Alternate energy harvesting and information relaying in cooperative AF networks

Abstract

This paper studies an energy harvesting (EH) based cooperative relaying system, where two half-duplex relays operate with EH and alternately amplify and forward source data to the destination. When one relay joins in the cooperative data transmission, the other relay will harvest wireless energy by overhearing the transmissions from both the source and the transmitting relay. Both the time-switching and power-splitting architectures are considered for the EH and data reception at relays. Since the EH can be implicitly performed by each relay through listening the ongoing transmissions, more energy can be harvested for the cooperative data transmission. The outage probability and throughput of the proposed scheme are derived. Simulation results are provided to verify the correctness of our theoretical analysis and show that our scheme can significantly outperform the single-relay system in terms of throughput.

Appendix: Derivation of \(p_{out}^{t1}\)

Substituting (6) into (26), $p_{out}^{t1}$ can be expressed as

$$\begin{aligned} p_{out}^{t1}&=\Pr \left\{ \frac{p_{s}p_{t1}|h_{s1}|^2 |h_{1d}|^2/N_0}{p_{t1}|h_{1d}|^2d_{s1}^m+d_{1d}^m(p_{s}|h_{s1}|^2+d_{s1}^mN_0)}<\gamma _0\right\} . \end{aligned}$$

(31)

The above expression can be further expressed as the sum of two probabilities, i.e., $p_{out}^{t1}=\hat{p}_{out}^{t1}+\tilde{p}_{out}^{t1}$. The probability $\hat{p}_{out}^{t1}$ is given as

$$\begin{aligned} \hat{p}_{out}^{t1}&=\Pr \left\{ |h_{s1}|^2\le \frac{d_{s1}^mN_0\gamma _0}{p_s}\right\} . \end{aligned}$$

(32)

The probability $\tilde{p}_{out}^{t1}$ is given as

$$\begin{aligned} \tilde{p}_{out}^{t1}&=\Pr \left\{ |h_{s1}|^2>\frac{d_{s1}^mN_0\gamma _0}{p_s}, |h_{1d}|^2<\right. \nonumber \\&\quad \quad \quad \left. d_{1d}^mN_0\gamma _0\left( \frac{p_s|h_{s1}|^2+d_{s1}^m N_0}{p_sp_{t1}|h_{s1}|^2-p_{t1}d_{s1}^m N_0 \gamma _0}\right) \right\} . \end{aligned}$$

(33)

Following (32), $\hat{p}_{out}$ can be derived as

$$\begin{aligned} \hat{p}_{out}^{t1}&=1-\exp \left( -\frac{d_{s1}^mN_0\gamma _0}{p_s}\right) , \end{aligned}$$

(34)

where we consider in the derivation that the small-scale power fading $|h_{s1}|^2$ is exponentially distributed with unit mean.

Following (33), $\tilde{p}_{out}^{t1}$ can be derived as

$$\begin{aligned} \tilde{p}_{out}^{t1}&=\int _{\frac{N_0\gamma _0d_{s1}^m}{p_s}}^\infty \exp (-z) \Pr \bigg \{|h_{1d}|^2\nonumber \\&< N_0\gamma _0d_{1d}^m\left( \frac{p_sz+d_{s1}^m N_0}{p_sp_{t1}z-p_{t1}d_{s1}^m N_0 \gamma _0}\right) \bigg \}\, \mathrm{d}z \nonumber \\&=\exp \left( -\frac{d_{s1}^mN_0\gamma _0}{p_s}\right) \left[ 1-2N_0\exp \left( -\frac{d_{1d}^mN_0\gamma _0}{p_{t1}}\right) \right. \nonumber \\&\times \left. \sqrt{\frac{d_{s1}^md_{1d}^m\gamma _0(1+\gamma _0)}{p_sp_{t1}}} K_1\left( 2N_0\sqrt{\frac{d_{s1}^md_{1d}^m\gamma _0(1+\gamma _0)}{p_sp_{t1}}}\right) \right] \end{aligned}$$

(35)

where $z=|h_{s1}|^2$ and $K_1(\cdot )$ is the first-order modified Bessel function of the second kind, and the last equality is obtained according to $\int _0^\infty e^{-\frac{\beta }{4x}-\gamma x} \, dx =\sqrt{\frac{\beta }{\gamma }}K_1(\sqrt{\beta \gamma })$ [30, (3.324)].

Substituting (34) and (35) into $p_{out}^{t1}=\hat{p}_{out}^{t1}+\tilde{p}_{out}^{t1}$, we can derive the result of $p_{out}^{t1}$ as given in (27).