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Wireless Personal Communications

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Open Access 16.05.2024

NOMA for Hybrid RF/VLC Systems Using Intelligent Reflecting Surfaces

verfasst von: Nadhir Ben Halima

Erschienen in: Wireless Personal Communications | Ausgabe 4/2024

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Abstract

In this article, Intelligent Reflecting Surfaces (IRS) are used for Non Orthogonal Multiple Access (NOMA) in hybrid Radio Frequency (RF) Visible Light Communications (VLC). The source broadcasts the symbols of K users. The broadcasted signal by the source is reflected by IRS on RF link to reach the relay node R with the same phase. Relay node detects the symbols of K users using Interference Cancelation (IC). Then, relay nodes broadcasts the symbols of K users on VLC link. We show that NOMA using IRS for hybrid RF/VLC offers 12–18 dB gain versus conventional hybrid RF/VLC without reflectors for $N= 32$,168 reflectors. The main advantage of the paper is to enhance the throughput of RF/VLC systems using IRS. The main limitation of the paper is that the results are not valid when energy harvesting is performed.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

1 Introduction

Visible Light Communications (VLC) systems offer large data rates since the available spectrum is huge going from 430 THz to 790 THz [1‐5]. The spectrum of VLC communications is free of licence. Laser Emitting Diode (LED) is used for lighting and to send data on VLC link to multiple users [1‐5]. Recently, Intelligent Reflecting Surfaces (IRS) were suggested to improve data rates of wireless networks. The reflected signals on IRS reach the receiver with the same phase [6‐12]. A hardware implementation of IRS has been suggested in [13]. In NOMA using IRS, some reflectors are associated to the different users [14]. IRS for millimeter wave and optical communications were proposed in [15‐24]. IRS for RF/VLC using Non Orthogonal Multiple Access NOMA was not studied before. Pulse design for radar communications using classical orthogonal polynomials was suggested in [25]. Polyphase codes were modified in [26] to mitigate side lobes in pulse compression radar. Side lobe suppression for radar systems was suggested in [27].

In this article, we use IRS for NOMA systems using RF/VLC systems. IRS for RF/VLC offers 12–18 dB gain versus conventional hybrid RF/VLC without reflectors for $N=8,16,32$.

Next section evaluates the outage probability at relay node on RF link using IRS as well as the outage probability at K users on VLC link. Section 3 derives the Packet Error Probability (PEP) as well the total throughput. Section 4 gives some results. Conclusions are given in the last section.

2 NOMA in Hybrid RF/VLC Using IRS

The network model is shown in Fig. 1 where S broadcasts a combination of K symbols to relay node R. The NOMA broadcasted symbol is written as

$$\begin{aligned} s_k=\sum _{q=1}^Ks_k^{(q)}\sqrt{P_q} \end{aligned}$$

(1)

where $s_k^{(q)}$ is the k-th transmitted NOMA symbol to q-th strong user, $0<P_q<1$ such that

$$\begin{aligned} \sum _{q=1}^KP_q=1 \end{aligned}$$

(2)

and $0<P_1<P_2<\cdots <P_K$.

IRS is between S and the relay node R. All reflections have the same phase at R. The relay R decodes the transmitted symbols and broadcasts them to NOMA users using VLC communications.

2.1 RF Link

Let $h_p$ be the channel between source S and IRS with $E(|h_p|^2)=\frac{1}{d_{S,IRS}^{pla}}$, $d_{U,V}$ is the distance U-V, pla is the path loss attenuation. Let $g_p$ be the channel between IRS and relay R with $E(|g_p|^2)=\frac{1}{d_{IRS,R}^{pla}}$.

Let $h_p=a_pe^{-jb_p}$ where $a_p=|h_p|$. Similarly, we can write $g_p=c_pe^{-jd_p}$ where $c_p=|g_p|$.

IRS phase shifts are given by

$$\begin{aligned} v_p=b_p+d_p. \end{aligned}$$

(3)

The signal at R is given by

$$\begin{aligned} r_k=s_k\sqrt{E_S}\sum _{p=1}^Nh_pg_pe^{jv_p}+n_k \end{aligned}$$

(4)

where $n_k$ is Gaussian with variance $N_0$ and $E_X$ is the symbol energy of X.

Equations (1-4) give

$$\begin{aligned} r_k=s_k \sqrt{E_S} A +n_k=\left[ \sum _{q=1}^Ks_k^{(q)}\sqrt{P_q}\right] \sqrt{E_S} A +n_k, \end{aligned}$$

(5)

where

$$\begin{aligned} A=\sum _{q=1}^Na_qc_q. \end{aligned}$$

(6)

The mean and variance of A are $m_A=\frac{N\pi }{4d_{S,IRS}^{0.5pla}d_{IRS,R}^{0.5pla}}$ and variance $\sigma _A^2=N(1-\frac{\pi ^2}{16})\frac{1}{d_{S,IRS}^{pla}d_{IRS,R}^{pla}}$.

We define X as

$$\begin{aligned} X=E_SA^2. \end{aligned}$$

(7)

We have

$$\begin{aligned} F_{X}(x)= & {} P(E_SA^2\le x)=P\left( -\sqrt{\frac{x}{E_S}}\le A\le \sqrt{\frac{x}{E_S}}\right) \nonumber \\\simeq & {} 0.5erfc\left( \frac{-\sqrt{\frac{x}{E_S}}-m_A}{\sqrt{2}\sigma _A}\right) -0.5erfc\left( \frac{\sqrt{\frac{x}{E_S}}-m_A}{\sqrt{2}\sigma _A}\right) \end{aligned}$$

(8)

Relay R detects $s_k^{(K)}$ with SINR

$$\begin{aligned} \Gamma ^{R \rightarrow K}=\frac{P_KX}{X\sum _{q=1}^{K-1}P_q+N_0}. \end{aligned}$$

(9)

The CDF of SINR $\Gamma ^{R \rightarrow K}$ is

$$\begin{aligned} F_{\Gamma ^{R \rightarrow K}}(x)=P(\Gamma ^{R \rightarrow K}\le x)=F_X\left( \frac{N0x}{P_K-x\sum _{q=1}^{K-1}P_q}\right) . \end{aligned}$$

(10)

Then, relay node detects $s_k^{(K-1)}$ with SINR

$$\begin{aligned} \Gamma ^{R \rightarrow K-1}=\frac{P_{K-1}X}{X\sum _{q=1}^{K-2}P_q+N_0}. \end{aligned}$$

(11)

Relay detects $s_k^{(p)}$ with SINR

$$\begin{aligned} \Gamma ^{R \rightarrow p}=\frac{P_{p}X}{X\sum _{q=1}^{p-1}P_q+N_0}. \end{aligned}$$

(12)

The probability of an outage at R is computed as

$$\begin{aligned} P_{outage,R,RF}(x)=F_X\left( \underset{1\le p\le K}{max}\left( \frac{N_0x}{P_p-x\sum _{q=1}^{p-1}P_q}\right) \right) . \end{aligned}$$

(13)

2.2 VLC Link

The k-th NOMA symbol broadcasted by R is given by

$$\begin{aligned} S_k=\sum _{q=1}^K\widehat{s}_k^{(q)}\sqrt{C_q} \end{aligned}$$

(14)

where $\widehat{s}_k^{(q)}$ is the k-th detected symbol at the relay associated to user $U_q$, $0<C_q<1$ is the power coefficient to q-th strong user such that

$$\begin{aligned} \sum _{q=1}^KC_q=1 \end{aligned}$$

(15)

and $0<C_1<C_2<\cdots <C_K$.

The received signal at user $U_i$ during k-th symbol period is equal to

$$\begin{aligned} y_k^{(i)}=\sqrt{E_R}S_k h_i+w_k=\sqrt{E_R}\left[ \sum _{q=1}^K\widehat{s}_k^{(q)}\sqrt{C_q}\right] h_i+w_k \end{aligned}$$

(16)

where $w_k$ is Gaussian with variance $N_0$ and $h_i$ is the channel between R and user $U_i$. $U_i$ detects $\widehat{s}_k^{(K)}$ with SINR

$$\begin{aligned} \Gamma ^{U_i \rightarrow K}=\frac{C_KY_i}{Y_i\sum _{q=1}^{K-1}C_q+N_0} \end{aligned}$$

(17)

where $Y_i=E_Rh_i^2$.

Then, $U_i$ performs IC to remove $\widehat{s}_k^{(K)}$ and detects $\widehat{s}_k^{(K-1)}$ with SINR

$$\begin{aligned} \Gamma ^{U_i \rightarrow K-1}=\frac{C_{K-1}Y_i}{Y_i\sum _{q=1}^{K-2}C_q+N_0} \end{aligned}$$

(18)

$U_i$ will continue the detections of symbols until it detects its own symbol. $U_i$ will detect $\widehat{s}_k^{(p)}$ with SINR

$$\begin{aligned} \Gamma ^{U_i \rightarrow p}=\frac{C_{p}Y_i}{Y_i\sum _{q=1}^{p-1}C_q+N_0} \end{aligned}$$

(19)

The outage probability at user $U_i$ on VLC link is computed as

$$\begin{aligned} P_{outage,U_i,VLC}(x)=F_{Y_i}\left( \underset{i\le p\le K}{max}\left( \frac{N_0x}{C_p-x\sum _{q=1}^{p-1}C_q}\right) \right) \end{aligned}$$

(20)

2.3 CDF of $Y_i$

M is equal to [1‐5]

$$\begin{aligned} M=\frac{-1}{log_2(cos(\phi _{1/2}))} \end{aligned}$$

(21)

where $\phi _{1/2}$ is the half angle of LED.

The channel between R and $U_i$ can be written as [1‐5]

$$\begin{aligned} h_i=\frac{J(M+1)R_p cos(\psi _i)g(\psi _i)U(\psi _i)cos(\phi _i)^M}{2\pi d^2} \end{aligned}$$

(22)

where $U(\psi _i)$ is the optical filter gain while $g(\psi _i)$ is the gain of the concentrator, D is the area of the detector, $R_p$ is the response of photo detector, $\phi _i$ is the angle of irradiance and $\psi _i$ is the angle of incidence.

The distance $d_i$ between $U_i$ and LED is expressed as

$$\begin{aligned} d_i=\sqrt{r_i^2+L^2} \end{aligned}$$

(23)

We also have [1‐5]

$$\begin{aligned} cos(\psi _i)=cos(\phi _i)=\frac{L}{d_i}=\frac{L}{\sqrt{r_i^2+L^2}} \end{aligned}$$

(24)

Using (23-25), we deduce

$$\begin{aligned} h_i=\frac{J(M+1)L^{M+1}}{(r^2+L^2)^{(M+3)/2}} \end{aligned}$$

(25)

where

$$\begin{aligned} J(M)=\frac{DR_pU(\psi _i)g(\psi _i)}{2\pi } \end{aligned}$$

(26)

The PDF of $r_i$ can be easily derived as

$$\begin{aligned} f_{r_i}(u)=\frac{2u}{Rc^2} \end{aligned}$$

(27)

The PDF of $h_i$ is deduced from (28)

$$\begin{aligned} f_{h_i}(x)=\frac{2(J(M+1)L^{M+1})^{\frac{2}{M+3}}x^{\frac{-2}{M+3}-1}}{Rc^2(M+3)} \end{aligned}$$

(28)

We have

$$\begin{aligned} Y_i=h_i^2E_{R} \end{aligned}$$

(29)

The PDF of $Y_i$ is deduced from that of $r_i$:

$$\begin{aligned} f_{Y_i}(y)=\frac{E_{R}^{\frac{1}{M+3}}(J(M+1)L^{M+1})^{\frac{2}{M+3}}}{(M+3)Rc^2} y^{-1-\frac{1}{M+3}} \end{aligned}$$

(30)

with $y_{min}\le y\le y_{max}$. $y_{max}$ is the maximum value of $Y_i$ obtained when $U_i$ is in the close to LED ie $r_i=0$ and $d_i=L$. Equations (25) and (29) give

$$\begin{aligned} y_{max}= & {} \frac{E_{R}(L^{M+1}J(M+1))^2}{L^{2(M+3)}} \end{aligned}$$

(31)

$$\begin{aligned} y_{min}= & {} \frac{E_{R}(L^{M+1}J(M+1))^2}{(Rc^2+L^2)^{M+3}} \end{aligned}$$

(32)

By a primitive of CDF, we obtain the CDF of $Y_i$

$$\begin{aligned} F_{Y_i}(y)=\frac{-1}{Rc^2}(J(M+1)L^{M+1})^{\frac{2}{M+3}} \left( \frac{y}{E_{R}}\right) ^{-\frac{1}{M+3}}+1+\frac{L^2}{Rc^2} \end{aligned}$$

(33)

with $y_{max}\le y$ $\le y_{max}$. We easily check that $F_{Y_i}(y_{min})=0$ and $F_{Y_i}(y_{max})=1$

3 PEP and Throughput of NOMA Using Hybrid RF/VLC and IRS

The probability of an outage event at $U_i$ is given by

$$\begin{aligned} P_{outage,U_i,RF-VLC}(x)=1-[1-P_{outage,R,RF}(x)][1-P_{outage,U_i,VLC}(x)] \end{aligned}$$

(34)

The PEP at $U_i$ is given by [28]

$$\begin{aligned} PEP_i(P_1,P_2,\ldots ,P_K,C_1,C_2,\ldots ,C_K)<P_{outage, U_i,RF-VLC}(WTH_0) \end{aligned}$$

(35)

where

$$\begin{aligned} WTH_0=\int _0^{+\infty }1-[1-SEP(z)]^{PL}dz, \end{aligned}$$

(36)

where PL is packet length.

For QAM modulation with size I, the Symbol Error Probability (SEP) is given by [29]

$$\begin{aligned} SEP(z)=2\left( 1-\frac{1}{\sqrt{I}}\right) erfc\left( \sqrt{\frac{3z}{I-1}}\right) \end{aligned}$$

(37)

For PSK modulation, we have [29]

$$\begin{aligned} SEP(y)=erfc\left( \sqrt{ysin^2\left( \frac{\pi }{I}\right) }\right) \end{aligned}$$

(38)

The throughput at $U_i$ is given by

$$\begin{aligned} Thr_i(P_1,P_2,\ldots ,P_K,C_1,C_2,\ldots ,C_K)=0.5log_2(I)[1-PEP_i(P_1,P_2,\ldots ,P_K,C_1,C_2,\ldots ,C_K)] \end{aligned}$$

(39)

The total throughput is equal to

$$\begin{aligned} TThr(P_1,P_2,\ldots ,P_K,C_1,C_2,\ldots ,C_K)=\sum _{i=1}^KThr_i(P_1,P_2,\ldots ,P_K,C_1,C_2,\ldots ,C_K). \end{aligned}$$

(40)

We suggest an Optimal Power Allocation (OPA) that consists to use power allocation coefficients that maximizes TThr

$$\begin{aligned} TThr^{max}= \underset{0<P_1<P_2<\cdots<P_K<1, 0<C_1<C_2<\cdots<C_K<1}{max[TThr(P_1,P_2,\ldots ,P_K,C_1,C_2,\ldots ,C_K)]}. \end{aligned}$$

(41)

under the following constraints $\sum _{q=1}^KP_q=1$ and $\sum _{q=1}^KC_q=1$.

The main methodology of the paper is to derive the outage probability of RF and VLC communications when IRS are used and to deduce the throughput using (13), (20), (33-35) and (40).

4 Results

The parameters of VLC are: $B=1$, $L=50$, $\phi _{1/2}=\frac{\pi }{3}$, $Rc=50$, $d_{S,IRS}=1.5$ and $d_{IRS,R}=1.2$. Packet length is $PL=500$ and the $PLE=3$. Figures 2, 3, 4, 5 depict the PEP and throughput at $U_2$ and $U_1$ for 4-PSK and $K=2$ and $P_1=1-P_2=0.3$ and $C_1=1-C_2=0.3$. We observe that the performance improves as N increases from $N=8$ to $N=16,32$. The obtained PEP is lower than that of NOMA using RF/VLC without reflectors [1‐5]. The use of IRS offers 12,15,18 dB gain versus NOMA using RF/VLC without reflectors [1‐5] for $N=8,16,32$. The plotted curves were obtained using (13), (20), (33-35) and (40). There are no approximation and the results were validated using computer simulations. The improvement suggested in the paper is to use IRS to enhance the throughput of RF/VLC. The main limitation is that the results are not valid for energy harvesting systems.

Figure 6 depicts the total throughput for $K=2$. Optimal Power Allocation (OPA) offers 1–3 dB versus hybrid RF/VLC using NOMA and fixed power allocation $P_1=1-P_2=0.3$ and $C_1=1-C_2=0.3$. IRS with $N=32$ reflectors and OPA offers 18 dB gain versus NOMA using RF/VLC without reflectors [1‐5].

Figure 7 depicts the total throughput for $K=3$. Power allocated to NOMA users are $P_1=0.2$, $P_2=0.3$, $P_3=0.5$ and $C_1=0.2$, $C_2=0.3$, $C_3=0.5$. We observe that IRS with $N=8,16,32$ reflectors offers 11,14,17 dB gain versus NOMA using RF/VLC without reflectors [1‐5]. Hybrid RF/VLC using 32 IRS reflectors and OPA offers 18 dB gain versus NOMA using RF/VLC without reflectors [1‐5].

5 Conclusion

In this article, we suggested the use of IRS for NOMA systems using hybrid RF/VLC communications. We derived the throughput when IRS are used to improve the quality of service in RF link as all IRS reflections have the same phase at relay node. Relay node detects and forwards the symbols of all users on VLC link. The suggested NOMA system using hybrid RF/VLC and 8,16,32 IRS reflectors offers 12,15,18 dB gain versus NOMA using RF/VLC without reflectors [1‐5].

Declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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Titel: NOMA for Hybrid RF/VLC Systems Using Intelligent Reflecting Surfaces
verfasst von: Nadhir Ben Halima
Publikationsdatum: 16.05.2024
Verlag: Springer US
Erschienen in: Wireless Personal Communications / Ausgabe 4/2024
Print ISSN: 0929-6212
Elektronische ISSN: 1572-834X
DOI: https://doi.org/10.1007/s11277-024-11130-2

Springer Professional

NOMA for Hybrid RF/VLC Systems Using Intelligent Reflecting Surfaces

Abstract

Publisher's Note

1 Introduction

2 NOMA in Hybrid RF/VLC Using IRS

2.1 RF Link

2.2 VLC Link

2.3 CDF of \(Y_i\)

3 PEP and Throughput of NOMA Using Hybrid RF/VLC and IRS

4 Results

5 Conclusion

Declarations

Conflict of interest

Publisher's Note

Springer Professional

Abstract

Publisher's Note

1 Introduction

2 NOMA in Hybrid RF/VLC Using IRS

2.1 RF Link

2.2 VLC Link

2.3 CDF of \(Y_i\)

3 PEP and Throughput of NOMA Using Hybrid RF/VLC and IRS

4 Results

5 Conclusion

Declarations

Conflict of interest

Publisher's Note

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