New series representation for the trivariate non-central chi-squared distribution

Abstract

Abstract-This paper derives a new infinite series representation for the trivariate Non-central chi-squared distribution when the underlying correlated Gaussian variables have a tridiagonal form of an inverse covariance matrix. The joint probability density function is derived using Miller's approach and Dougall's identity. Moreover, the trivariate cumulative distribution function (cdf) and characteristic function (chf) are also derived. Finally, the bivariate non-central chi-squared distribution and some known forms are shown to be special cases of the more general distribution. However, the derivation of non-central chi-squared distribution for an arbitrary covariance matrix seems intractable via Miller's approach. Two applications of the newly derived results are provided for performance analysis of multiple input multiple output (MIMO) systems with transmit antenna selection over a correlated Rician fading environment. Some numerical results are also presented to verify the accuracy of the analytical expressions.

DADFN: dynamic adaptive deep fusion network based on imaging genomics for prediction recurrence of lung cancer

“…Due to the high dimensionality of the gene data and the dimension inconsistency of the gene expression data, we need to standardize the gene data and select related genes before declaring the regression model. Thus, we first process the gene data using the z-score standardization and then use LASSO (Tibshirani 1996, Aonpong et al 2019, F-test (ANOVA) (Gaddis 1998), CHI-2 (Dharmawansa et al 2009) to select the genes associated with the recurrence of NSCLC, and take the intersection of related genes obtained by the three feature selection methods. The gene screening process is shown in figure 3.…”

Multiuser‐MIMO systems employing a broadcasting protocol under equally correlated generalised‐Rician fading for even degrees of freedom

“…However, the findings in this paper can be employed as upper bounds on findings obtained under e.c. fading environments, which commonly lead to intractability under correlated LoS fading environments [26, 34]. The proposed upper bounds have been shown to be tight bounds, which offer useful approximate network performance if mathematical prediction becomes intractable, such as distributions of trivariate e.c.…”

“…The proposed upper bounds have been shown to be tight bounds, which offer useful approximate network performance if mathematical prediction becomes intractable, such as distributions of trivariate e.c. Rician fading [26].…”

“…fading environments, in which statistics of e.c. Rician fading environments are notoriously and computationally challenging to derive [12, 26].…”

“…The SCO cdf of trivariate e.c. non‐central chi‐square fading was studied in [26, (17)]. These facts show that theoretical developments for correlated fading and correlated generalised‐Rician fading (i) have not been unified, in which mathematical mistakes do exist, (ii) have not been rigorously verified against existing results from the same authors and from other authors, (iii) are insufficient for future wireless networks where channel architecture including narrow‐beam antenna correlation must be considered under a wide range of fading scenarios [1].…”