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

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 (MIMO) channels. We put a special interested in optimizing the number of tiers in such UAV-assisted systems for a given total number of UAVs to maximize the ergodic capacity. To achieve this goal, in a first part we derive a lower-bound in closed-form for the ergodic capacity which is shown to be asymptotically tight as signal-to-noise ratio (SNR) increases. With the derived bound, in a second part we analyze the optimal number of UAV-tiers, and propose a low-complexity procedure that significantly reduces the search-size and yields near-optimal performance. Moreover, asymptotic properties both for the ergodic capacity of Rayleigh product channel, and the optimal solutions on number of tiers are extensively analyzed.