Exploring the Random Location Problem Inside a Truncated Conic Shape: Application in UAV Communications

Abstract

More often than not, transmitters (Txs) in wireless networks operate using directional radiation patterns where the main radiation lobe creates a three-dimensional conic-shaped volume. In this context, any receiver (Rx) placed inside it can establish a strong communication link. Since the Rx location is not always known, it is desirable to investigate its random position effect to describe the link performance in a reliable manner. As in most cases, Rxs lie far away from the apex where the Tx is placed, we investigate the random location problem inside a truncated conic shape where the cone arises as a limiting case. To this end, we deduce a set of statistical metrics, including the random distance from the apex to a random point position. As an application, we focus on the outage performance of an unmanned aerial vehicle (UAV) communications scenario susceptible to Nakagami-<inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading and derive novel closed-form expressions for the composite model.