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This paper proposes a novel approach to the statistical characterization of non-central complex Gaussian quadratic forms (CGQFs). Its key strategy is the generation of an auxiliary random variable (RV) that converges in distribution to the original CGQF. Since the mean squared error between both is given in a simple closed-form formulation, the auxiliary RV can be particularized to achieve the required accuracy. The technique is valid for both definite and indefinite CGQFs and yields simple expressions of the probability density function (PDF) and the cumulative distribution function (CDF) that involve only elementary functions. This overcomes a major limitation of previous approaches, in which the complexity of the resulting PDF and CDF prevents from using them for subsequent calculations. To illustrate this end, the proposed method is applied to maximal ratio combining systems over correlated Rician channels, for which the outage probability and the average bit error rate are derived.

We present a general and tractable fading model for line-of-sight (LOS) scenarios, which is based on the product of two independent and non-identically distributed $\kappa$-$\mu$ shadowed random variables. Simple closed-form expressions for the probability density function, cumulative distribution function and moment-generating function are derived, which are as tractable as the corresponding expressions derived from a product of Nakagami-$m$ random variables. This model simplifies the challenging characterization of LOS product channels, as well as combinations of LOS channels with non-LOS ones. We leverage these results to analyze performance measures of interest in the contexts of wireless powered and backscatter communications, where both forward and reverse links are inherently of LOS nature, as well as in device-to-device communications subject to composite fading. In these contexts, the model shows a higher flexibility when fitting field measurements with respect to conventional approaches based on product distributions with deterministic LOS, together with a more complete physical interpretation of the underlying propagation characteristics., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

We here introduce an extension and natural generalization of both the \kappa-\mu$\,$shadowed and the classical Beckmann fading models: the Fluctuating Beckmann (FB) fading model. This new model considers the clustering of multipath waves on which the line-of-sight (LoS) components randomly fluctuate, together with the effect of in-phase/quadrature power imbalance in the LoS and non-LoS components. Thus, it unifies a variety of important fading distributions as the one-sided Gaussian, Rayleigh, Nakagami-m, Rician, \kappa-\mu, \eta-\mu, \eta-\kappa, Beckmann, Rician shadowed and the \kappa-\mu$\,$shadowed distribution. The chief probability functions of the FB fading model, namely probability density function, cumulative distribution function and moment generating function are derived. The second-order statistics such as the level crossing rate and the average fade duration are also analyzed. These results can be used to derive some performance metrics of interest of wireless communication systems operating over FB fading channels., 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 accesible

We analyze the level crossing rate (LCR) and the average fade duration of the output signal-to-noise-ratio (SNR) in generalized switched diversity systems. By using a common approach, we study these higher order statistics for two different kinds of configurations: (1) Colocated diversity, i.e. receiver equipped with multiple antennas, and (2) Distributed diversity, i.e. relaying link with multiple single-antenna threshold-based decode-and-forward (DF) relays. In both cases, we consider the switched diversity combining strategies Selection Combining and Switch \& Stay Combining (SSC). Whenever using threshold-based techniques such as DF or SSC, the output SNR is a discontinuous random process and hence classic Rice approach to calculate the LCR is not applicable. Thus, we use an alternative formulation in terms of the one and two-dimensional cumulative distribution functions of the output SNR. Our results are general, and hold for any arbitrary distribution of fading at the different diversity branches. Moreover, we develop a general asymptotic framework to calculate these higher order statistics in high mean SNR environments which only needs of the univariate probability density function.

This paper shows that the recently proposed $\kappa$-$\mu$ shadowed fading model includes, besides the $\kappa$-$\mu$ model, the $\eta$-$\mu$ fading model as a particular case. This has important relevance in practice, as it allows for the unification of these popular fading distributions through a more general, yet equally tractable, model. The convenience of new underlying physical models is discussed. Then, we derive simple and novel closed-form expressions for the asymptotic ergodic capacity in $\kappa$-$\mu$ shadowed fading channels, which illustrate the effects of the different fading parameters on the system performance. By exploiting the unification here unveiled, the asymptotic capacity expressions for the $\kappa$-$\mu$ and $\eta$-$\mu$ fading models are also obtained in closed-form as special cases., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

This paper shows that the proposed Rician shadowed model for multi-antenna communications allows for the unification of a wide set of models, both for multiple-input multiple output (MIMO) and single-input single output (SISO) communications. The MIMO Rayleigh and MIMO Rician can be deduced from the MIMO Rician shadowed, and so their SISO counterparts. Other SISO models, besides the Rician shadowed proposed by Abdi et. al., are included in the model, such as the $\kappa$-$\mu$ defined by Yacoub, and its recent generalization, the \mbox{$\kappa$-$\mu$} shadowed model. Moreover, the SISO \mbox{$\eta$-$\mu$} and \mbox{Nakagami-$q$} models can be seen as particular cases of the MIMO Rician shadowed. The literature already presents the probability density function (pdf) of the Rician shadowed Gram channel matrix in terms of the well-known gamma-Wishart distribution. We here derive its moment generating function in a tractable form. Closed-form expressions for the cumulative distribution function and the pdf of the maximum eigenvalue are also carried out., Comment: This work has been submitted to an international for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

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 pubs-permissions@ieee.org

An analysis of the characteristic function of Gaussian quadratic forms is presented in [1] to study the performance of multichannel communication systems. This technical report reviews this analysis, obtaining alternative expressions to original ones in compact matrix format., Comment: 5 pages, 3 talbes and 1 figure