Probabilistic Behavior Analysis of MIMO Fading Channels under Geometric Mean Decomposition

Geometric mean decomposition (GMD) has been proposed as a method to realize multiple spatial links with identical gains that are intrinsic to a MIMO channel. In order to simplify system design and implementation based on knowledge regarding probability behavior of MIMO-GMD schemes, the main objective of this paper is to statistically characterize the link gains and channel capacities that can be provided via GMD. In particular, closed-form univariate and bivariate probability density functions (PDFs) for these metrics under Rayleigh fading are derived using Gamma approximations. By applying these analytical results, the fluctuations of MIMO-GMD schemes are examined by modeling both link gains and capacities using finite-state Markov chains (FSMCs)