Optimal power allocation and harvesting duration for mixed RF/FSO using Non Orthogonal Multiple Access

Abstract

In this paper, we suggest to optimize power allocation coefficients and harvesting duration in mixed Radio Frequency (RF)/Free Space Optical (FS0) communications using Non Orthogonal Multiple Access (NOMA). The system model contains three time slots. In the first time slot, relay node R harvests energy from RF signal received from node H. Node H can be any node transmitting RF signals. In the second time slot, an FSO transmitter T transmits a linear combination of symbols of K users to relay node R using NOMA. In the third and last slot, relay R detects the receive symbols and sends a linear combination of detected symbols to K users using NOMA. We show that power allocation and harvesting duration optimization allow to increase the throughput of RF/FSO communications. We consider two users’ ranking techniques using average or instantaneous channel gains.

Appendix: Performance analysis with nonlinear energy harvesting model

For a nonlinear energy harvesting model $E_{nonlinear}=\Psi (E)$, the CDF of $E_{nonlinear}$ is computed as

$$\begin{aligned} F_{E_{nonlinear}}(x)=F_{E}(\Psi ^{-1}(x))=1-e^{-\frac{\Psi ^{-1}(x)}{\epsilon L_0 \lambda _{HR}E_H\zeta }} \end{aligned}$$

(51)

where

$$\begin{aligned} \Psi ^{-1}(x)=\frac{ln(y)+ln(M)+ab-ln(M-y)}{2a} \end{aligned}$$

(52)

Variable $V_i=E_R|h_i|^2$ should be replaced by

$$\begin{aligned} V_{i,nonlinear}=\frac{E_{nonlinear}|h_i|^2}{0.5(1-\zeta )L_0}. \end{aligned}$$

(53)

The throughput of mixed RF/FSO is computed as Sects. 3 and 4 where the CDF $F_{V_i}(x)$ should be replaced by $F_{V_{i,nonlinear}}(x)$ given by

$$\begin{aligned} F_{V_{i,nonlinear}}(x) &= \int _0^{+\infty }F_{E_{nonlinear}}\left( \frac{0.5(1-\zeta )L_0x}{y}\right) \frac{e^{-\frac{y}{\lambda _i}}}{\lambda _i}dy,\nonumber \\ &= 1-\int _0^{+\infty }e^{-\frac{\Psi ^{-1}\left( \frac{0.5(1-\zeta )L_0x}{y}\right) }{L_0 \epsilon \lambda _{HR}E_H\zeta }}\frac{e^{-\frac{y}{\lambda _i}}}{\lambda _i}dy. \end{aligned}$$

(54)