Co-channel Interference Energy Harvesting for Decode-and-Forward Relaying

Abstract

In this paper, co-channel interferences are exploited for energy harvesting in a Cooperative Network (CICN) in which a power constrained relay uses a power splitting architecture (CICN-PS) and a time switching architecture (CICN-TS) to harvest energy from the radio-frequency signals received from a source node and co-channel interferences. In the proposed CICN-PS and CICN-TS protocols, the relay applies decode-and-forward technology to decode the information of the source node, and then forwards the recoded information to a destination with the overall harvested energies. The system performance of the proposed protocols is discussed and evaluated using the exact throughput analyses and is then checked using Monte Carlo simulations over Rayleigh fading channels. The optimal power splitting ratio and energy harvesting time are derived by the Golden Section Search method, and throughput performance evaluations are performed. Our numerical and simulation results show distributions as follows. Firstly, the CICN-PS protocol outperforms the CICN-TS protocol. Secondly, the proposed protocols strictly depend on the location, amount and power of the co-channel interferences. Thirdly, when signal-to-noise ratio increases, the proposed CICN-PS protocol achieves the perfect throughputs where the cooperative relay applies the ideal receiver and co-channel interferences do not affect the destination. Finally, the numerical analyses agree well with the simulation results.

Appendix: Proof of Lemma 1

The joint CDF of RV Y and the condition ${g_1} \ge {u_1} + \phi {\gamma _t}{X_3}$ is expressed as

$$\begin{aligned} \begin{array}{ll} {F_{Y,{g_1} \ge {u_1} + \phi {\gamma _t}{X_3}}}\left( y \right) &= \Pr \left[ {Y< y,\,\,{g_1} \ge {u_1} + \phi {\gamma _t}{X_3}} \right] \\ &= \Pr \left[ {{g_1} + \phi {X_3} < y,\,\,{g_1} \ge {u_1} + \phi {\gamma _t}{X_3}} \right] \end{array} \end{aligned}$$

(40)

We see easily that ${F_{Y,{g_1} \ge {u_1} + \phi {\gamma _t}{X_3}}}\left( y \right) = 0$ when $y \le {u_1}$.

When $y > {u_1}, {F_{Y,{g_1} \ge {u_1} + \phi {\gamma _t}{X_3}}}\left( y \right)$ in (40) is obtained as

$$\begin{aligned} {F_{Y,{g_1} \ge {u_1} + \phi {\gamma _t}{X_3}}}\left( y \right) = \int \limits _0^{{{\left( {y - {u_1}} \right) }/{\left( {\phi \left( {1 + {\gamma _t}} \right) } \right) }}} {{f_{{X_3}}}\left( z \right) } \times \left\{ {{F_{{g_1}}}\left( {y - \phi z} \right) - {F_{{g_1}}}\left( {{u_1} + \phi {\gamma _t}z} \right) } \right\} dz \end{aligned}$$

(41)

Substituting (23) into (41), ${F_{Y,{g_1} \ge {u_1} + \phi {\gamma _t}{X_3}}}\left( y \right)$ is solved as

$$\begin{aligned} \begin{array}{ll} {F_{Y,{g_1} \ge {u_1} + \phi {\gamma _t}{X_3}}}\left( y \right) &= \frac{{\lambda _3^L}}{{\left( {L - 1} \right) !}} \times \int \limits _0^{{{\left( {y - {u_1}} \right) }/{\left( {\phi \left( {1 + {\gamma _t}} \right) } \right) }}} {{z^{L - 1}}} \\ &\quad \times {e^{ - {\lambda _3}z}} \times \left\{ {{e^{ - {\lambda _1}\left( {{u_1} + \phi {\gamma _t}z} \right) }} - {e^{ - {\lambda _1}\left( {y - \phi z} \right) }}} \right\} dz\\ &= \frac{{\lambda _3^L{e^{ - {\lambda _1}{u_1}}}}}{{\left( {L - 1} \right) !}} \times \int \limits _0^{{{\left( {y - {u_1}} \right) } /{\left( {\phi \left( {1 + {\gamma _t}} \right) } \right) }}} {{z^{L - 1}} \times {e^{ - z\left( {{\lambda _3} + {\lambda _1}\phi {\gamma _t}} \right) }}dz} \\ &\quad - \frac{{\lambda _3^L{e^{ - {\lambda _1}y}}}}{{\left( {L - 1} \right) !}} \times \int \limits _0^{{{\left( {y - {u_1}} \right) }/{\left( {\phi \left( {1 + {\gamma _t}} \right) } \right) }}} {{z^{L - 1}} \times {e^{ - z\left( {{\lambda _3} - {\lambda _1}\phi } \right) }}dz} \\ &= {e^{ - {\lambda _1}{u_1}}} \times {\left( {\frac{{{\lambda _3}}}{{{\lambda _3} + {\lambda _1}\phi {\gamma _t}}}} \right) ^L} - \frac{{{e^{ - {\lambda _1}{u_1}}}}}{{\left( {L - 1} \right) !}} \times {\left( {\frac{{{\lambda _3}}}{{{\lambda _3} + {\lambda _1}\phi {\gamma _t}}}} \right) ^L} \\ &\quad \times \varGamma \left\{ {L,\frac{{\left( {y - {u_1}} \right) \left( {{\lambda _3} + {\lambda _1}\phi {\gamma _t}} \right) }}{{\phi \left( {1 + {\gamma _t}} \right) }}} \right\} \\ &\quad - {e^{ - {\lambda _1}y}} \times {\left( {\frac{{{\lambda _3}}}{{{\lambda _3} - \phi {\lambda _1}}}} \right) ^L} - \frac{{{e^{ - {\lambda _1}y}}}}{{\left( {L - 1} \right) !}} \times {\left( {\frac{{{\lambda _3}}}{{{\lambda _3} - \phi {\lambda _1}}}} \right) ^L} \\ &\quad \times \varGamma \left\{ {L,\frac{{\left( {y - {u_1}} \right) \left( {{\lambda _3} - \phi {\lambda _1}} \right) }}{{\phi \left( {1 + {\gamma _t}} \right) }}} \right\} \end{array} \end{aligned}$$

(42)

where $\varGamma \left\{ {a,z} \right\}$ is the incomplete gamma function, $\varGamma \left\{ {a,z} \right\} = \int \limits _z^\infty {{t^{a - 1}} \times {e^{ - t}}dt}$, [22, Eq. (8.350.2)].

Hence, Lemma 1 is completely proven.