SBR image approach for radio wave propagation in tunnels with and without traffic

We propose a deterministic approach to model the radio propagation channels in tunnels with and without traffic. This technique applies the modified shooting and bouncing ray (SBR) method to find equivalent sources (images) in each launched ray tube and sums the receiving complex amplitude contributed by all images coherently. In addition, the vector effective antenna height (VEH) is introduced to consider the polarization-coupling effect resulting from the shape of the tunnels. We verify this approach by comparing the numerical results in two canonical examples where closed-form solutions exist. The good agreement indicates that our method can provide a good approximation of high-frequency radio propagation inside tunnels where reflection is dominant. We show that the propagation loss in tunnels can vary considerably according to the tunnel shapes and the traffic inside them. From the results we also find a "focusing" effect, which makes the power received in an arched tunnel higher than that in a rectangular tunnel. Besides, the deep fading that appears in a rectangular tunnel is absent in an arched tunnel. The major effect of the traffic is observed to be the fast fading due to the reflection/obstruction of vehicles. Additional considerations, such as time delay, wall roughness, and wedge diffraction of radio wave propagation in tunnels are left for future studies.