Composite Fading Models based on Inverse Gamma Shadowing: Theory and Validation

We introduce a general approach to characterize composite fading models based on inverse gamma (IG) shadowing. We first determine to what extent the IG distribution is an adequate choice for modeling shadow fading, by means of a comprehensive test with field measurements and other distributions conventionally used for this purpose. Then, we prove that the probability density function and cumulative distribution function of any IG-based composite fading model are directly expressed in terms of a Laplace-domain statistic of the underlying fast fading model and, in some relevant cases, as a mixture of wellknown state-of-the-art distributions. Also, exact and asymptotic expressions for the outage probability are provided, which are valid for any choice of baseline fading distribution. Finally, we exemplify our approach by presenting several application examples for IG-based composite fading models, for which their statistical characterization is directly obtained in a simple form.Comment: This work has been submitted to the IEEE for publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

A New Framework for the Performance Analysis of Wireless Communications under Hoyt (Nakagami-q) Fading

(c) 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. DOI:10.1109/TIT.2017.2655342We present a novel relationship between the distribution of circular and non-circular complex Gaussian random variables. Specifically, we show that the distribution of the squared norm of a non-circular complex Gaussian random variable, usually referred to as the squared Hoyt distribution, can be constructed from a conditional exponential distribution. From this fundamental connection we introduce a new approach, the Hoyt transform method, that allows to analyze the performance of a wireless link under Hoyt (Nakagami-q) fading in a very simple way. We illustrate that many performance metrics for Hoyt fading can be calculated by leveraging well-known results for Rayleigh fading and only performing a finite-range integral. We use this technique to obtain novel results for some information and communication-theoretic metrics in Hoyt fading channels.Universidad de Málaga. Campus de Execelencia Internacional. Andalucía Tech

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]

On the Calculation of the Incomplete MGF with Applications to Wireless Communications

(c) 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. DOI: 10.1109/TCOMM.2016.2626440The incomplete moment generating function (IMGF) has paramount relevance in communication theory, since it appears in a plethora of scenarios when analyzing the performance of communication systems. We here present a general method for calculating the IMGF of any arbitrary fading distribution. Then, we provide exact closed-form expressions for the IMGF of the very general κ-μ shadowed fading model, which includes the popular κ-μ, η-μ, Rician shadowed, and other classical models as particular cases. We illustrate the practical applicability of this result by analyzing several scenarios of interest in wireless communications: 1) physical layer security in the presence of an eavesdropper; 2) outage probability analysis with interference and background noise; 3) channel capacity with side information at the transmitter and the receiver; and 4) average bit-error rate with adaptive modulation, when the fading on the desired link can be modeled by any of the aforementioned distributions.Universidad de Málaga. Campus de Execelencia Internacional. Andalucía Tech

The κ-µ Shadowed Fading Model with Integer Fading Parameters

(c) 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. DOI: 10.1109/TVT.2017.2678430We show that the popular and general κ-μ shadowed fading model with integer fading parameters μ and m can be represented as a mixture of squared Nakagami- m̂ (or Gamma) distributions. Thus, its PDF and CDF can be expressed in closed-form in terms of a finite number of elementary functions (powers and exponentials). The main implications arising from such connection are then discussed, which can be summarized as: (1) the performance evaluation of communication systems operating in κ-μ shadowed fading becomes as simple as if a Nakagami- m̂ fading channel was assumed; (2) the κ-μ shadowed distribution can be used to approximate the κ-μ distribution using a closed-form representation in terms of elementary functions, by choosing a sufficiently large value of m; and (3) restricting the parameters μ and m to take integer values has limited impact in practice when fitting the κ-μ shadowed fading model to field measurements. As an application example, the average channel capacity of communication systems operating under κ-μ shadowed fading is obtained in closed-form.Universidad de Málaga. Campus de Excelencia Internacional. Andalucía Tech