On Ergodic Capacity and Optimal Number of Tiers in UAV-Assisted Communication Systems
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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 to maximize the ergodic capacity for a given total number of UAVs. To achieve this goal, we firstly 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. In addition, an upper-bound using the Jensen's inequality is also derived. With the derived bounds, we analyze the optimal number of tiers in such systems, and propose a low-complexity procedure that significantly reduces the complexity and yields near-optimal performance. Moreover, asymptotic properties of the ergodic capacity of Rayleigh product channel with different settings, and the optimal solutions on number of tiers are extensively analyzed.
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