Inconsistent Rays in Propagation Prediction by Ray Launching in Rectangular Tunnels

Abstract

Ray tracing is replacing the less accurate statistical and empirical approaches of radio channel modeling. Although being high-frequency asymptotic method, ray tracing has been shown to be mathematically equivalent to purely analytical modal methods in rectangular tunnels and waveguides. The equivalence applies to modeling reflections using image theory, while other variants of the ray tracing algorithm are still subject to approximation errors that can systematically add up. Failure to recognize this leads to indiscriminate use of the less appropriate algorithmic variants. In particular, the use of ray tracing by ray launching can be questionable in tunnel environments, at least when characteristic sequences are used to avoid double counting errors. In addition to the known path inaccuracies, we first identify previously untreated inconsistent rays as the most problematic, leading to a significantly overestimated signal at distances greater than 100 m. We show that the problem is not equivalent to double counting of rays since the inconsistent rays represent valid wavefronts for the points in space at which they are detected. The discrepancy arises from the use of reception spheres, which allow some spatial displacement of ray paths. We quantify the errors in terms of estimated power, channel impulse response, and delay spread in a rectangular tunnel. We propose an improvement in the double-count filters to detect inconsistent rays. However, evaluation of signals deeper in the tunnel at frequencies below 1 GHz must be avoided by ray launching due to the remaining path inaccuracies.