Analytic Detection Thresholds for Measurements of Linearly Polarized Intensity Using Rotation Measure Synthesis

A fully analytic statistical formalism does not yet exist to describe radio-wavelength measurements of linearly polarized intensity that are produced using rotation measure synthesis. In this work we extend the analytic formalism for standard linear polarization, namely that describing measurements of the quadrature sum of Stokes Q and U intensities, to the rotation measure synthesis environment. We derive the probability density function and expectation value for Faraday-space polarization measurements for both the case where true underlying polarized emission is present within unresolved Faraday components, and for the limiting case where no such emission is present. We then derive relationships to quantify the statistical significance of linear polarization measurements in terms of standard Gaussian statistics. The formalism developed in this work will be useful for setting signal-to-noise ratio detection thresholds for measurements of linear polarization, for the analysis of polarized sources potentially exhibiting multiple Faraday components, and for the development of polarization debiasing schemes.Comment: 14 pages, 6 figures, accepted for publication in MNRA

Eigenvalue Dynamics of a Central Wishart Matrix with Application to MIMO Systems

We investigate the dynamic behavior of the stationary random process defined by a central complex Wishart (CW) matrix ${\bf{W}}(t)$ as it varies along a certain dimension $t$. We characterize the second-order joint cdf of the largest eigenvalue, and the second-order joint cdf of the smallest eigenvalue of this matrix. We show that both cdfs can be expressed in exact closed-form in terms of a finite number of well-known special functions in the context of communication theory. As a direct application, we investigate the dynamic behavior of the parallel channels associated with multiple-input multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the complex random matrix that defines the MIMO channel, we characterize the second-order joint cdf of the signal-to-noise ratio (SNR) for the best and worst channels. We use these results to study the rate of change of MIMO parallel channels, using different performance metrics. For a given value of the MIMO channel correlation coefficient, we observe how the SNR associated with the best parallel channel changes slower than the SNR of the worst channel. This different dynamic behavior is much more appreciable when the number of transmit ($N_T$) and receive ($N_R$) antennas is similar. However, as $N_T$ is increased while keeping $N_R$ fixed, we see how the best and worst channels tend to have a similar rate of change.Comment: 15 pages, 9 figures and 1 table. This work has been accepted for publication at IEEE Trans. Inf. Theory. Copyright (c) 2014 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]

Partner selection in indoor-to-outdoor cooperative networks: an experimental study

In this paper, we develop a partner selection protocol for enhancing the network lifetime in cooperative wireless networks. The case-study is the cooperative relayed transmission from fixed indoor nodes to a common outdoor access point. A stochastic bivariate model for the spatial distribution of the fading parameters that govern the link performance, namely the Rician K-factor and the path-loss, is proposed and validated by means of real channel measurements. The partner selection protocol is based on the real-time estimation of a function of these fading parameters, i.e., the coding gain. To reduce the complexity of the link quality assessment, a Bayesian approach is proposed that uses the site-specific bivariate model as a-priori information for the coding gain estimation. This link quality estimator allows network lifetime gains almost as if all K-factor values were known. Furthermore, it suits IEEE 802.15.4 compliant networks as it efficiently exploits the information acquired from the receiver signal strength indicator. Extensive numerical results highlight the trade-off between complexity, robustness to model mismatches and network lifetime performance. We show for instance that infrequent updates of the site-specific model through K-factor estimation over a subset of links are sufficient to at least double the network lifetime with respect to existing algorithms based on path loss information only.Comment: This work has been submitted to IEEE Journal on Selected Areas in Communications in August 201

The κ - μ shadowed fading model with arbitrary intercluster correlation

In this paper, we propose a generalization of the well-known κ-μ shadowed fading model. Based on the clustering of multipath waves as the baseline model, the novelty of this new distribution is the addition of an arbitrary correlation for the scattered components within each cluster. It also inherits the random fluctuation of the dominant component, which is assumed to be the same for all clusters. Thus, it unifies a wide variety of models: Rayleigh, Rician, Rician shadowed, Nakagami- m, κ-μ and κ-μ shadowed as well as multivariate Rayleigh, Rician and Rician shadowed. The main statistics of the newly proposed model, i.e. moment generating function, probability density function and cumulative density function, are given in terms of exponentials and powers, and some numerical results are provided in order to analyze the impact of the arbitrary intercluster correlation.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Mobile to mobile channel modelling for wireless communications

Wireless communication has been experiencing many recent advances in mobile to mobile (M2M) applications. M2M communication systems differ from conventional fixed to mobile systems by having both transmitter and receiver in low elevation and in motion. This raises the need to come up with new channel models and perform statistical analysis on M2M communication channels looking from a different perspective. This need motivated us to perform the research outlined in this thesis. In reviewing the literature we found that though in general the M2M channel models are sparse, a major gap exists in the non geometrical stochastic based mathematical channel models. In filling this gap, we develop a novel mathematical non geometrical stochastic multiple input multiple output (MIMO) M2M channel model for two dimensional (2D) and three dimensional (3D) scattering environments. This model is based on the underlying physics of free space wave propagation and can be used as a framework for any environment by selecting suitable complex scattering gain functions. In addition, we extend this novel model to multicarrier M2M which is the first multicarrier channel model in the non geometrical stochastic M2M category. Based on our novel M2M channel model, we carry out an extensive analysis in space-time correlation, space-frequency correlation and second order channel statistics. With the choice of suitable parameters, this analysis and channel model can be used for any wireless environment. Thus, we claim that our novel channel model together with the analysis performed in this thesis can be taken as a generalized framework. A significant contribution of our analysis is the consideration of the impact of transmitter and receiver speed to space-time and space-frequency correlation, which is not available in the literature. Using a von Mises-Fisher distribution as the angular power distribution, the usefulness of the derived temporal correlation function is discussed. The simulation results corroborate the fact that both space-time and space-frequency correlations are reduced when transmitter or receiver speed increases. The rate of reduction of space-time correlation in von Mises-Fisher distribution scattering environment is more than in the isotropic environment. Under second order channel statistics, we consider Rice, Rayleigh and Nakagami fading channels in four different non-isotropic scattering environments with angle of departure (AoD) and angle of arrival (AoA) distributions given by (i) separable Truncated Gaussian, (ii) separable von-Mises, (iii) truncated Gaussian bivariate and (iv) truncated Laplacian bivariate distributions. We show that the major second order statistics, namely, the level crossing rate (LCR) and the average fade duration (AFD), in different fading channels can be expressed in terms of known scattering coefficients of the AoD and AoA distributions. As the channel models and their respective measurements provide reliable knowledge of the channel for the design and analysis of M2M systems, the proposed channel model and the corresponding analysis will be useful for the design, testing and performance evaluation of future M2M communication systems