  Time reversal methods are widely used to achieve wave focusing in acoustics
and electromagnetics. A typical time reversal experiment requires that a
transmitter be initially present at the target focusing point, which limits the
application of this technique. In this paper, we propose a method to focus
waves at an arbitary location inside a complex enclosure using a numerically
calculated wave excitation signal. We use a semi-classical ray algorithm to
calculate the signal that would be received at a transceiver port resulting
from the injection of a short pulse at the desired target location. The
time-reversed version of this signal is then injected into the transceiver port
and an approximate reconstruction of the short pulse is created at the target.
The quaility of the pulse reconstruction is quantified in three different ways
and the values of these metrics are predicted by the statistics of the
scattering-parameter $|S_{21}|^2$ between the transceiver and target points in
the enclosure. We experimentally demonstrate the method using a flat microwave
billiard and quantify the reconstruction quality as a function of enclosure
loss, port coupling and other considerations.
