A unified complex noncentral Wishart type distribution inspired by massive MIMO systems

Abstract

The eigenvalue distributions from a complex noncentral Wishart matrix S = X H X has been the subject of interest in various real world applications, where X is assumed to be complex matrix variate normally distributed with nonzero mean M and covariance. This paper focuses on a weighted analytical representation of S to alleviate the restriction of normality; thereby allowing the choice of X to be complex matrix variate elliptically distributed for the practitioner. New results for eigenvalue distributions of more generalised forms are derived under this elliptical assumption, and investigated for certain members of the complex elliptical class. The distribution of the minimum eigenvalue enjoys particular attention. This theoretical investigation has proposed impact in communications systems (where massive datasets can be conveniently formulated in matrix terms), in particular the case where the noncentral matrix has rank one which is useful in practice.

Upper Bounds for the Capacity for Severely Fading MIMO Channels under a Scale Mixture Assumption

“…However, limited work has been done to introduce the platform of scale mixture of normal distributions within a MIMO context. Within MIMO, a normal assumption is made, but evidence exists that there are practical considerations from fieldwork which supports the argument that a departure from normality does not seem far-fetched [ 9 , 10 , 11 , 12 ]. In this light, the consideration of a scale mixture of (complex) matrix variate normals (SMCN) for the candidacy of makes a meaningful contribution, as the scale mixture class has different distributional members which may very well suitably adapt to the practitioners need [ 9 , 13 ].…”

“…These members include the usual normal-, t-, contaminated normal-, and slash distribution among others—all of which provide a heavier-than-normal tailed alternative for potential practical considerations of . In fact, [ 11 ] illustrates an SMCN assumption for a zero mean in the MIMO context specifically where superior capacity performance is observed for an underlying complex matrix variate t model for , and [ 10 , 12 ] demonstrates the added value of the scale mixture approach when exhibits a nonzero mean; specifically focusing on rank-1 noncentrality and the condition number of the quadratic form, respectively. The data-driven consideration of the scale mixture approach in the MIMO environment is therefore well-motivated, and a valuable theoretical consideration.…”

“…Key characteristics under these challenges (such as pdfs of the joint eigenvalues, and thus capacity) are often derived in mathematically elegant yet computationally challenging forms of zonal- and Hayakawa polynomials (see [ 2 ], for example). This limits the practical consideration, and this paper will make additional assumptions (similar to [ 10 , 14 , 15 ]), such as to circumvent the cumbersome potential computational implementation of the results.…”

An Enriched α − μ Model as Fading Candidate

“…e proposed SMN platform in this paper allows theoretical and resultant practical access to previously unconsidered models, providing flexibility for modelling that may yield improved fits to experimental data in practice when these data exhibit potential heavier tail behaviour [2,13]…”

“…To the authors' knowledge, this representation of the α − μ model within communications systems has not yet been considered. Some performance measures of a fading channel subject to this enriched α − μ model are comparatively investigated against that of the well-studied normal (for recent contributions in this domain, see [11][12][13]).…”