  Predicting the statistics of realistic wave-chaotic scattering systems
requires, in addition to random matrix theory, introduction of system-specific
information. This paper investigates experimentally one aspect of
system-specific behavior, namely the effects of short ray trajectories in
wave-chaotic systems open to outside scattering channels. In particular, we
consider ray trajectories of limited length that enter a scattering region
through a channel (port) and subsequently exit through a channel (port). We
show that a suitably averaged value of the impedance can be computed from these
trajectories and that this can improve the ability to describe the statistical
properties of the scattering systems. We illustrate and test these points
through experiments on a realistic two-port microwave scattering billiard.
