal as (fast) Rician fading with (slow) log-normal shadowing and cochannel interfering signals as uncorrelated (fast) Rayleigh fading superimposed over (slow) log-normal shadowing. Spectrum efficiency is defined in terms of reuse distance, i.e., cluster size, traffic intensity, bandwidth of the system, and area of a cell by considering cochannel interference probability. The expression for cochannel interference probability is derived using appropriate path-loss law for microcells for four different cases: Rician plus log-normal desired signal and Rayleigh plus log-normal interfering signals; Rician desired signal and Rayleigh fading plus log-normal shadowing interfering signals; Rician desired signal and Rayleigh interfering signals; and both desired and interfering signals as Rician fading. The performance of a microcellular system is compared with that of a conventional macrocellular system     

Maximum Likelihood Phase Demodulation for Spatially Turbulent Channels

The likelihood equation for the maximum likelihood estimate (MLE) of a temporal phase modulation (a sample function of a wide-sense stationary zero-mean Gaussian random process) received in a spatial aperture after transmission through a spatially turbulent channel and addition to a white Gaussian noise field is derived for unknown, Gaussian, and limiting cases of log-normal received signal fields. The received signal field estimation performed by the demodulator structure is explicitly exhibited and other clarifications made. The likelihood equation is linearized and solved and the resulting mean-square estimation error calculated. The Cramer-Rao lower bound is given. In an example it is shown that the linear estimate is efficient and has variance inversely proportional toM, the number of coherence areas required to disjunctly cover the receiver spatial aperture. A heterodyne receiver with an optimized aperture weighting is shown to use essentially only one coherence area; its asymptotic mean-square error is also calculated.     

Novel results for the performance of single and double stages cognitive radio systems through Nakagami-<Emphasis Type="Italic">m</Emphasis> fading and log-normal shadowing

Previously reported results presented approximate expressions for the performance of cognitive radio systems through Nakagami fading and log-normal shadowing. In this article, exact expressions for the Receiver Operating Characteristics of cognitive radio system are derived analytically for a single stage and a double stage system. By single stage, it is assumed that the secondary users are close to the fusion centre therefore, they can be considered directly coupled to it. For the second stage system the secondary users are considered far from the fusion centre, thus another communication link is assumed between the secondary users and the fusion centre with similar characteristics as the first link. In both scenarios Nakagami fading and log-normal shadowing are assumed. Results for integer and non-integer Nakagami fading parameter ‘m’ are obtained. Depicted results show that better performance is obtained with the increase of the number of secondary users and increase of ‘m’. Deterioration due to shadowing is also indicated.