On the Multivariate Gamma-Gamma (ΓΓ\Gamma \Gamma) Distribution with Arbitrary Correlation and Applications in Wireless Communications

The statistical properties of the multivariate Gamma-Gamma ($\Gamma \Gamma$) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative distribution function (CDF) and moment generation function of the multivariate $\Gamma \Gamma$ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the PDF and CDF of the sum of $\Gamma \Gamma$ random variables with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency and optical wireless communication systems. It is noteworthy that the presented expressions include several previous results in the literature as special cases.Comment: 7 pages, 6 figures, accepted by IEEE Transactions on Vehicular Technolog

Performance analysis of downlink shared channels in a UMTS network

In light of the expected growth in wireless data communications and the commonly anticipated up/downlink asymmetry, we present a performance analysis of downlink data transfer over \textsc{d}ownlink \textsc{s}hared \textsc{ch}annels (\textsc{dsch}s), arguably the most efficient \textsc{umts} transport channel for medium-to-large data transfers. It is our objective to provide qualitative insight in the different aspects that influence the data \textsc{q}uality \textsc{o}f \textsc{s}ervice (\textsc{qos}). As a most principal factor, the data traffic load affects the data \textsc{qos} in two distinct manners: {\em (i)} a heavier data traffic load implies a greater competition for \textsc{dsch} resources and thus longer transfer delays; and {\em (ii)} since each data call served on a \textsc{dsch} must maintain an \textsc{a}ssociated \textsc{d}edicated \textsc{ch}annel (\textsc{a}-\textsc{dch}) for signalling purposes, a heavier data traffic load implies a higher interference level, a higher frame error rate and thus a lower effective aggregate \textsc{dsch} throughput: {\em the greater the demand for service, the smaller the aggregate service capacity.} The latter effect is further amplified in a multicellular scenario, where a \textsc{dsch} experiences additional interference from the \textsc{dsch}s and \textsc{a}-\textsc{dch}s in surrounding cells, causing a further degradation of its effective throughput. Following an insightful two-stage performance evaluation approach, which segregates the interference aspects from the traffic dynamics, a set of numerical experiments is executed in order to demonstrate these effects and obtain qualitative insight in the impact of various system aspects on the data \textsc{qos}

On the Temporal Effects of Mobile Blockers in Urban Millimeter-Wave Cellular Scenarios

Millimeter-wave (mmWave) propagation is known to be severely affected by the blockage of the line-of-sight (LoS) path. In contrast to microwave systems, at shorter mmWave wavelengths such blockage can be caused by human bodies, where their mobility within environment makes wireless channel alternate between the blocked and non-blocked LoS states. Following the recent 3GPP requirements on modeling the dynamic blockage as well as the temporal consistency of the channel at mmWave frequencies, in this paper a new model for predicting the state of a user in the presence of mobile blockers for representative 3GPP scenarios is developed: urban micro cell (UMi) street canyon and park/stadium/square. It is demonstrated that the blockage effects produce an alternating renewal process with exponentially distributed non-blocked intervals, and blocked durations that follow the general distribution. The following metrics are derived (i) the mean and the fraction of time spent in blocked/non-blocked state, (ii) the residual blocked/non-blocked time, and (iii) the time-dependent conditional probability of having blockage/no blockage at time t1 given that there was blockage/no blockage at time t0. The latter is a function of the arrival rate (intensity), width, and height of moving blockers, distance to the mmWave access point (AP), as well as the heights of the AP and the user device. The proposed model can be used for system-level characterization of mmWave cellular communication systems. For example, the optimal height and the maximum coverage radius of the mmWave APs are derived, while satisfying the required mean data rate constraint. The system-level simulations corroborate that the use of the proposed method considerably reduces the modeling complexity.Comment: Accepted, IEEE Transactions on Vehicular Technolog

The Color Glass Condensate and High Energy Scattering in QCD

At very high energies or small values of Bjorken x, the density of partons, per unit transverse area, in hadronic wavefunctions becomes very large leading to a saturation of partonic distributions. When the scale corresponding to the density per unit transverse area, the saturation scale Q_s, becomes large (Q_s\gg \Lambda_{QCD}), the coupling constant becomes weak (\alpha_S(Q_s)\ll 1) which suggests that the high energy limit of QCD may be studied using weak coupling techniques. This simple idea can be formalized in an effective theory, the Color Glass Condensate (CGC), which describes the behavior of the small x components of the hadronic wavefunction in QCD. The Green functions of the theory satisfy Wilsonian renormalization group equations which reduce to the standard linear QCD evolution equations in the limit of low parton densities. The effective theory has a rich structure that has been explored using analytical and numerical techniques. The CGC can be applied to study a wide range of high energy scattering experiments from Deep Inelastic Scattering at HERA and the proposed Electron Ion Collider (EIC) to proton/deuterium-nucleus and nucleus-nucleus experiments at the RHIC and LHC colliders.Comment: review for QGP3, Eds. R. C. Hwa and X.-N. Wang, World Scientific, 106 pages, 31 fig

Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom

This review summarizes and amplifies on recent investigations of coupled quantum dynamical systems in the short wavelength limit. We formulate and attempt to answer three fundamental questions: (i) What drives a dynamical quantum system to behave classically ? (ii) What determines the rate at which two coupled quantum--mechanical systems become entangled ? (iii) How does irreversibility occur in quantum systems with few degrees of freedom ? We embed these three questions in the broader context of the quantum--classical correspondence, which motivates the use of short--wavelength approximations to quantum mechanics such as the trajectory-based semiclassical methods and random matrix theory. Doing so, we propose a novel investigative procedure towards decoherence and the emergence of classicality out of quantumness in dynamical systems coupled to external degrees of freedom. We reproduce known results derived using master equation or Lindblad approaches but also generate novel ones. In particular we show how local exponential instability also affects the temporal evolution of quantum chaotic dynamical systems. We extensively rely on numerical experiments to illustrate our findings and briefly comment on possible extensions to more complex problems involving environments with $n \gg 1$ interacting dynamical systems, going beyond the uncoupled harmonic oscillator model of Caldeira and Leggett.Comment: Final version, to appear in Advances in Physic

Adaptive OFDM Index Modulation for Two-Hop Relay-Assisted Networks

In this paper, we propose an adaptive orthogonal frequency-division multiplexing (OFDM) index modulation (IM) scheme for two-hop relay networks. In contrast to the traditional OFDM IM scheme with a deterministic and fixed mapping scheme, in this proposed adaptive OFDM IM scheme, the mapping schemes between a bit stream and indices of active subcarriers for the first and second hops are adaptively selected by a certain criterion. As a result, the active subcarriers for the same bit stream in the first and second hops can be varied in order to combat slow frequency-selective fading. In this way, the system reliability can be enhanced. Additionally, considering the fact that a relay device is normally a simple node, which may not always be able to perform mapping scheme selection due to limited processing capability, we also propose an alternative adaptive methodology in which the mapping scheme selection is only performed at the source and the relay will simply utilize the selected mapping scheme without changing it. The analyses of average outage probability, network capacity and symbol error rate (SER) are given in closed form for decode-and-forward (DF) relaying networks and are substantiated by numerical results generated by Monte Carlo simulations.Comment: 30 page

On the Usage of Geolocation-Aware Spectrum Measurements for Incumbent Location and Transmit Power Detection

© 2017 IEEE. Determining the geographical area that needs to be excluded due to incumbent activity is critical to realize high spectral utilization in spectrum sharing networks. This can be achieved by estimating the incumbent location and transmit power. However, keeping the hardware complexity of sensing nodes to a minimum and scalability are critical for spectrum sharing applications with commercial intent. We present a discrete-space l1-norm minimization solution based on geolocation-aware energy detection measurements. In practice, the accuracy of geolocation tagging is limited. We capture the impact as a basis mismatch and derive the necessary condition that needs to be satisfied for successful detection of multiple incumbents' location and transmit power. We find the upper bound for the probability of eliminating the impact of limited geolocation tagging accuracy in a lognormal shadow fading environment, which is applicable to all generic I1-norm minimization techniques. We propose an algorithm based on orthogonal matching pursuit that decreases the residual in each iteration by allowing a selected set of basis vectors to rotate in a controlled manner. Numerical evaluation of the proposed algorithm in a Licensed Shared Access (LSA) network shows a significant improvement in the probability of missed detection and false alarm