3D Placement of a New Tethered UAV to UAV Relay System for Coverage Maximization

In this paper, a new relay system that uses the UAV as a relay station between the tethered UAV and ground user (TU2U2G) is proposed. The TU2U2G system replaces the base station (BS) in the cellular system with a tethered UAV (TUAV). The TUAV is a UAV that receives power over a cable from a ground control station. It has advantages of high and variable altitude up to (100m) compared to BS. In addition, it overcomes the UAV drawback of the batteries' limited capacity. After that, a 3D placement Algorithm of the UAV as a relay station in the TU2U2G system is proposed. It is presented to maximize the coverage by jointly optimizing the transmitting power and relaying distance. The TU2U2G system shows better results than the traditional cellular system in terms of optimum UAV height, maximum coverage radius, and maximum distance between BS and UAV.

General Properties on Differential Sets of a Graph

Let G=(V,E) be a graph, and let β∈R. Motivated by a service coverage maximization problem with limited resources, we study the β-differential of G. The β-differential of G, denoted by ∂β(G), is defined as ∂β(G):=max{|B(S)|−β|S|suchthatS⊆V}. The case in which β=1 is known as the differential of G, and hence ∂β(G) can be considered as a generalization of the differential ∂(G) of G. In this paper, upper and lower bounds for ∂β(G) are given in terms of its order |G|, minimum degree δ(G), maximum degree Δ(G), among other invariants of G. Likewise, the β-differential for graphs with heavy vertices is studied, extending the set of applications that this concept can have.