Spectrum sharing protocol in two-way cognitive radio networks with energy accumulation in relay node

Abstract

In this paper, we consider a two-way cognitive radio network where an energy-constrained secondary transmitter (ST) first performs energy accumulation and then assists bidirectional communication for a pair of primary users (PUs) based on the principle of two-way relaying (TWR) strategy. To be specific, the ST can harvest energy from the received radio frequency (RF) signals broadcasting by both the primary users. After the residual energy at the ST is sufficient for data transmission, the ST will forward PUs’ signals by using decode-and-forward (DF) manner. In return, the ST is allowed to access the primary spectrum for its own data transmission. Moreover, according to whether the ST can correctly decode PUs’ signals or not, the ST will opportunistically switch between the silent mode and data transmission mode. A discrete Markov chain is used to simulate the charging and discharging processes of the ST’s battery. Based on this, closed-form expressions of outage probabilities for both the primary and secondary systems are derived. In addition, the optimal sub-slot switching coefficient and power allocation coefficient are determined by maximizing the spectrum efficiency of the secondary system while the spectrum efficiency of the primary system exceeding a given threshold. Numerical results not only validate the accuracy of the analytical results but also show that the proposed spectrum sharing protocol can provide a better performance in terms of energy efficiency over other similar TWR schemes.

Appendix

1.1 Proof of Proposition 1

We define g₁ = ηP₁|h_{P1, ST}|² and g₂ = ηP₂|h_{P2, ST}|², where g₁ and g₂ follow the exponential distribution with mean ${\overline{\lambda}}_1=\eta {P}_1{\lambda}_{P1, ST}$ and ${\overline{\lambda}}_2=\eta {P}_2{\lambda}_{P2, ST}$, respectively. Thus, the amount of harvested energy E₀ is the sum of two exponential random variables and the joint probability distribution of g₁ and g₂ is given by

$$ f\left({g}_1,{g}_2\right)={f}_{G_1}\left({g}_1\right){f}_{G_2}\left({g}_2\right)=\frac{1}{{\overline{\lambda}}_1{\overline{\lambda}}_2}\exp \left(-\frac{g_1}{{\overline{\lambda}}_1}-\frac{g_2}{{\overline{\lambda}}_2}\right), $$

(42)

where ${f}_{G_1}\left({g}_1\right)$ and ${f}_{G_2}\left({g}_2\right)$ denote the probability density functions (p.d.f.) of g₁ and g₂, respectively. The first equality of (42) holds since the g₁ and g₂ are mutual independence. Based on (1), we can obtain that g₂ = E₀ − g₁ and its value range is [0, E₀]. Then, the p.d.f. of the harvested energy E₀ can be calculated as

$$ {\displaystyle \begin{array}{c}{f}_{E_0}\left({e}_0\right)={\int}_0^{e_0}f\left({g}_1,{e}_0-{g}_1\right)d{g}_1\\ {}={\int}_0^e\frac{1}{{\overline{\lambda}}_1{\overline{\lambda}}_2}\exp \left(-\frac{g_1}{{\overline{\lambda}}_1}-\frac{e_0-{g}_1}{{\overline{\lambda}}_2}\right)d{g}_1\\ {}=\frac{1}{{\overline{\lambda}}_1-{\overline{\lambda}}_2}\left(\exp \left(-\frac{e_0}{{\overline{\lambda}}_1}\right)-\exp \left(-\frac{e_0}{{\overline{\lambda}}_2}\right)\right).\end{array}} $$

(43)

As a result, the c.d.f. of E₀ is derived by integrating (43), which is shown as follows

$$ {\displaystyle \begin{array}{c}{F}_{E_0}(t)={\int}_0^t{f}_{E_0}\left({e}_0\right)d{e}_0\\ {}={\int}_0^t\frac{1}{{\overline{\lambda}}_1-{\overline{\lambda}}_2}\left(\exp \left(-\frac{e_0}{{\overline{\lambda}}_1}\right)-\exp \left(-\frac{e_0}{{\overline{\lambda}}_2}\right)\right)d{e}_0\\ {}=\frac{1}{{\overline{\lambda}}_1-{\overline{\lambda}}_2}\left[{\overline{\lambda}}_1\left(1-\exp \left(-\frac{t}{{\overline{\lambda}}_1}\right)\right)-{\overline{\lambda}}_2\left(1-\exp \left(-\frac{t}{{\overline{\lambda}}_2}\right)\right)\right].\end{array}} $$

(44)