  In most multiple-input multiple-output (MIMO) communication systems, the
amount of information that can be transmitted reliably depends on the effective
degrees of freedom (EDoF) of the wireless channel. Conventionally, one can
model the channel matrix and study the EDoF, based on an electromagnetic (EM)
channel model that is built with the free space Green's function. However, the
EDoF of free-space channel model may not fit the practical scenario when EM
waves only transmit above the ground. In this paper, we analyze the EDoF for
both discrete and continuous aperture MIMO systems in the half space. We also
propose an approach to quickly calculate the Green function in the half space
from the Sommerfeld identity. Simulation results show that the difference
between the EDoF in the half space and that in the free space is non-negligible
for the near field communications, which indicates that the ground exerts
noticeable influence on EDoF. The proposed study establishes a fundamental
electromagnetic framework for MIMO wireless communication in the half space.
