On Ergodic Capacity and Optimal Number of Tiers in UAV-Assisted Communication Systems

Abstract

In this paper, we consider unmanned aerial vehicle (UAV) assisted communication systems, where a number of UAVs are utilized as multi-tier relays between a number of users and a base-transceiver station (BTS). We model the wireless propagation channel between the users and the BTS as a Rayleigh product channel, which is a product of a series of independent and identically distributed (i.i.d.) Rayleigh multi-input multi-output channels. We put a special interest in optimizing the number of tiers in such UAV-assisted systems for a given total number of UAVs through maximizing the ergodic capacity. To achieve this goal, in the first part, we derive a lower-bound in a closed form for the ergodic capacity, which is shown to be asymptotically tight. In the second part, we analyze the optimal number of UAV-tiers with the derived bound, and propose a low-complexity solution that significantly reduces the search-size and yields near-optimal performance. Further, asymptotic properties both for the ergodic capacity and the solution for optimal number of tiers are extensively analyzed.