Trajectory optimization and resource allocation for UAV-assisted relaying communications

Abstract

In this paper, we study the unmanned aerial vehicles (UAV) assisted relaying communication system, where a UAV acts the mobile relay and provides the information transfer from the source to the destination. The simultaneous wireless information and power transfer techniques are considered at the UAV relays, where the UAV harvests energy from the source node, and exclusively uses the harvested energy for the data relaying. To maximize the system throughput, we jointly consider the UAV trajectory optimization and resource allocation problem, where the UAV trajectory is optimized the UAV positions to harvest the benefits of the line-of-sight links, and resource allocation, including power allocation and the subcarrier allocation, is used to achieve optimal network performance with the power constraints. An alternating maximization algorithm is proposed to solve the optimization problem, in which the UAV trajectory optimization and resource allocation are solved iteratively to maximize the total throughput. Compared with other benchmarks, the proposed algorithm can achieve higher throughput by the benefits from UAV trajectory optimization and resource allocation.

Appendices

Appendix 1

Proving by contradiction, for the optimal power allocation scheme $\{p_n^{a*}[m]\}$ and $\{p_n^{b*}[m]\}$, we have opposite proposition as

$$\begin{aligned}&\sum \limits _{n=1}^{N}\frac{1}{2}\log \left( 1+\frac{p_n^{b*}[m] h^n_{u,d}[m]}{\sigma _{d,n}}\right) \nonumber \\&\quad < \sum \limits _{n \in \mathbf {N}_I}\frac{1}{2}\log \left( 1+\frac{p_n^{a*}[m] h^n_{s,u}[m]}{\sigma _{s,n}}\right) , \end{aligned}$$

(19)

Then, we have

$$\begin{aligned} \begin{aligned}&\min \left\{ \sum \limits _{n=1}^{N}\frac{1}{2}\log \left( 1+\frac{p_n^{b*}[m] h^n_{u,d}[m]}{\sigma _{d,n}}\right) ,\right. \\&\qquad \left. \sum \limits _{n \in \mathbf {N}_I}\frac{1}{2}\log \left( 1+\frac{p_n^{a*}[m] h^n_{s,u}[m]}{\sigma _{s,n}}\right) \right\} \\&\quad = \sum \limits _{n=1}^{N}\frac{1}{2}\log \left( 1+\frac{p_n^{b*}[m] h^n_{u,d}[m]}{\sigma _{d,n}}\right) , \end{aligned} \end{aligned}$$

(20)

Then, we reduce the transmit power at the source $\{p_n^{a*}[m]\}$, or reduce the SCs amount in $\mathbf {N}_I$ until

$$\begin{aligned}&\sum \limits _{n=1}^{N}\frac{1}{2}\log \left( 1+\frac{p_n^{b*}[m] h^n_{u,d}[m]}{\sigma _{d,n}}\right) \nonumber \\&\quad = \sum \limits _{n \in \mathbf {N}_I}\frac{1}{2}\log \left( 1+\frac{p_n^{a*}[m] h^n_{s,u}[m]}{\sigma _{s,n}}\right) , \end{aligned}$$

(21)

where (20) still holds. In fact, the reduction of transmit power for information at the source is equal to increasing the power for relaying. Namely, when (19) holds, the power allocation at transmit $\{p_n^{a*}[m]\}$ is not optimal, which is contradicted with the proposition. Thus, the assumed proposition (19) is not true, and then we complete the proof.

Appendix 2

Proving it by contradiction, we have

• (a) $\exists u \in [1,n)$ satisfies $0 \le p_{\kappa (u)}^{a*}< P_{\text {max}}$;

• (b) $\exists u \in (n, {|\mathbf {N}_E|}]$ satisfies $0 \le p_{\kappa (u)}^{a*}< P_{\text {max}}$;

We give the proof of case (a) and similar approach can be applied to case (b). For $\forall u, 0< u < n$, and we have $h^{\kappa (z)}_{s,u} \ge h^{\kappa (n)}_{s,u}$. Let denote

$$\begin{aligned} \bar{p}_{\kappa (z)}^{a}= & {} \left\{ \begin{array}{ll} 0, &{} \qquad {\mathrm {if}} \ {p}_{\kappa (z)}^{a*}+{p}_{\kappa (n)}^{a*} \le P_{\text {max}}, \\ {p}_{\kappa (z)}^{a*}+{p}_{\kappa (n)}^{a*} - P_{\text {max}}, &{} \qquad {\mathrm {if}} \ {p}_{\kappa (z)}^{a*}+{p}_{\kappa (n)}^{a*} > P_{\text {max}}, \end{array} \right. \end{aligned}$$

(22)

$$\begin{aligned} \bar{p}_{\kappa (u)}^{a}= & {} \left\{ \begin{array}{ll} {p}_{\kappa (z)}^{a*}+{p}_{\kappa (n)}^{a*}, &{} \qquad {\mathrm {if}} \ {p}_{\kappa (z)}^{a*}+{p}_{\kappa (n)}^{a*} \le P_{\text {max}}, \\ P_{\text {max}}, &{} \qquad {\mathrm {if}} \ {p}_{\kappa (z)}^{a*}+{p}_{\kappa (n)}^{a*} > P_{\text {max}}, \end{array} \right. \end{aligned}$$

(23)

where $\bar{p}_{\kappa (z)}^{a}$ and $\bar{p}_{\kappa (n)}^{a}$ are feasible for the constrain in the problem P1, and we have

$$\begin{aligned} \bar{p}_{\kappa (z)}^{a}h^{\kappa (z)}_{s,u} +\bar{p}_{\kappa (n)}^{a}h^{\kappa (n)}_{s,u}> {p}_{\kappa (z)}^{a*}h^{\kappa (z)}_{s,u}+ {p}_{\kappa (n)}^{a*} h^{\kappa (n)}_{s,u} \end{aligned}$$

(24)

Clearly, UAV harvest more energy if the power allocation $\bar{p}_{\kappa (z)}^{a}$ and $\bar{p}_{\kappa (n)}^{a}$ are taken at the source than these under ${p}_{\kappa (z)}^{a*}$ and ${p}_{\kappa (n)}^{a*}$. Assume the inequation (24) holds when $\bar{p}_{\kappa (u)}^{a}= \bar{p}_{\kappa (u)}^{a}- \tau$, $\tau >0$, and $\tau$ energy is reallocated for information transfer at the source while the information throughput between UAV and destination is non-decreasing by this reallocation. Thus, higher throughout can be achieved with $\bar{p}_{\kappa (z)}^{a}$ and $\bar{p}_{\kappa (n)}^{a}$ than the optimal power allocation scheme $\{{p}_{\kappa (z)}^{a*}\}$ and $\{{p}_{\kappa (n)}^{a*}\}$, which is contradicted the case (a). Similarly, we can induce the contradiction in case (b). Then, it completes the proof.