On the Physical Limitations of the Interaction of a Spherical Aperture and a Random Field

This paper derives physical limitations on the interactions of antennas exciting TM or TE modes (but not both) and wireless propagation channels. The derivation is based on the spherical vector wave expansion of the electromagnetic field outside a sphere circumscribing the antennas. The result is an extension of the seminal work of Chu on the classical limitations on maximum antenna gain and radiation
$Q$
. Rather than maximizing antenna gain in a single direction we obtain physical limitations on the antenna gain pattern, which is directly translated to more condensed parameters, i.e., the instantaneous effective gain
$G_{\rm i}$
and the mean effective gain
$G_{\rm e}$
if instantaneous realizations or correlation statistics of the expansion coefficients of the electromagnetic field are known, respectively. The obtained limitations are on the maximum of
$G_{\rm i}/Q$
and
$G_{\rm e}/Q$
, which establish a trade-off between link gain and
$Q$
.