  We propose a stochastic multipath model for the received signal for the case
where the transmitter and receiver, both with directive antennas, are situated
in the same rectangular room. This scenario is known to produce channel impulse
responses with a gradual specular-to-diffused transition in delay. Mirror
source theory predicts the arrival rate to be quadratic in delay, inversely
proportional to room volume and proportional to the product of the antenna beam
coverage fractions. We approximate the mirror source positions by a homogeneous
spatial Poisson point process and their gain as complex random variables with
the same second moment. The multipath delays in the resulting model form an
inhomogeneous Poisson point process which enables derivation of the
characteristic functional, power/kurtosis delay spectra, and the distribution
of order statistics of the arrival delays in closed form. We find that the
proposed model matches the mirror source model well in terms of power delay
spectrum, kurtosis delay spectrum, order statistics, and prediction of mean
delay and rms delay spread. The constant rate model, assumed in e.g. the
Saleh-Valenzuela model, is unable to reproduce the same effects.
