A Novel Resource Allocation for SWIPT-NOMA Enabled AF Relay Based Cooperative Network

Abstract

In this work, a novel resource allocation scheme is proposed to find the optimal time-switching and power-splitting factors in a SWIPT assisted non-orthogonal multiple access (NOMA) relay network with combined time switching and power splitting protocol. The system model consists of a source node broadcasting a multiplexed NOMA signal to the far and near user via an amplify-and-forward energy harvesting relay node in a Rayleigh-flat-fading channel environment. Here, effective SNR maximization at both the near and far users is formulated as an optimization problem under total transmit power constraint and to deal with this both the Lagrangian multiplier approach and differential-evolution algorithm have been exploited. Furthermore, performance study is presented about the comparison of proposed scheme with the fixed allocation scheme in terms of outage probability under the impact of distinct target rates, relay locations, and channel conditions. Finally, the simulation results signify the performance improvement in the system with the optimal values obtained from the proposed scheme over the fixed time and power splitting factors.

Appendix

Derivation to acquire the optimal power allocation coefficients $a_{1} , \, a_{2}$ of NOMA users using Lagrange method.

Solution to get the power allocation fractions $a_{1} , \, a_{2}$ with regard to D₁ can be derived as follows:

The Lagrange function (J) can be formulated as

$$J = \gamma_{{eff_{x1} }} + \lambda P_{s} \, (a_{1} + a_{2} - 1) = 0$$

(26)

where

$$\gamma_{{eff_{x1} }} = \frac{{\gamma_{{sr_{1} }} \gamma_{{rd_{1} }} }}{{\gamma_{{sr_{1} }} + \gamma_{{rd_{1} }} }}$$

(27)

$$\gamma_{{sr_{1} }} = \frac{{P_{s} |h_{sr} |^{2} a_{1} }}{{P_{s} |h_{sr} |^{2} a_{2} + N_{0} }},\gamma_{rd1} = \frac{{\beta^{2} P_{s} |h_{sr} |^{2} |h_{rd} |^{2} a_{{_{1} }} }}{{\beta^{2} .P_{s} |h_{sr} |^{2} |h_{rd} |^{2} a_{2} + \beta^{2} |h_{rd} |^{2} N_{0} + N_{0} }}$$

By substituting $\gamma_{{sr_{1} }}$ and $\gamma {}_{rd1}$ in “(27)”, the effective SNR obtained as

$$\begin{aligned} \gamma_{{eff_{x1} }} & = \frac{{\beta^{2} P_{s}^{2} |h_{sr} |^{4} |h_{rd1} |^{2} a_{1}^{2} }}{{2.a_{2} a_{1} \beta^{2} P_{s}^{2} |h_{sr} |^{4} |h_{rd1} |^{2} + 2.a_{1} N_{0} \beta^{2} P_{s}^{2} |h_{sr} |^{2} |h_{rd1} |^{2} + a_{1} P_{s} |h_{sr} |^{2} N_{0} }} \\ \gamma_{{eff_{x1} }} & = \frac{1}{{\frac{{2.a_{2} }}{{a_{1} }} + \frac{{2.N_{0} }}{{P_{s} |h_{sr} |^{2} a_{1} }} + \frac{{N_{0}^{2} }}{{P_{s} P_{r} |h_{sr} |^{2} |h_{rd1} |^{2} a_{1} }} + \frac{{N_{0} }}{{P_{r} |h_{rd1} |^{2} a_{1} }}}} \\ \end{aligned}$$

(28)

where ‘λ’ is the Lagrangian multiplier.

By solving $\frac{dJ}{{da_{1} }} = 0 \, and \, \frac{dJ}{{da_{2} }} = 0$

$$\frac{\partial J}{{\partial a_{2} }} = 0$$

$$\Rightarrow a_{1}^{2} - (Z_{1} + 2 + \frac{1}{{2.P_{s} \lambda }}).a_{1} + 1 + Z_{1} + \frac{{Z_{1}^{2} }}{4} = 0$$

Finally, the power allocation factor for D₁ can be expressed as

$$a_{1} = - (Z_{2} + \frac{1}{{P_{s} .\lambda }})$$

(29)

where $Z_{1} = \frac{{2.N_{0} }}{{P_{s} |h_{sr} |^{2} }} + \frac{{N_{0}^{2} }}{{P_{s} P_{r} |h_{sr} |^{2} |h_{rd} |^{2} }} + \frac{{N_{0} }}{{P_{r} |h_{rd} |^{2} }}$; $z_{2} = \frac{{2.N_{0} }}{{P_{s} |h_{sr} |^{2} }} + \frac{{N_{0} }}{{P_{r} |h_{rd} |^{2} }} + \frac{{N_{0}^{2} }}{{P_{s} P_{r} |h_{sr} |^{2} |h_{rd} |^{2} }}$.

Similarly, by solving $\frac{\partial J}{{\partial a_{1} }} = 0$

$$\Rightarrow a_{2} - (a_{1}^{2} + Z_{2}^{2} + 2.a_{1} .Z_{2} )P_{s} \lambda = 0$$

Finally, the power allocation factor for near user (D₂) is given by

$$a_{2} = \frac{{ - (1 + \lambda P_{s} Z_{1} )}}{{2.P_{s} .\lambda }}$$

(30)

Optimal values of $a_{1} , \, a_{2}$ can be formulated as

$$\left[ {a_{1} } \right]^{ + } = Max\left( {0,a_{1} } \right){\text {and }}\left[ {a_{2} } \right]^{ + } = Max\left( {0,a_{2} } \right)$$

(31)