  We present an analysis of enhanced wave transmission through random media
with mirror symmetry about a reflecting barrier. The mathematical model is the
acoustic wave equation and we consider two setups, where the wave propagation
is along a preferred direction: in a randomly layered medium and in a randomly
perturbed waveguide. We use the asymptotic stochastic theory of wave
propagation in random media to characterize the statistical moments of the
frequency dependent random transmission and reflection coefficients, which are
scalar valued in layered media and matrix valued in waveguides. With these
moments, we can quantify explicitly the enhancement of the net mean transmitted
intensity, induced by wave interference near the barrier.
