Joint downlink user power allocation and rate maximization in UAV relay assisted SWIPT-NOMA network

Abstract

In this paper, in order to improve the performance of wireless fifth generation (5G) communication system and save power consumption, the research objectives of optimal power allocation and maximizing the total user rate in a multi-user cluster in the downlink of non-orthogonal multiple access (NOMA) access system are realized based on the simultaneous wireless information and power transfer (SWIPT). A SWIPT-NOMA system assisted by dynamic unmanned aerial vehicle (UAV) relay is constructed. The UAV relay dynamic programming under two-hop communication was firstly studied, and the global optimal power allocation strategy for downlink users of SWIPT-NOMA system is found. Finally, the optimal relay selection algorithm was used to maximize the total user rate, which was verified by Monto Carlo simulation. Simulation results show that compared with the traditional FDMA system scheme, the performance of the proposed system model in terms of outage probability, energy consumption and total user rate of multi-user cluster deployed in dynamic UAV relay system under different distribution scenarios is better than that of the benchmark scheme.

Appendices

Appendix 1

Using downlink NOMA transmission, the derivation process of the expression of the total transmission rate to the user node substitutes (13) into (14) to obtain:

$$R_{U,n} = B\log \left( {\frac{{\mathop {\left| {\mathop h\nolimits_{U,i = 1} } \right|}\nolimits^{2} \sum\limits_{i = 1}^{n} {\mathop \gamma \nolimits_{i} \mathop P\nolimits_{U} + \mathop \theta \nolimits^{2} } }}{{\mathop {\left| {\mathop h\nolimits_{U,j} } \right|}\nolimits^{2} \sum\limits_{j = 1}^{n - 1} {\mathop \gamma \nolimits_{j} \mathop P\nolimits_{U} + \mathop \theta \nolimits^{2} } }}} \right)$$

(35)

Then the total downlink transmission rate can be pushed to:

$$\begin{aligned} \sum\limits_{n = 1}^{N} {R_{U,n} } & = B\log \left( {\mathop {\mathop {\left| {\mathop h\nolimits_{U,1} } \right|}\nolimits^{2} \gamma }\nolimits_{1} \mathop P\nolimits_{U} + \mathop \theta \nolimits^{2} } \right) \\ & \quad + B\log \left( {\frac{{\mathop {\mathop {\left| {\mathop h\nolimits_{U,1} } \right|}\nolimits^{2} \gamma }\nolimits_{1} \mathop P\nolimits_{U} + \mathop {\mathop {\left| {\mathop h\nolimits_{U,2} } \right|}\nolimits^{2} \gamma }\nolimits_{2} \mathop P\nolimits_{U} + \mathop \theta \nolimits^{2} }}{{\mathop {\mathop {\left| {\mathop h\nolimits_{U,1} } \right|}\nolimits^{2} \gamma }\nolimits_{1} \mathop P\nolimits_{U} + \mathop \theta \nolimits^{2} }}} \right) \\ & \quad + \cdots + B\log \left( {\frac{{\mathop {\mathop {\sum\limits_{i = 1}^{N} {\mathop {\mathop {\left| {\mathop h\nolimits_{U,i} } \right|}\nolimits^{2} \gamma }\nolimits_{i} \mathop P\nolimits_{U} } }\nolimits_{{}} + \mathop \theta \nolimits^{2} }\nolimits^{{}} }}{{\mathop {\mathop {\sum\limits_{j = 1}^{N - 1} {\mathop {\mathop {\left| {\mathop h\nolimits_{U,j} } \right|}\nolimits^{2} \gamma }\nolimits_{j} \mathop P\nolimits_{U} } }\nolimits_{{}} + \mathop \theta \nolimits^{2} }\nolimits^{{}} }}} \right) \\ & = B\log \left( {\mathop {\sum\limits_{i = 1}^{N} {\mathop {\mathop {\left| {\mathop h\nolimits_{U,i} } \right|}\nolimits^{2} \gamma }\nolimits_{i} \mathop P\nolimits_{U} } }\nolimits_{{}} + \mathop \theta \nolimits^{2} } \right) \\ \end{aligned}$$

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Appendix 2

derivation process of interrupt probability expression of base station source node and UAV interrupt node.

Let

$$\begin{aligned} & \mathop {\theta_{U,S} }\nolimits^{2} = \mathop \theta \nolimits^{2} = 1 \\ & \mathop {\left| {\mathop h\nolimits_{U,S} } \right|}\nolimits^{2} = X;\mathop {\left| {\mathop h\nolimits_{U,n} } \right|}\nolimits^{2} = Y;\mathop {\left| {\mathop h\nolimits_{U,1} } \right|}\nolimits^{2} = Z;\mathop {\left| {\mathop h\nolimits_{U,N} } \right|}\nolimits^{2} = W \\ & a = \eta (1 - \beta )P_{S} ;b = \theta^{2} \\ & m = \beta \mathop {\theta_{U,S} }\nolimits^{2} + \mathop \theta \nolimits^{2} ;d = \beta P_{S} ;x_{0} = \frac{Lm}{d};L = \frac{{dx_{0} }}{m} \\ & F = \frac{Lb}{{\mathop \gamma \nolimits_{1} - \sum\limits_{i = 1}^{N - 1} {\mathop \gamma \nolimits_{i} .L} }};u(x) = \frac{F}{ax};P_{U} = \frac{ax}{b};H = \frac{Lb}{{\mathop \gamma \nolimits_{N} }} \\ \end{aligned}$$

Then the outage probability of the base station source node is

$$\begin{aligned} P_{{out_{S} }} & = \Pr (min(R_{U,S} ,R) \le R_{k}^{\min } )\\ & = 1 - \Pr (R_{U,S} \ge R_{k}^{\min } ,R \ge R_{k}^{\min } ) \\ & = 1 - \Pr (Blog(1 + SINR_{U,S} )\\ & \ge Blog(1 + L),Blog(1 + SINR_{U,n} ) \ge Blog(1 + L)) \\ & = 1 - Pr(\frac{{\beta P_{S} \mathop {\left| {\mathop h\nolimits_{U,S} } \right|}\nolimits^{2} }}{{\beta \mathop {\theta_{U,S} }\nolimits^{2} + \mathop \theta \nolimits^{2} }} \ge L,\mathop {\left| {\mathop h\nolimits_{U,i} } \right|}\nolimits^{2} P_{U} \sum\limits_{i = 1}^{N} {\mathop \gamma \nolimits_{i} \ge L} )\\ & = 1 - Pr\left( {\tfrac{dX}{m} \ge L,\frac{{axY\sum\limits_{i = 1}^{N} {\gamma_{i} } }}{b} \ge L} \right) \\ & = 1 - Pr\left( {X \ge \frac{Lm}{d},Y \ge \frac{Lb}{{ax\sum\limits_{i = 1}^{N} {\gamma_{i} } }}} \right) \\ & = 1 - Pr\left( {X \ge \frac{Lm}{d},Y \ge \frac{{bdx_{0} }}{{max\sum\limits_{i = 1}^{N} {\gamma_{i} } }}} \right) \\ & = 1 - \int_{{x_{0} }}^{\infty } {\left( {\int_{{\frac{{bdx_{0} }}{{max\sum\limits_{i = 1}^{N} {\gamma_{i} } }}}}^{\infty } {f_{Y} (y)dy} } \right)\lambda_{h} e}^{{ - \lambda_{h} x}} dx \\ & = 1 - \int_{{x_{0} }}^{\infty } {\lambda_{h} e}^{{ - \lambda_{h} x}} e^{{ - \lambda_{g} \frac{{bdx_{0} }}{{max\sum\limits_{i = 1}^{N} {\gamma_{i} } }}}} dx \\ & = 1 - \lambda_{h} \int_{{x_{0} }}^{\infty } e^{{ - \left( {\lambda_{h} x + \lambda_{g} \frac{{bdx_{0} }}{{max\sum\limits_{i = 1}^{N} {\gamma_{i} } }}} \right)}} dx \\ \end{aligned}$$

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The outage probability of UAV relay node is:

$$\begin{aligned} P_{{out_{U} }} & = \Pr (min(R_{U,1} ,R_{U,N} ) \le R_{k}^{\min } ) \\ & = 1 - \Pr (R_{U,1} \ge R_{k}^{\min } ,R_{U,N} \ge R_{k}^{\min } ) \\ & = 1 - \Pr (Blog(1 + SINR_{U,1} ) \ge Blog(1 + L),\\ & \quad Blog(1 + SINR_{U,N} ) \ge Blog(1 + L)) \\ & = 1 - Pr\left( {\frac{{\mathop {\left| {\mathop h\nolimits_{U,1} } \right|}\nolimits^{2} \gamma_{1} P_{U} }}{{\mathop {\left| {\mathop h\nolimits_{U,1} } \right|}\nolimits^{2} \sum\limits_{i = 1}^{N - 1} {\gamma_{i} P_{U} } + b_{{}} }} \ge L,\frac{{\mathop {\left| {\mathop h\nolimits_{U,N} } \right|}\nolimits^{2} P_{U} \mathop \gamma \nolimits_{N} }}{b} \ge L} \right) \\ & = 1 - Pr\left( {\tfrac{{Z\gamma_{1} P_{U} }}{{Z\sum\limits_{i = 1}^{N - 1} {\gamma_{i} P_{U} } + b_{{}} }} \ge L,\frac{{WP_{U} \mathop \gamma \nolimits_{N} }}{b} \ge L} \right) \\ & = 1 - Pr\left( {Z \ge \frac{Lb}{{(\gamma_{1} - \sum\limits_{i = 1}^{N - 1} {\gamma_{i} .L)ax} }},W \ge \frac{Lb}{{ax\gamma_{N} }}} \right) \\ & = 1 - Pr\left( {Z \ge u(x),W \ge \frac{H}{ax}} \right) \\ & = 1 - \int_{0}^{\infty } {\Pr } (Z \ge u(x))Pr\left( {W \ge \frac{H}{ax}} \right)dx \\ & = 1 - \int_{{_{0} }}^{\infty } {\left( {\int_{u(x)}^{\infty } {\lambda_{g} e^{{ - \lambda_{g} z}} } dz\int_{H}^{\infty } {\lambda_{w} e^{{ - \lambda_{w} W}} } dW} \right)} \lambda_{h} e^{{ - \lambda_{h} x}} dx \\ & = 1 - \lambda_{h} \int_{{_{0} }}^{\infty } e^{{ - (\lambda_{h} x + \lambda_{g} u(x) + \lambda_{w} H)}} dx \\ \end{aligned}$$

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