In millimeter-wave applications, it is essential to use highly directional and steerable antennas. Phased array antennas are the most common choice, but they have restricted scanning coverage because of their effective aperture. To enhance the scanning coverage, a dielectric lens can be placed on top of the array. However, full-wave simulations require a lot of computing time to simulate this type of structure. In this work, a two-dimensional ray-tracing model has been adapted and improved to efficiently compute the radiation pattern of arrays combined with multilayered dielectric radomes for satellite communications applications. Moreover, this model can also calculate the absorption and reflection losses and the transmitted power required to comply with the regulatory mask. This model has been used to design a lens that increases the scanning range of an array while maintaining a maximum height and ensuring that it complies with the regulatory masks for satellite communications.