Arbitrary Correlation Research Articles

Arbitrary emittance partitioning between any two dimensions for electron beams

The flat-beam transform (FBT) for round symmetric beams can be extended using the concept of eigenemittances. By tailoring the initial beam conditions at the cathode, including adding arbitrary correlations between any two dimensions, this extension can be used to provide greater freedom in controlling the beam's final emittances. In principle, this technique can be used to generate extraordinarily transversely bright electron beams. Examples are provided where an equivalent FBT is established between the horizontal and the longitudinal beam dimensions.

Variance swaps on time-changed Lévy processes

We prove that a multiple of a log contract prices a variance swap, under arbitrary exponential Levy dynamics, stochastically time-changed by an arbitrary continuous clock having arbitrary correlation with the driving Levy process, subject to integrability conditions. We solve for the multiplier, which depends only on the Levy process, not on the clock. In the case of an arbitrary continuous underlying returns process, the multiplier is 2, which recovers the standard no-jump variance swap pricing formula. In the presence of negatively skewed jump risk, however, we prove that the multiplier exceeds 2, which agrees with calibrations of time-changed Levy processes to equity options data. Moreover, we show that discrete sampling increases variance swap values, under an independence condition; so if the commonly quoted multiple 2 undervalues the continuously sampled variance, then it undervalues even more the discretely sampled variance. Our valuations admit enforcement, in some cases, by hedging strategies which perfectly replicate variance swaps by holding log contracts and trading the underlying.

An Approach to the Triple Branch Selection Diversity Analysis Over Correlated α-μ Fading Channels in the Presence of CCI

In this paper, an approach to derivation of the joint trivariate ?-μ probability density function (pdf) and cumulative distribution function (cdf) expressions will be presented. Capitalizing on this, closed-form expressions for the cdf and pdf at the output of triple branch selective combiner (SC) in the presence of correlated co-channel interference (CCI) will be determined. The main contribution of this paper is generality of our model, since the expressions accommodate arbitrary correlation structures. General results, from this paper, could be reduced to the specific ones for various fading models and types of correlation. Important performance measures like outage probability (Pout) and average output signal-to-interference ratio (SIR) will also be determined and graphically illustrated for various values of existing parameters.

Negatively Correlated Bandits

We analyse a two-player game of strategic experimentation with two-armed bandits. Either player has to decide in continuous time whether to use a safe arm with a known pay-off or a risky arm whose expected pay-off per unit of time is initially unknown. This pay-off can be high or low and is negatively correlated across players. We characterize the set of all Markov perfect equilibria in the benchmark case where the risky arms are known to be of opposite type and construct equilibria in cut-off strategies for arbitrary negative correlation. All strategies and pay-offs are in closed form. In marked contrast to the case where both risky arms are of the same type, there always exists an equilibrium in cut-off strategies, and there always exists an equilibrium exhibiting efficient long-run patterns of learning. These results extend to a three-player game with common knowledge that exactly one risky arm is of the high pay-off type.

MIMO-OFDM Pilot Placement Algorithms for Wideband Indoor Communications

To facilitate coherent detection of orthogonal frequency division multiplexed transmissions, pilot symbols can be transmitted in some of the subcarriers. Their placement to minimise the mean squared error in channel estimation is considered. Such problems have been widely addressed previously for channels subject to wide sense stationary uncorrelated scattering processes. While the stationarity assumption is usually realistic, indoor wideband channels, for example, are subject to significantly correlated scattering processes. Furthermore, practical multiple antenna transmitters/receivers are bound to exhibit spatial correlations. This work considers pilot placement optimisation in a multiple antenna setting subject to arbitrary correlations in the delay and spatial domains. Noting that the naive approach incurs a prohibitive complexity, low complexity greedy solutions are developed. It is further proven that the conventional equi-spaced placement becomes optimal at high SNR even with correlations, when the correlation matrices are of full rank. A measurement campaign is conducted to estimate real-world channel statistics in an indoor wideband environment, and observe the applicability of developed algorithms. It is confirmed that practical channels are correlated to the extent of exhibiting rank deficiencies, and that the proposed placement algorithms result in improved channel estimation performance.

Space Shift Keying (SSK—) MIMO over Correlated Rician Fading Channels: Performance Analysis And a New Method for Transmit-Diversity

In this paper, we study the performance of Space Shift Keying (SSK) modulation for a generic Multiple—Input—Multiple—Output (MIMO) wireless system over correlated Rician fading channels. In particular, our contribution is twofold. i) First, we propose a very general framework for computing the Average Bit Error Probability (ABEP) of SSK—MIMO systems over a generic Rician fading channel with arbitrary correlation and channel parameters. The framework relies upon the Moschopoulos method. We show that it is exact for MIMO systems with two transmit—antenna and arbitrary receive—antenna, while an asymptotically—tight upper—bound is proposed to handle the system setup with an arbitrary number of transmit—antenna. ii) Second, moving from the consideration that conventional SSK—MIMO schemes can offer only receive—diversity gains, we propose a novel SSK—MIMO scheme that can exploit the transmit—antenna to increase the diversity order. The new method has its basic foundation on the transmission of signals with good time—correlation properties, and is called Time—Orthogonal—Signal—Design (TOSD—) assisted SSK modulation (TOSD—SSK). It is shown that the proposed method can increase twofold the diversity order for arbitrary transmit— and receive—antenna. In particular, for MIMO systems with two transmit—antenna and N_r receive—antenna full—diversity equal to 2N_r can be achieved. Analytical frameworks and theoretical findings are substantiated via Monte Carlo simulations for various system setups.

Depolarization Effects of Incoherently Scattered Electromagnetic Waves by Inhomogeneous Magnetized Plasma Slab

Scattering of the electromagnetic waves by a randomly inhomogeneous electrically gyrotropic slab are studied using the perturbation method. Second order statistical moments of the ordinary and extraordinary waves scattered by the magnetized plasma slab are obtained using the boundary conditions for an arbitrary correlation function of electron density fluctuations. Normalized correlation functions at quasi-longitudinal propagation along the external magnetic field are calculated for the carrier frequency 0.1 MHz and 40 MHz. Isolines of the normalized variance of Faraday angle are constructed for the anisotropic Gaussian correlation function at various anisotropy factors of irregularities. Obtained results are in a good agreement with the experimental data.

Initial correlations in open-systems dynamics: The Jaynes-Cummings model

Employing the trace distance as a measure for the distinguishability of quantum states, we study the influence of initial correlations on the dynamics of open systems. We concentrate on the Jaynes-Cummings model for which the knowledge of the exact joint dynamics of system and reservoir allows the treatment of initial states with arbitrary correlations. As a measure for the correlations in the initial state we consider the trace distance between the system-environment state and the product of its marginal states. In particular, we examine the correlations contained in the thermal equilibrium state for the total system, analyze their dependence on the temperature and on the coupling strength, and demonstrate their connection to the entanglement properties of the eigenstates of the Hamiltonian. A detailed study of the time dependence of the distinguishability of the open system states evolving from the thermal equilibrium state and its corresponding uncorrelated product state shows that the open system dynamically uncovers typical features of the initial correlations.

Correlation of GPS signal fades due to ionospheric scintillation for aviation applications

Deep and frequent Global Positioning System (GPS) signal fading due to strong ionospheric scintillation is a major concern for GPS-guided aviation in equatorial areas during high solar activity. A GPS aviation receiver may lose carrier tracking lock under deep fading, and a lost channel cannot be used for position calculation until lock is reestablished. Hence, frequent loss of lock due to frequent fading can significantly reduce the availability of GPS aviation. However, the geometric diversity of the satellites can mitigate scintillation impact on GPS aviation depending on the correlation level of deep fades between satellites. This paper proposes a metric to measure the correlation level of two fading channels from the perspective of GPS aviation. Using this metric, the satellite-to-satellite correlation is studied based on real scintillation data. The low satellite-to-satellite correlation shown in this paper envisions notable availability benefit from the geometric diversity of satellites under strong scintillation. In addition, this paper proposes a way to generate correlated fading processes with arbitrary correlation coefficients. Using this correlated fading process model, the availability of Localizer Performance with Vertical guidance (LPV)-200 under severe scintillation scenarios is analyzed. The result emphasizes the importance of a fast reacquisition capability of an aviation receiver after a brief outage, which is not currently mandated by the aviation receiver performance standards.

Rigorous representation and exact simulation of real Gaussian stationary processes

It is shown that the real Gaussian stationary process with zero mean can be exactly interpreted as a convolution defined by its covariance and a complex white noise plus the conjugate pair of the complex white noise. When the algorithm for generating the white noise is given, such a representation thereby offers a direct and convenient technique to numerically simulate Gaussian processes with arbitrary correlations. Moreover, the fast Fourier transform can be invoked for solving the convolution, which leads to a feasible implementation of the simulation method. As a primary test, a Gaussian process in quantum dissipation is simulated. This stochastic process has an infinitely long correlation time and is hardly treated by other approaches.

Generation of arbitrary two-point correlated directed networks with given modularity

In this Letter, we introduce measures of correlation in directed networks and develop an efficient algorithm for generating directed networks with arbitrary two-point correlation. Furthermore, a method is proposed for adjusting community structure in directed networks without changing the correlation. Effectiveness of both methods is verified by numerical results.

Exact Inference for Complex Clustered Data Using Within-Cluster Resampling

This paper introduces exact permutation methods for use when there are independent clusters of data with arbitrary within-cluster correlation. To eliminate the problem of clustering, we randomly select a data point from each cluster and for this now independent data, and calculate our test statistic and the associated support points for all possible permutations. While clearly valid, this is also inefficient. We repeat this process until all possible independent data sets have been created and use the support points averaged over the randomly created data sets as our reference distribution for the averaged test statistic. This approach uses all of the data and is a permutation extension of within-cluster resampling (WCR). We discuss both exact and Monte Carlo versions of the approach and apply it to several data sets. WCR permutation can be applied in quite general settings when within cluster correlation is a nuisance and exact inference is necessary.

On the Construction of Bivariate Exponential Distributions with an Arbitrary Correlation Coefficient

In this article we use the concept of multivariate phase-type distributions to define a class of bivariate exponential distributions. This class has the following three appealing properties. Firstly, we may construct a pair of exponentially distributed random variables with any feasible correlation coefficient (also negative). Secondly, the class satisfies that any linear combination (projection) of the marginal random variables is a phase-type distribution. The latter property is partially important for the development of hypothesis testing in linear models. Finally, it is easy to simulate the exponential random vectors.

Switch-and-Examine Diversity Over Arbitrarily Correlated Nakagami- $m$ Fading Channels

The performance of switch-and-examine diversity (SED) over L arbitrarily correlated and not necessarily identically distributed Nakagami-m fading channels is studied. Analytical expressions for the distribution of the SED output signal-to-noise ratio (SNR) are obtained for the constant correlation model. For the most general case of arbitrary correlation, by assuming half-integer or integer values for the fading parameter m, analytical expressions for the distribution of the output SNR with L ? 3 are derived. Moreover, for L > 3, analytical approximations for the output SNR are presented. The derived expressions are used to study the outage and average symbol error probability of SED receivers. Performance results obtained by numerical evaluation and verified by means of computer simulations show that the performance of the receivers under consideration is degraded with increasing branch correlation. Nevertheless, SED receivers outperform uncorrelated switch-and-stay diversity receivers, even when they operate under high branch correlation.

Electronic states and transport properties in the Kronig–Penney model with correlated compositional and structural disorder

We study the structure of the electronic states and the transport properties of a Kronig–Penney model with weak compositional and structural disorder. Using a perturbative approach we obtain an analytical expression for the localisation length which is valid for disorder with arbitrary correlations. We show how to generate disorder with self- and cross-correlations and we analyse both the known delocalisation effects of the long-range self-correlations and new effects produced by cross-correlations. We finally discuss how both kinds of correlations alter the transport properties in Kronig–Penney models of finite size.

Application layer ARQ for protecting video packets over an indoor MIMO-OFDM link with correlated block fading

The quality of experience (QoE) of IP-packetized streaming video is affected by both packet loss and packet delay variations. When the network delivering the video content contains a wireless link, occasional deep fades give rise to bursts of packet losses. In order to maintain a sufficient video QoE at the end user, video packets must be protected against losses by means of a suitable form of error control. In this contribution, we consider an indoor radio MIMO-OFDM transceiver operating over a Rayleigh block-fading channel with arbitrary correlation in the time and frequency dimensions, which makes use of an application layer Automatic Repeat reQuest (ARQ) protocol to provide additional protection of the video content against packet loss. We analyze the resulting residual packet loss performance, under a latency constraint imposed by the requirement of a small TV channel switching delay. This analysis makes direct use of the fading characterization (correlation functions in time and frequency dimensions) of the indoor environment, rather than relying on a Markov model that only approximately describes the packet loss process. Numerical results are obtained by Monte Carlo integration combined with an efficient importance sampling technique devised for the problem at hand. Assuming a 2.4 GHz wireless link, we point out how to select the system parameters (number of antennas, number of retransmissions) in order to achieve a residual packet loss performance yielding a satisfactory QoE for HDTV transmission.

Estimating panel data models in the presence of endogeneity and selection

We consider estimation of panel data models with sample selection when the equation of interest contains endogenous explanatory variables as well as unobserved heterogeneity. Assuming that appropriate instruments are available, we propose several tests for selection bias and two estimation procedures that correct for selection in the presence of endogenous regressors. The tests are based on the fixed effects two-stage least squares estimator, thereby permitting arbitrary correlation between unobserved heterogeneity and explanatory variables. The first correction procedure is parametric and is valid under the assumption that the errors in the selection equation are normally distributed. The second procedure estimates the model parameters semiparametrically using series estimators. In the proposed testing and correction procedures, the error terms may be heterogeneously distributed and serially dependent in both selection and primary equations. Because these methods allow for a rather flexible structure of the error variance and do not impose any nonstandard assumptions on the conditional distributions of explanatory variables, they provide a useful alternative to the existing approaches presented in the literature.

Strong nonlocality: a trade-off between states and measurements

Measurements on entangled quantum states can produce outcomes that are nonlocally correlated. But according to Tsirelson's theorem, there is a quantitative limit on quantum nonlocality. It is interesting to explore what would happen if Tsirelson's bound were violated. To this end, we consider a model that allows arbitrary nonlocal correlations, colloquially referred to as ‘box world’. We show that while box world allows more highly entangled states than quantum theory, measurements in box world are rather limited. As a consequence there is no entanglement swapping, teleportation or dense coding.

Identification in Differentiated Products Markets Using Market Level Data

We consider nonparametric identification in models of differentiated products markets, using only market level observables. On the demand side we consider a nonparametric random utility model nesting random coefficients discrete choice models widely used in applied work. We allow for product/market-specific unobservables, endogenous product characteristics (e.g., prices), and high-dimensional taste shocks with arbitrary correlation and heteroskedasticity. On the supply side we specify marginal costs nonparametrically, allow for unobserved firm heterogeneity, and nest a variety of equilibrium oligopoly models. We pursue two approaches to identification. One relies on instrumental variables conditions used previously to demonstrate identification in a nonparametric regression framework. With this approach we can show identification of the demand side without reference to a particular supply model. Adding the supply side allows identification of firms' marginal costs as well. Our second approach, more closely linked to classical identification arguments for supply and demand models, employs a change of variables approach. This leads to constructive identification results relying on exclusion and support conditions. Our results lead to a testable restriction that provides the first general formalization of Bresnahan's (1982) intuition for empirically discriminating between alternative models of oligopoly competition.

Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes

The covariance structure of spatial Gaussian predictors (aka Kriging predictors) is generally modeled by parameterized covariance functions; the associated hyperparameters in turn are estimated via the method of maximum likelihood. In this work, the asymptotic behavior of the maximum likelihood of spatial Gaussian predictor models as a function of its hyperparameters is investigated theoretically. Asymptotic sandwich bounds for the maximum likelihood function in terms of the condition number of the associated covariance matrix are established. As a consequence, the main result is obtained: optimally trained nondegenerate spatial Gaussian processes cannot feature arbitrary ill-conditioned correlation matrices. The implication of this theorem on Kriging hyperparameter optimization is exposed. A nonartificial example is presented, where maximum likelihood‐based Kriging model training is necessarily bound to fail.