Generalized Selection Combining for Cognitive Relay Networks over Nakagami-m Fading

We consider transmit antenna selection with receive generalized selection combining (TAS/GSC) for cognitive decodeand-forward (DF) relaying in Nakagami-m fading channels. In an effort to assess the performance, the probability density function and the cumulative distribution function of the endto-end SNR are derived using the moment generating function, from which new exact closed-form expressions for the outage probability and the symbol error rate are derived. We then derive a new closed-form expression for the ergodic capacity. More importantly, by deriving the asymptotic expressions for the outage probability and the symbol error rate, as well as the high SNR approximations of the ergodic capacity, we establish new design insights under the two distinct constraint scenarios: 1) proportional interference power constraint, and 2) fixed interference power constraint. Several pivotal conclusions are reached. For the first scenario, the full diversity order of the
outage probability and the symbol error rate is achieved, and the high SNR slope of the ergodic capacity is 1/2. For the second scenario, the diversity order of the outage probability and the symbol error rate is zero with error floors, and the high SNR slope of the ergodic capacity is zero with capacity ceiling.

Shadowed Fading in Indoor Off-Body Communications Channels: A Statistical Characterization using the κ – μ / Gamma Composite Fading Model

This paper investigates the characteristics of the shadowed fading observed in off-body communications channels at 5.8 GHz. This is realized with the aid of the $\kappa-\mu$ / gamma composite fading model which assumes that the transmitted signal undergoes $\kappa-\mu$ fading which is subject to \emph{multiplicative} shadowing. Based on this, the total power of the multipath components, including both the dominant and scattered components, is subject to non-negligible variations that follow the gamma distribution. For this model, we present an integral form of the probability density function (PDF) as well as important analytic expressions for the PDF, cumulative distribution function, moments and moment generating function. In the case of indoor off-body communications, the corresponding measurements were carried out in the context of four explicit individual scenarios namely: line of sight (LOS) and non-LOS (NLOS) walking, rotational and random movements. The measurements were repeated within three different indoor environments and considered three different hypothetical body worn node locations. With the aid of these results, the parameters for the $\kappa-\mu$ / gamma composite fading model were estimated and analyzed extensively. Interestingly, for the majority of the indoor environments and movement scenarios, the parameter estimates suggested that dominant signal components existed even when the direct signal path was obscured by the test subject's body. Additionally, it is shown that the $\kappa-\mu$ / gamma composite fading model provides an adequate fit to the fading effects involved in off-body communications channels. Using the Kullback-Leibler divergence, we have also compared our results with another recently proposed shadowed fading model, namely the $\kappa-\mu$ / lognormal LOS shadowed fading model. It was found that the $\kappa-\mu$ / gamma composite fading model provided a better fit for the majority of the scenarios considered in this study.

Polinómios de Appell multidimensionais e sua representação matricial

Nesta dissertação é apresentada uma abordagem a polinómios de Appell multidimensionais dando-se especial relevância à estrutura da sua função geradora. Esta estrutura, conjugada com uma escolha adequada de ordenação dos monómios que figuram nos polinómios, confere um carácter unificador à abordagem e possibilita uma representação matricial de polinómios de Appell por meio de matrizes particionadas em blocos. Tais matrizes são construídas a partir de uma matriz de estrutura simples, designada matriz de criação, subdiagonal e cujas entradas não nulas são os sucessivos números naturais. A exponencial desta matriz é a conhecida matriz de Pascal, triangular inferior, onde figuram os números binomiais que fazem parte integrante dos coeficientes dos polinómios de Appell. Finalmente, aplica-se a abordagem apresentada a polinómios de Appell definidos no contexto da Análise de Clifford.

Asymptotic Approximations in the Near-Integrated Model with a Non-Zero Initial Condition

This paper considers various asymptotic approximations in the near-integrated firstorder autoregressive model with a non-zero initial condition. We first extend the work of Knight and Satchell (1993), who considered the random walk case with a zero initial condition, to derive the expansion of the relevant joint moment generating function in this more general framework. We also consider, as alternative approximations, the stochastic expansion of Phillips (1987c) and the continuous time approximation of Perron (1991). We assess how these alternative methods provide or not an adequate approximation to the finite-sample distribution of the least-squares estimator in a first-order autoregressive model. The results show that, when the initial condition is non-zero, Perron's (1991) continuous time approximation performs very well while the others only offer improvements when the initial condition is zero.

Oligarchies in Spatial Environments

In spatial environments we consider social welfare functions satisfying Arrow’s requirements, i.e. weak Pareto and independence of irrelevant alternatives. Individual preferences measure distances between alternatives according to the Lp-norm (for a fixed p => 1). When the policy space is multi-dimensional and the set of alternatives has a non-empty interior and it is compact and convex, any quasi-transitive welfare function must be oligarchic. As a corollary we obtain that for transitive welfare functions weak Pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty interior and it is compact and convex.

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Analysis of Some Stochastic Inventory Models with Pooling/ Retrial of Customers

In this thesis we have presented several inventory models of utility. Of these inventory with retrial of unsatisfied demands and inventory with postponed work are quite recently introduced concepts, the latt~~ being introduced for the first time. Inventory with service time is relatively new with a handful of research work reported. The di lficuity encoLlntered in inventory with service, unlike the queueing process, is that even the simplest case needs a 2-dimensional process for its description. Only in certain specific cases we can introduce generating function • to solve for the system state distribution. However numerical procedures can be developed for solving these problem.

Lecture notes

Lecture notes in LaTex

Exercise sheet 2 pdf

Exercises and solutions in PDF

Exercise sheet 2

Exercises and solutions in LaTex

Lecture notes pdf

Lecture notes in PDF

Asymptotic expansions for Taylor coefficients of the composition of two functions

We give an asymptotic expansion for the Taylor coe±cients of L(P(z)) where L(z) is analytic in the open unit disc whose Taylor coe±cients vary `smoothly' and P(z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences.

Generalized beta generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets.

Performance analysis of AF cooperative systems with HPA nonlinearity in semi-blind relays

In this paper, dual-hop amplify-and-forward (AF) cooperative systems in the presence of high-power amplifier (HPA) nonlinearity at semi-blind relays, are investigated. Based on the modified AF cooperative system model taking into account the HPA nonlinearity, the expression for the output signal-to-noise ratio (SNR) at the destination node is derived, where the interference due to both the AF relaying mechanism and the HPA nonlinearity is characterized. The performance of the AF cooperative system under study is evaluated in terms of average symbol error probability (SEP), which is derived using the moment-generating function (MGF) approach, considering transmissions over Nakagami-m fading channels. Numerical results are provided and show the effects of some system parameters, such as the HPA parameters, numbers of relays, quadrature amplitude modulation (QAM) order, Nakagami parameters, on performance.

Two-way CSI-assisted AF relaying with HPA nonlinearity

In this paper, we investigate half-duplex two-way dual-hop channel state information (CSI)-assisted amplify-and-forward (AF) relaying in the presence of high-power amplifier (HPA) nonlinearity at relays. The expression for the end-to-end signal-to-noise ratio (SNR) is derived as per the modified system model by taking into account the interference caused by relaying scheme and HPA nonlinearity. The system performance of the considered relaying network is evaluated in terms of average symbol error probability (SEP) in Nakagami-$m$ fading channels, by making use of the moment-generating function (MGF) approach. Numerical results are provided and show the effects of several parameters, such as quadrature amplitude modulation (QAM) order, number of relays, HPA parameters, and Nakagami parameter, on performance.