Clustered-NOMA Based Resource Allocation in Wireless Powered Communication Networks

Abstract

Wireless Powered Communication (WPC) provides an effective solution to the contradiction between information transmission and energy consumption for Internet of Things (IoT) terminals. In this paper, a clustered-Non-Orthogonal Multiple Access (C-NOMA) based WPC model is proposed. Base Station (BS) transfers Radio Frequency (RF) energy to all terminals in the downlink, while terminals transmit information to BS in the uplink by utilizing the harvested energy. A terminal clustering scheme based on maximizing the sum of channel condition difference between terminals is adopted. Specifically, Orthogonal Frequency Division Multiple Access (OFDMA) is used for inter-cluster terminals, while NOMA is used for intra-cluster terminals. In addition, a time-sharing mechanism is adopted to decode information. The sum rate in the uplink is maximized by jointly optimizing transmit power of BS, uplink and downlink subslot. Simulation results demonstrate that, the proposed C-NOMA based WPC model can not only maximize the sum rate in the uplink, but also enhance the fairness between terminals.

Appendix A

In Section 3, the information rate of each terminal is given by Eq. 4, let ${a_{k,n}} = \frac {{{G_{0}}{G_{k,n}}\xi {{\left | {{h_{k,n}}} \right |}^{4}}{P_{0}}}}{{{N_{0}}}}$, the sum rate in the k-th cluster is derived as follows:

$$ \begin{array}{ll} {R_{k}} &= \sum\limits_{{j_{w,n}} = 1}^{N} {{R_{k,{j_{w,n}}}}} \\ &= \sum\limits_{w = 1}^{W} {{\tau_{w}}{T_{1}}\left( {\sum\limits_{{j_{w,n}} = 1}^{N - 1} {{{\log }_{2}}\left( {\frac{{\sum\limits_{i = {j_{w,n}}} {{a_{k,i}}{T_{0}} + {T_{1}}} }}{{\sum\limits_{i > {j_{w,n}}} {{a_{k,{j_{w,n}}}}{T_{0}} + {T_{1}}} }}} \right) + {{\log }_{2}}\left( {\frac{{{a_{k,N}}{T_{0}}{\text{ + }}{T_{1}}}}{{{T_{1}}}}} \right)} } \right)} \\ &= \sum\limits_{w = 1}^{W} {\tau_{w}}{T_{1}}\begin{array} {*{20}{c}}{\left( {{{\log }_{2}}\left( {\frac{{\sum\limits_{i = 1} {{a_{k,1}}{T_{0}} + {T_{1}}} }}{{\sum\limits_{i > 1} {{a_{k,i}}{T_{0}} + {T_{1}}} }}} \right) + {{\log }_{2}}\left( {\frac{{\sum\limits_{i = 2} {{a_{k,2}}{T_{0}} + {T_{1}}} }}{{\sum\limits_{i > 2} {{a_{k,i}}{T_{0}} + {T_{1}}} }}} \right) + ...} \right.}\\ {\left. { + {{\log }_{2}}\left( {\frac{{\sum\limits_{i = N - 1} {{a_{k,N - 1}}{T_{0}} + {T_{1}}} }}{{\sum\limits_{i > N - 1} {{a_{k,i}}{T_{0}} + {T_{1}}} }}} \right) + {{\log }_{2}}\left( {\frac{{{a_{k,N}}{T_{0}}{\text{ + }}{T_{1}}}}{{{T_{1}}}}} \right)} \right)} \end{array} \\ &= \sum\limits_{w = 1}^{W} {{\tau_{w}}{T_{1}}\left( {{{\log }_{2}}\left( {\frac{{\sum\limits_{i = 1} {{a_{k,1}}{T_{0}} + {T_{1}}} }}{{\sum\limits_{i = 2} {{a_{k,i}}{T_{0}} + {T_{1}}} }} \cdot \frac{{\sum\limits_{i = 2} {{a_{k,2}}{T_{0}} + {T_{1}}} }}{{\sum\limits_{i = 3} {{a_{k,i}}{T_{0}} + {T_{1}}} }} \cdot ... \cdot \frac{{\sum\limits_{i = N - 1} {{a_{k,N - 1}}{T_{0}} + {T_{1}}} }}{{{a_{k,N}}{T_{0}}{\text{ + }}T}} \cdot \frac{{{a_{k,N}}{T_{0}}{\text{ + }}{T_{1}}}}{{{T_{1}}}}} \right)} \right)} \\ &= \sum\limits_{w = 1}^{W} {{\tau_{w}}{T_{1}}{{\log }_{2}}\left( {1 + \frac{{\sum\limits_{n = 1}^{N} {{a_{k,n}}{T_{0}}} }}{{{T_{1}}}}} \right)} \\ &= {T_{1}}{\log_{2}}\left( {1 + \frac{{\sum\limits_{n = 1}^{N} {{a_{k,n}}{T_{0}}} }}{{{T_{1}}}}} \right) \end{array} $$

(20)

It can be found from the above expression that the sum rate in each NOMA cluster is independent of τ_w. Moreover, the fixed decoding order can be seen as a special case of time-sharing, i.e. W = 1. This is corresponding to the case of only one decoding order, i.e. τ₁ = 1. Thus, the sum rate in the uplink can be expressed as:

$$ {R_{{\text{sum}}}} = \sum\limits_{k = 1}^{K} {{R_{k}}} = \sum\limits_{k = 1}^{K} {{T_{1}}{{\log }_{2}}\left( {1 + \frac{{\sum\limits_{n = 1}^{N} {{a_{k,n}}{T_{0}}} }}{{{T_{1}}}}} \right)} $$

(21)