Nowadays, Unmanned Aerial Vehicles (UAVs) are widely used in heterogeneous contexts and, thanks to a continuous technological evolution, are going to be used for several applications such as, for example, Beyond Visual Line of Sight (BVLOS) operations. Since in BVLOS flights the UAV and the ground control center may not have a direct visibility with each other, a robust communication system is needed to provide reliable connectivity. Although a cellular (4G/5G) network is the current best candidate to enable BVLOS applications, there are still some limitations to overcome, as 4G (LTE) and 5G (NR) cellular networks are natively designed for terrestrial use. In this paper, we first investigate current cellular communication limitations for UAV-based applications, in particular taking into account both results available in the literature, as well as experimental performance campaigns. Then, a viable solution for mitigating these drawbacks exploiting selective on-board antennas is proposed, whose performance is experimentally investigated with a preliminary prototypical architecture.