Mode Group Diversity Multiplexing (MGDM) is an Optical Multiple-Input-Multiple-Output (O-MIMO) technique that provides larger robustness and capacity for data communication over MultiMode Fiber (MMF). The utility of a MGDM system in terms of capacity expansion gives a major interest in most applications of optical communication. In this paper, we propose a transfer matrix decompositioon of O-MIMO systems using MGDM technique in order to increase the capacity of the system. This treatment can be divided into 3 stages: noise whitening, channel diagonalization and dimension reduction. Numerical Matlab simulations results of a 3×3 MGDM link are given to support the efficiency of this study.