A Gaussian Beam Approximation Approach for Embedding Antennas Into Vector Parabolic Equation-Based Wireless Channel Propagation Models

Vector parabolic equation (VPE) methods have been widely applied to the modeling of radio-wave propagation in tunnel environments, offering high computational efficiency and fidelity. While the propagation environment can be discretized and represented in detail, the representation of radiating sources (such as transmitting antennas) requires the calculation, analytical if possible or numerical via another method such as ray-tracing (RT), of the fields that the sources generate on the initial plane of the VPE model. These initial conditions are necessary for subsequently applying VPE. However, the solutions offered so far compromise either the accuracy or the efficiency of VPE. For example, generating the initial conditions for VPE through RT adds significant computational overhead to the typically fast VPE solver. To address this significant limitation of VPE methods, we introduce a technique that allows one to directly embed antennas into a VPE mesh, via a Gaussian beam approximation of their radiated fields. Hence, the initial conditions for VPE are generated for practical antenna patterns, without invoking other techniques and with no compromise on the inherent efficiency of VPE. Concrete guidelines on how to choose parameters for Gaussian beams are provided. Numerical results are compared to experimental measurements in various tunnel scenarios, demonstrating the validity and usefulness of the technique.