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On Some Unifications Arising from the MIMO Rician Shadowed Model

Laureano Moreno-Pozas, Eduardo Martos-Naya

TL;DR

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.

Abstract

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 $κ$-$μ$ defined by Yacoub, and its recent generalization, the \mbox{$κ$-$μ$} shadowed model. Moreover, the SISO \mbox{$η$-$μ$} 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.

On Some Unifications Arising from the MIMO Rician Shadowed Model

TL;DR

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.

Abstract

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 - defined by Yacoub, and its recent generalization, the \mbox{-} shadowed model. Moreover, the SISO \mbox{-} and \mbox{Nakagami-} 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.

Paper Structure

This paper contains 9 sections, 17 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. System model definition
  4. Unification of popular fading models through the MIMO Rician shadowed
  5. Unifying models for SISO communication
  6. Unifying models for MIMO communication
  7. Maximum eigenvalue distribution
  8. Numerical Results
  9. Conclusions

Figures (3)

  • Figure 1: Comparison of the analytical and simulated cdf of the maximum eigenvalue of the MIMO Rician shadowed model for different matrix dimensions and various parameters. For all the cases $p=4$.
  • Figure 2: Analytical and simulated pdf of the MIMO Rician shadowed maximum eigenvalue for the last case of Fig. 1.
  • Figure 3: Evolution of the pdf of the MIMO Rician shadowed maximum eigenvalue when $m$ grows. The other parameters are fixed to $n=2$, $p=4$ and $\sigma_\Sigma^2=1$, with $m\cdot\sigma_M^{-2}=40$.