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

Johannes T Ferreira

doi:10.3390/e23070845

Johannes T Ferreira

Open Access

https://doi.org/10.3390/e23070845

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Abstract

A cornerstone in the modeling of wireless communication is MIMO systems, where a complex matrix variate normal assumption is often made for the underlying distribution of the propagation matrix. A popular measure of information, namely capacity, is often investigated for the performance of MIMO designs. This paper derives upper bounds for this measure of information for the case of two transmitting antennae and an arbitrary number of receiving antennae when the propagation matrix is assumed to follow a scale mixture of complex matrix variate normal distribution. Furthermore, noncentrality is assumed to account for LOS scenarios within the MIMO environment. The insight of this paper illustrates the theoretical form of capacity under these key assumptions and paves the way for considerations of alternative distributional choices for the channel propagation matrix in potential cases of severe fading, when the assumption of normality may not be realistic.

Highlights

Expressions which are effectively an upper bound for the capacity are derived under the SMCN assumption, assuming noncentrality for H
H H H, and this paper investigates the eigenvalue relations of this SMCW distribution, as well as its uncorrelated counterpart
An upper bound for the capacity for both these cases are derived for the case when p = 2, which in a MIMO context implies a two transmitter environment and is often employed for dual branch MIMO systems in practice, while considering arbitrary number of receivers n

Summary

MIMO Channels and Capacity

Research in random matrix theory has seen unprecedented growth in theoretical advances over the last two decades, and coupled with a variety of developments in fields of application including wireless communication. Λ1 denotes the largest eigenvalue of H H H, and its distribution is essential in the evaluation of (2) This assumption for H is restrictive in the practical case when severe fading is observed, and it is the main focus of this paper to alleviate this restriction via the platform of scale mixture of complex matrix variate normals for H. 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 H 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].

Main Contribution of this Paper

Eigenvalue Pdfs and an Upper Bound

Approximation for Case 1 and Case 2

Exact Expression for Case 2

Conclusions