Stochastic Multipath Model for the In-Room Radio Channel based on Room Electromagnetics

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-diffuse 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.