Unified exact ergodic capacity results for L-branch coherent diversity combiners including equal-gain combining (EGC) and maximal-ratio combining (MRC) are not known. This paper develops a novel generic framework for the capacity analysis of L-branch EGC/MRC over generalized fading channels. The framework is used to derive new results for the gamma-shadowed generalized Nakagami-m fading model which can be a suitable model for the fading environments encountered by high frequency (60 GHz and above) communications. The mathematical formalism is illustrated with some selected numerical and simulation results confirming the correctness of our newly proposed framework.

A Unified MGF-Based Capacity Analysis of Diversity Combiners over Generalized Fading Channels

Since the trail-blazing paper of C. Shannon in 1948, channel capacity has been regarded as the fundamental information-theoretic performance measure to predict the maximum information rate of a communication system. However, in contrast with the analysis of other important performance measures of wireless communication systems, a unified and general approach for computing the channel capacity over fading channels has yet to be proposed. Motivated by this consideration, we propose a novel and unified communication-theoretic framework for the analysis of channel capacity over fading channels. It is shown that the framework can handle various fading channel models, communication types, and adaptation transmission policies. In particular, the specific contributions of this paper are as follows: (1) We introduce a transform operator, called the E i-transform, which is shown to provide a unified tool to compute the channel capacity with either side information at the receiver or side information at the transmitter and the receiver, directly from the moment-generating function (MGF) or the MGF and the truncated MGF of the Signal-to-Noise-Ratio (SNR) at the receiver, respectively; (2) we show that when either a channel inversion or a truncated channel inversion adaptation policy is considered, the channel capacity can readily be computed from the Mellin or the Hankel transform of the MGF of the received SNR, respectively; (3) a simple yet effective numerical method for the analysis of higher order statistics (HOS) of the channel capacity with side information at the receiver is introduced; and (4) some efficient and ad hoc numerical methods are explicitly introduced to allow the efficient computation of the proposed frameworks. Numerical and simulation results are also shown and compared to substantiate the analytical derivation.

Channel Capacity Over Generalized Fading Channels: A Novel MGF-Based Approach for Performance Analysis and Design of Wireless Communication Systems

The concept of multiple scattering radio propagation channels-in contrast to the conventional single (Rayleigh) scattering-has been proposed and found to be a fitting model in certain propagation scenarios. Except for some special cases, expressions for the amplitude distribution of such channels are unknown. In this paper, we derive distribution functions for the amplitude of the general multiple scattering radio channel. Rice, Rayleigh, and double-Rayleigh distributions are special cases of the general result. We also derive a computationally simple moment-based estimator for the parameters of the distribution. In addition to the measurement analysis of multiple scattering propagation channels, our results can also be applied in the performance evaluation of communication schemes over such media

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Statistical Analysis of the Multiple Scattering Radio Channel

Availability appears to be a more appropriate measure than reliability for measuring the effectiveness of maintained systems because it includes reliability as well as maintainability. This paper is a survey and a systematic classification of the literature relevant to availability. Emphasis in this paper is centered on the current state of the art on a variety of topics related to availability. Among the topics discussed are: the definition and concepts of the availability; the probability density functions (pdf) of failure times, the pdf of repair times, system configurations, and the various approaches employed to obtain the availability models; confidence intervals of availability; effect of preventive maintenance policies on availability; availability parameters in the model; and systems optimization.

Availability of Maintained Systems: A State-of-the-Art Survey

Unified exact average capacity results for L-branch coherent diversity receivers including equal-gain combining (EGC) and maximal-ratio combining (MRC) are not known. This paper develops a novel generic framework for the capacity analysis of $L$-branch EGC/MRC over generalized fading channels. The framework is used to derive new results for the Gamma shadowed generalized Nakagami-m fading model which can be a suitable model for the fading environments encountered by high frequency (60 GHz and above) communications. The mathematical formalism is illustrated with some selected numerical and simulation results confirming the correctness of our newly proposed framework.

This paper introduces a new probability distribution based on the H-function of Fox. The distribution is shown to be a generalization of most common “nonnegative” (Pr $\Pr ([X < 0] = 0)$ distributions. Furthermore, it is proved that products, quotients and powers of H-function variates are H-function variates. Several examples are given.

The Distribution of Products, Quotients and Powers of Independent H-Function Variates

The problem treated here is the theoretical one of deriving exact Bayesian confidence intervals for the reliability of a system consisting of some independent cascade subsystems with exponential failure probability density functions (pdf) mixed with other independent cascade subsystems whose failure pdf's are unknown. The Mellin integral transform is used to derive the posterior pdf of the system reliability. The posterior cumulative distribution function (cdf) is then obtained in the usual manner by integrating the pdf, which serves the dual purpose of yielding system reliability confidence limits while at the same time providing a check on the derived pdf. A computer program written in Fortran IV is operational. It utilizes multiprecision to obtain the posterior pdf to any desired degree of accuracy in both functional and tabular form. The posterior cdf is tabulated at any desired increments to any required degree of accuracy.

Bayesian Confidence Limits for the Reliability of Mixed Exponential and Distribution-Free Cascade Subsystems

A Bayes analysis of system availability A is carried out on the basis of snapshot data obtained on each of the N component subsystems Application of Bayes formula, using a natural conjugate prior probability density function (pdf), yields the posterior pdf of subsystem availability Determination of the posterior pdf of system availability requires the derivation of the pdf of the product of N independent random variables, which is accomplished through the use of the Mellin integral transform From the knowledge of the posterior pdf of A, confidence limits on system availability can be obtained

A Bayes Analysis of Availability for a System Consisting of Several Independent Subsystems

The Mellin convolution is used to derive in analytical form an exact 3-parameterprobabilitydensity function of the quotient of two noncentral normal random variables. In contrast with the 5-parameter probability density function previously derivedby Fieller (1932) and Hinkley (1969), this 3-parameter probability density function is feasible for computer evaluation of the mean and cumulative distribution function, which are needed, for example, when dealing with estimation and distribution problems in regression analysis and sampling theory. When the normal variables are independent, the probability density function reduces to a 2-parameter function, for which a computer program is operational. An illustrative example is given for one set of parameters when the normal variables are independent, in which themean and functional form of the probability density function are presented, together with a brief tabulation of the probability density function.

Distribution of the quotient of noncentral normal random variables

The validity of Jordan’s lemma in the evaluation of all H-function inversion integrals for real variables is established. Consequently, these inversion integrals can be evaluated by residues without imposing constraints (such as those of Cook and Barnes) other than those specified in the definition of the H-function inversion integral for nonnegative real variables. The analytical form $h( x )$ of the H-function inversion integral for real variables $x\geqq 0$ is then expressible as a sum of residues. The constraints imposed by Cook and Barnes for the validity of the method of residues are required only if one makes the unnecessary demand that the inversion integral always be evaluated over the left Bromwich contour when the poles are in the LHP and always over the right Bromwich contour when the poles are in the RHP, without permitting certain legitimate transformations of the poles into the opposite half plane. It is always possible to use one of the two Bromwich contours by utilizing the transformation...

Melvin D. Springer

Papers

The Distribution of Products, Quotients and Powers of Independent H-Function Variates

Bayesian Confidence Limits for the Reliability of Mixed Exponential and Distribution-Free Cascade Subsystems

A Bayes Analysis of Availability for a System Consisting of Several Independent Subsystems

Distribution of the quotient of noncentral normal random variables

Evaluation of the H -function inversion integral for real variables using Jordan's lemma and residues