Abstract
In this paper, the performance of dual-hop amplify-and-forward (AF) two-way relaying systems is considered, where the terminals and relay are interfered by a finite number of co-channel interferers. In addition, the derived expressions are evaluated in terms of outage probability and throughput in delay-limited transmission mode. To make the analysis mathematically tractable, the unique expressions of outage probability are adopted to deal with energy harvesting protocols related to time switching and power splitting coefficients and expression of the throughput is also calculated. Based on the analytic results, this paper investigates the impact of system parameters such as energy harvesting time/power fractions, number of interferers and signal-to-noise ratio (SNR) on throughput performance. Monte Carlo simulation results are presented to prove the tightness of the proposed energy harvesting two-way relaying system.
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Notes
In practice, at the beginning of each block time, the relay node needs a certain amount of energy for operating. In this scenario, the relay node needs a certain amount of energy of previous blocks to initially operate in the next adjacent time slot. However, for simplicity, we assume that initializing energy at the beginning of each frame is not considered.
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Appendix: Proof of proposition 1
Appendix: Proof of proposition 1
This appendix derives the CDF of γ u ,u = {X,Y} in {(22), (23)}, respectively. Thus, the CDF of the end-to-end SINR of γ u is expressed as
Note that, in order to achieve (31), we applied the cumulative distribution function of X and Y which can be given as \( F_{u} \left (x \right ) = 1 - \exp \left ({ - \frac {x}{{\lambda _{u} }}} \right )\). Subsequently, the triple integral can be divided separately as follow
As can be seen, in order to derive \( F_{\gamma _{u} } \left (\gamma \right )\), we have to derive I 1 and I 2 first. After substituting the PDF of Z R given in Eq. 25 into (32), I 1 can be rewritten as
With the help of identities [21, Eq. 3.351.3], the above integration is calculated as follow
Substituting (34) into (33), new expression is then obtained as
Secondly, I 2 is derived by first substituting \( f_{Z_{u} } \left (y \right ) \) as given in Eq. 24 and \( f_{u} \left (y \right ) = \frac {1}{{\lambda _{u} }}\exp \left ({ - \frac {y}{{\lambda _{u} }}} \right ) \) into (32), and thus, I 2 can be rewritten as
where \( {\Psi } = \int \limits _{0}^{\infty } {y^{i_{2} - 1} \exp \left ({ - \frac {y}{{\mu _{u\left \langle {i_{1} } \right \rangle } }}} \right )\int \limits _{0}^{\infty } {\frac {1}{{\lambda _{u} }}\exp \left ({ - \frac {{\gamma \left ({y + 1} \right )}}{{\lambda _{v} \mathcal {C}_{X} }}\frac {1}{x} - \frac {x}{{\lambda _{u} }}} \right )dxdy} } \)
By applying [21, Eq. 3.478.4] to the second integration, we obtain
Consequently, Ψ is rewritten as
After some algebraic manipulations, Ψ is obtained as
Since index i 2 − 1 ≥ 0 we can apply the Newton’s binomial theorem in [21, Eq. 1.111] to finally derive the following result
This is end the proof.
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Luan, N.T., Do, DT. A new look at AF two-way relaying networks: energy harvesting architecture and impact of co-channel interference. Ann. Telecommun. 72, 669–678 (2017). https://doi.org/10.1007/s12243-017-0590-7
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DOI: https://doi.org/10.1007/s12243-017-0590-7