Throughput enhancement for millimeter wave communications using reconfigurable intelligent surfaces

Abstract

In this paper, we propose to extend the coverage of millimeter-wave (mmwave) communications using Reconfigurable Intelligent Surfaces (RIS). The first hop between the source and the relay node uses millimeter-wave communications. The received signal at relay node R is affected by P interferers. The relay node decodes the transmitted packet by the source. Then, the relay node transmits the decoded packet to the destination. A RIS is placed between relay R and destination D. RIS is implemented as a reflector to reflect signals from R to D. All reflected signals have the same phase so that the throughput is significantly enhanced. RIS is also implemented as a transmitter and illuminated with the antenna of relay node R. We show that RIS allows up 19, 25, 31, 37 dB gain with respect to conventional millimeter-wave communication without RIS for a number of reflectors $N=16,32,64,128$. We also propose RIS for mmwave communications using Non Orthogonal Multiple Access (NOMA). A set of RIS reflectors is dedicated to each NOMA user. The proposed NOMA system using RIS offers 10, 13, 16, 20, 24, 27 and 30 dB gain with respect to conventional NOMA using millimeter-wave communications without RIS for a number of reflector per user $N=N_1=N_2=8,16,32,64,128,256,512$.

Appendix A

Let $X=E_S|f|^2$ and $I=\sum _{q=1}^PI_q$. The SNR at R is expressed as $\Gamma _{SR,mmwave}=\frac{X}{I}$. X and I are two independent Gamma r.v. with joint PDF [34]

$$\begin{aligned} f_{X,I}(x,y)=\frac{x^{M-1}y^{PM-1}e^{-\frac{x}{\beta }}e^{-\frac{y}{\alpha }}}{\Gamma (M)\Gamma (MP)\beta ^{M}\alpha ^{MP}} \end{aligned}$$

(63)

Let $\Gamma _{SR,mmwave}=U=\frac{X}{I}$ and $V=X+I$, the determinant of Jacobian matrix is

$$\begin{aligned} |J|=\begin{vmatrix} \frac{\partial U}{\partial X}&\frac{\partial U}{\partial I} \\ \frac{\partial V}{\partial X}&\frac{\partial V}{\partial I} \\ \end{vmatrix}=\begin{vmatrix} \frac{1}{I}&\frac{-X}{I^2} \\ 1&1 \\ \end{vmatrix}=\frac{X+I}{I^2}=\frac{(1+U)^2}{V} \end{aligned}$$

(64)

We can write $I=\frac{V}{1+U}$ and $X=\frac{UV}{1+U}$. We deduce the joint PDF of (U, V)

$$\begin{aligned} f_{U,V}(u,v)= & {} \frac{f_{X,I}(x,y)}{|J|}=\frac{v}{(1+u)^2}\left( \frac{v}{1+u}\right) ^{PM-1}\nonumber \\&\left( \frac{vu}{1+u}\right) ^{M-1} \nonumber \\&\times \frac{e^{-\frac{vu}{(1+u)\beta }}e^{-\frac{v}{(1+u)\alpha }}}{\Gamma (M)\Gamma (MP)\beta ^{M}\alpha ^{MP}} \end{aligned}$$

(65)

The PDF of $U=\Gamma _{SR,mmwave}$ is computed as

$$\begin{aligned} f_U(u)=\int _0^{+\infty }f_{U,V}(u,v)dv. \end{aligned}$$

(66)

We have [33]

$$\begin{aligned} \int _0^{+\infty }e^{-Av}v^Bdv=\frac{\Gamma (B+1)}{A^{B+1}} \end{aligned}$$

(67)

Equations (65–67) give

$$\begin{aligned} f_{\Gamma _{SR,mmwave}}(u)= & {} \frac{\Gamma (M+PM)\alpha ^Mu^{M-1}}{\beta ^M\Gamma (M)\Gamma (PM)}\nonumber \\&\quad \left( 1+\frac{u\alpha }{\beta }\right) ^{-PM-M} \end{aligned}$$

(68)