Reconfigurable Intelligent Surface (RIS)-Assisted Wireless Systems: Potentials for 6G and a Case Study

Abstract

As one of the key technologies for deployment of future wireless networks, the state-of-the-art reconfigurable intelligent surfaces (RISs) have rapidly gained a massive interest among researchers. In a specific case study, we study the outage performance of RIS-aided wireless systems in the presence of non-orthogonal multiple access (NOMA) scheme. In particular, different power factors are allocated to users which belong to a dedicated group. We the derive the exact outage probability of two users in a group. Specifically, it is assumed that the RIS is placed between the source and the users and the far user has better performance under the assistance of RIS. We also provide a comparative analysis to investigate the effect of the main parameters on the outage performance of our proposed system, such as the number of tunable elements of the RIS, power allocation factors, target rates, and the average signal-to-noise ratio at the base station. By using Monte Carlo simulation, we verify our analytical results via simulations. Our main results reported in this paper show the positive effect once we deploy RISs for guaranteeing fairness among NOMA users in wireless systems.

7 Appendix A

The outage probability $P_{NU}$ can be further computed by

$$\begin{aligned} \begin{aligned} {P_{NU}} =&1 - \Pr \left( {{A^2} > {\varphi _1}\left( {\rho {{\left| {{h_I}} \right| }^2} + 1} \right) } \right) \\ =&1 - \int \limits _0^\infty {{f_{{{\left| {{h_I}} \right| }^2}}}\left( x \right) } \left[ {1 - {F_{{A^2}}}\left( {{\varphi _1}\left( {\rho x + 1} \right) } \right) } \right] dx\\ =&1 - \frac{1}{{{\Omega _{{h_I}}}}}\int \limits _0^\infty {{e^{ - \frac{x}{{{\Omega _{{h_I}}}}}}}} \left[ {1 - \sum \limits _{l = 0}^\infty {\frac{{{{\left( { - 1} \right) }^l}\varphi _1^{\frac{{a + l + 1}}{2}}}}{{l!\varGamma \left( {a + 1} \right) \left( {a + l + 1} \right) {b^{a + l + 1}}}}} {{\left( {\rho x + 1} \right) }^{\frac{{a + l + 1}}{2}}}} \right] dx\\ =&\sum \limits _{l = 0}^\infty {\frac{{{{\left( { - 1} \right) }^l}\varphi _1^{\frac{{a + l + 1}}{2}}}}{{l!{\Omega _{{h_I}}}\varGamma \left( {a + 1} \right) \left( {a + l + 1} \right) {b^{a + l + 1}}}}} \int \limits _0^\infty {{e^{ - \frac{x}{{{\Omega _{{h_I}}}}}}}{{\left( {\rho x + 1} \right) }^{\frac{{a + l + 1}}{2}}}} dx \end{aligned} \end{aligned}$$

(12)

Let $t = \rho x + 1 \rightarrow \frac{{t - 1}}{\rho } = x \rightarrow \frac{1}{\rho }dt = dx$, ${P_{NU}}$ can be reformulated by

$$\begin{aligned} {P_{NU}} = \sum \limits _{l = 0}^\infty {\frac{{{{\left( { - 1} \right) }^l}\varphi _1^{\frac{{a + l + 1}}{2}}{e^{\frac{1}{{\rho {\Omega _{{h_I}}}}}}}}}{{l!{\Omega _{{h_I}}}\varGamma \left( {a + 1} \right) \left( {a + l + 1} \right) \rho {b^{a + l + 1}}}}} \int \limits _1^\infty {{e^{ - \frac{t}{{\rho {\Omega _{{h_I}}}}}}}{t^{\frac{{a + l + 1}}{2}}}} dt. \end{aligned}$$

(13)

Using [35, Eq. (3.381.3)], (13) can be reformulated by (14)

$$\begin{aligned} {P_{NU}} = \sum \limits _{l = 0}^\infty {\frac{{{{\left( { - 1} \right) }^l}\varphi _1^{\frac{{a + l + 1}}{2}}{{\left( {\rho {\Omega _{{h_I}}}} \right) }^{\frac{{a + l + 3}}{2}}}{e^{\frac{1}{{{\Omega _{{h_I}}}}}}}}}{{l!{\Omega _{{h_I}}}\varGamma \left( {a + 1} \right) \left( {a + l + 1} \right) \rho {b^{a + l + 1}}}}} \varGamma \left( {\frac{{a + l + 3}}{2},\frac{1}{{\rho {\Omega _{{h_I}}}}}} \right) . \end{aligned}$$

(14)

This completes the proof.