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Computers, Materials & Continua
DOI:10.32604/cmc.2022.030793		 images
Article

Throughput Enhancement for NOMA Systems Using Intelligent Reflecting Surfaces

Raed Alhamad1,* and Hatem Boujemaa2

1Information Technology Department, Saudi Electronic University, Riaydh, Saudi Arabia
2UCAR-SUPCOM-COSIM, Ariana, 2083, Tunisia
*Corresponding Author: Raed Alhamad. Email: ralhamad@seu.edu.sa
Received: 01 April 2022; Accepted: 29 May 2022

Abstract: In this article, we optimize the powers associated to Non Orthogonal Multiple Access (NOMA) users, sensing and harvesting duration for Cognitive Radio Networks (CRN). The secondary source harvests energy from node A signal. Then, it senses the channel to detect primary source. Then, the secondary source transmits a signal that is reflected by Intelligent Reflecting Surfaces (IRS) so that all reflections have a zero phase at any user. A set Ii of reflectors are associated to user Ui. The use of M = Mi = 512, 256, 128, 64, 32, 16, 8 reflectors per user offers 45, 42, 39, 36, 33, 30, 27 dB gain vs. the absence of IRS. We also suggest the use of IRS in energy harvesting. The use P = 8 reflectors for energy harvesting and M = Mi = 8 reflectors per user for data communications offers 7 and 38 dB gain vs. one IRS M = Mi = 8 and the absence of IRS. The use of P = 16 reflectors for energy harvesting and M = Mi = 8 reflectors per user for data communications offers 9 and 42 dB gain vs. one IRS M = Mi = 8 and the absence of IRS.

Keywords: CRN; NOMA; spectrum sensing; energy harvesting; throughput maximization

1  Introduction

IRS are used to maximize the throughput of wireless systems as all reflections have a zero phase at the destination [1–5]. The phase of the p-th reflector is computed using the phase of channel gains of the links between the source and IRS as well as that of the link between IRS and the destination [6–8]. IRS have been used in NOMA systems where a set Ii of reflectors are associated to user Ui [9]. The results of [9] are not valid for CRN as a single network was studied without energy harvesting and spectrum sensing. IRS have been deployed to maximize the throughput of millimeter wave and optical systems [10–12]. The asymptotic behavior of wireless systems using IRS was derived in [13–16]. Experimental results of IRS were provided in [17–19]. Continuous reserve skyline queries in Wireless Sensor Networks (WSN) was proposed in [20]. A self adaptive multivariate data compression with error bound was proposed in [21] for WSN. A particle swarm optimization was used in [22] to enhance the coverage in WSN. A hamilton loop based data collection algorithm can also be used in WSN [23]. Optimal coverage using multipath scheduling scheme was suggested in [24]. In [25], asynchronous clustering has been combined with data gathering scheme for WSN. In [26], the authors proposed a power efficient gathering technique in sensor information systems. A minimal connected dominant set was optimized in [27] to enhance WSN routing protocol. Coverage and network connectivity were optimized in [28] for mobile sensor networks.

In this article, we optimize NOMA powers, sensing and harvesting durations to maximize the throughput. After energy harvesting from node A signal, secondary source SS senses the channel to detect primary activity. When no activity is detected, the secondary source transmits a signal that is reflected by IRS so that all reflections have a zero phase at any NOMA user. A set Ii of reflectors are associated to user Ui. The use of M = Mi = 512, 256, 128, 64, 32, 16, 8 reflectors per user offers 45, 42, 39, 36, 33, 30, 27 dB gain vs. wireless systems without IRS [29]. We also improve the energy harvesting process using IRS between A and SS. In this case, energy harvesting uses reflected signals with zero phase at SS. A second IRS contains different sets of optimized reflectors to deliver reflections with a zero phase at any user Ui. The use P = 8 reflectors for energy harvesting and M = Mi = 8 reflectors per user for data communications offers 7 and 38 dB gain vs. one IRS M = Mi = 8 and the without IRS [29]. Using P = 16 reflectors for energy harvesting and M = Mi = 8 reflectors per user for data communications offers 9 and 42 dB gain vs. one IRS M = Mi = 8 and the absence of IRS [29].

Next section optimizes the NOMA powers, sensing and harvesting durations. Section 3 improves the energy harvesting process using IRS. Section 4 gives some results and Section 5 concludes the paper.

2  Throughput Analysis with a Single IRS

2.1 System Model

In Fig. 1, there are a Primary Destination and Source PD and PS, a Secondary Source SS and K secondary users, node A and IRS used as a reflector. In the first phase, energy harvesting is performed at SS over μ T s using the signal of A where T is frame length in s and 0 < μ < 1. Then, SS senses the channel over (1−μ)ζT s using samples of the received signal from PS. When PS is inactive, SS broadcasts a signal to K NOMA users over (1−μ)(1−ζ)T s. The aim of the paper is to optimize the powers of NOMA users as well as sensing and harvesting durations throughput the parameters μ and ζ to maximize the total throughput while using intelligent reflecting surfaces.

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Figure 1: Network model

2.2 Energy Harvesting Without IRS

The harvested energy is given by

E=βμTPA|f|2=βμL0EA|f|2(1)

where β is an efficiency coefficient, PA = EA/Ts is the power of A, Ts is the symbol duration, f is channel gain from A to SS, L0 = T/Ts. We can write E(|f|2) = 1/dASSple where dXY is the distance from X to Y and ple is the path loss exponent.

The symbol energy of SS is computed as:

ESS=EL0(1−μ)(1−ζ)=βμEA|f|2(1−μ)(1−ζ)(2)

In Fig. 1, the users are ranked as follows: U1 is the strong user, Ui is the i-th strong user and UK is the weak user. The transmitted NOMA symbol by SS is equal to

s=ESS∑i=1K⁡POisi,(3)

si is the symbol of user Ui and 0 < POi < 1 is the power allocated to Ui such that 0 < PO1 < PO2 < ⋯< POK < 1 and ∑i=1K⁡POi=1.

Let hp be the channel from SS to p-th IRS reflector. Let gp be the channel from p-th IRS reflector to Ui. Ii is a set of reflectors associated to Ui and contains Mi = |Ii| reflectors. We have: E(|hp|2) = 1/dSSIRSple. Furthermore, we have E(|gp|2) = 1/dIRSUiple.

We have hp = apexp(−jbp) where ap = |hp|. E(aq) = Γ(m + 0.5)/[Γ(m)MdSSIRSple] and E(aq2) = 1/dSSIRSple [30]. We have gp = cpexp(−jep) where cp = |gp| and ep is the phase of gp. We have E(cq) = Γ(m + 0.5)/[Γ(m)MdIRSUiple] and E(aq2) = 1/dIRSUiple [30].

The phase of p-th reflector is equal to [1]

φp=bp+ep.(4)

The received signal at Ui is given by

ri=s∑i∈Ii⁡hpgpexp(−jφp)+ni,(5)

where ni is a Gaussian r.v. of variance N0.

Eq. (3) gives

ri=s∑i∈Ii⁡apcp+ni=Yis+ni,(6)

where

Yi=ESSFi2(7)

Fi=∑i∈Ii⁡apcp,(8)

In (6), we notice that the phase shifts of reflectors given in (4) have been chosen so that all reflections have a zero phase at user Ui.

Using (2), we deduce

Yi=Fi2βμEA|f|2(1−μ)(1−ζ)(9)

Fi follows a Gaussian distribution with mean mFi = Mi Γ(m + 0.5)2/[Γ(m)2dSSIRSple/2dIRSUiple/2] and variance σFi2 = M/[dSSIRSpledIRSUiple][1−Γ(m + 0.5)4/Mi2/Γ(m)4]. Therefore, Fi2 has a non-central-chisquare distribution with degree of freedom one. For Rayleigh channels, |f|2 has also a central-chisquare distribution with degrees of freedom 2 m. Therefore, Yi is the product of a non-central and a central chisquare random variables and we have [31]

PYi(x)=P(Yi<x)=e−0.5mX2σX2Γ(m)∑q=0+∞⁡(mX2σX2)q2qΓ(q+0.5)G1,32,1(N0(1−)(1−ζ)xmdASSple2βμEA|1q+0.5,m,0),(10)

where Gn,mp,l(x) is the Meijer G-function.

We deduce

ri=Yi∑j=1K⁡POjsj,++ni(11)

2.3 Signal to Interference Plus Noise Ratio (SINR) and Throughput Analysis

Ui performs Successive Interference Cancelation (SIC) and detects first sK since POK > POi. The corresponding SINR is

Γi→K=YiPOKN0+Yi∑p=1K−1⁡POp(12)

The contribution of the detected symbol sK is removed and Ui estimates sK−1 with the following SINR

Γi→K−1=YiPOK−1N0+Yi∑p=1K−2⁡POp(13)

The process is continued by detecting sl with SINR

Γi→l=YiPOlN0+Yi∑p=1l−1⁡POp(14)

The probability of an outage event at Ui is computed as

Pout,i(x)=1−P(Γi→i>x,…,Γi→K>x)

=PYi(maxi≤l≤KN0xPOl−x∑p=1l−1⁡POp)(15)

where PYi(y) is provided in (10). In Eq. (15) Γi→l>x corresponds to Yi>N0xPOl−x∑p=1l−1⁡POp. Therefore, Yi should be larger than the maximum of these values for l = i,…, K which is maxi≤l≤KN0xPOl−x∑p=1l−1⁡POp

The Packet Error Probability (PEP) at Ui is equal to [32]

PEPi(PO1,PO2,…,POK,μ,ζ)<Poutage(T0)(16)

where T0 is defined as [12]

T0=∫0+∞⁡1−[1−2(1−1Q)erfc(3ulog2(Q)2Q−2)]PLdu,(17)

where PL is packet length.

The total throughput is equal to

Thr(PO1,…,POK,μ,ζ)=(1−μ)(1−ζ)log2(Q)Pidle(1−Pf)×∑i=1K⁡[1−PEPi(PO1,…,POK,μ,ζ)](18)

where Pf is the probability of a false alarm

Pf=Γ(⌊(1−μ)ζL0⌋,T1/2)Γ(⌊(1−μ)ζL0⌋),(19)

where T1 is the energy detector threshold

The powers of NOMA users, sensing and harvesting durations μ and ζ are optimized as follows:

(PO1opt,…,POKopt,μopt,ζopt)=argmaxThr(PO1,…,POK,μ,ζ)(20)

3  IRS to Enhance the Energy Harvesting Process

3.1 System Model

Fig. 2 shows that data transmission can use two IRS. IRS1 contains P reflectors between A to SS to enhance the energy harvesting process. IRS2 is between SS and users Ui with Mi reflectors to improve the throughput.

images

Figure 2: IRS used in energy harvesting

3.2 Energy Harvesting Using IRS

When energy harvesting uses IRS, we have

E =βμL0EAC2,(21)

where

Z=∑p=1P⁡δpηp(22)

where δp = |up|, up is the channel from A to p-th IRS1 reflector and ηp = |vp|, vp is the channel from p-th reflector of IRS1 to SS.

The mean and variance of C are equal to

mC=PΓ(m+0.5)2mΓ(m)2dAIRS1ple/2dIRS1SSPLE/2(23)

σC2=PdAIRS1ple/2dIRS1SSple/2[1−Γ(m+0.5)M12Γ(m)44](24)

We deduce

ESS=EL0(1−μ)(1−ζ)=βμEAC2(1−μ)(1−ζ)(25)

The variable Yi should be replaced by Zi written as

Yi=Fi2βμEAC2(1−μ)(1−ζ)(26)

where Fi is defined in (8).

Zi is the product of two non central chisquare r.v. Therefore, we have [31]

PZi(x)=e−0.5mFi2σFi2e−0.5mC2σC2∑q=0+∞⁡∑l=0+∞⁡(mFi2σFi2)l(mC2σC2)q2q+lΓ(q+0.5)Γ(l+0.5)q!l!×G1,32,1(N0(1−)(1−ζ)xmβEA2|1q+0.5,l+0.5,0),(27)

4  Numerical Results

Fig. 3 depicts the total throughput for K = 2 users, QPSK modulation, m-fading figure m = 2, β = 0.5, T1 = 1, dASS = 1.1, dSSIRS = 1.2, dIRSU1 = 1.1, dIRSU2 = 1.5 and ple = 3. We notice that the use of M = Mi = 512, 256, 128, 64, 32, 16, 8 reflectors per user offers 45, 42, 39, 36, 33, 30, 27 dB gain vs. the absence of IRS [29]. Fig. 3 corresponds to optimal POi, μ and ζ.

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Figure 3: Total throughput for two users and QPSK

Figs. 4 and 5 compares the total throughput for M = Mi = 8, 16 with optimal μ and ζ to (μ = 1/3, ζ = 1/2). We observe that optimal harvesting and sensing duration μ and ζ offers a better throughput than (μ = 1/3, ζ = 1/2), (μ = 1/3, optimal ζ) and (optimal μ, ζ = 1/2).

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Figure 4: Total throughput for two users QPSK and M = 8

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Figure 5: Total throughput for two users, QPSK and M = 16

Fig. 6 shows the total throughput for K = 3 users and 16QAM modulation, m-fading figure m = 2, T1 = 1, d = 1, dSSIRS = 1.2, dIRSU1 = 1.1, dIRSU2 = 1.3, dIRSU3 = 1.5. M = Mi = 512, 256, 128, 64, 32, 16, 8 reflectors per user offers 47, 44, 41, 38, 35, 32, 29 dB gain vs. NOMA without IRS [29]. In Fig. 6, we used an optimal powers as well as optimal μ and ζ.

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Figure 6: Total throughput for three users and 16QAM

Fig. 7 depicts the throughput for M = Mi = 16 reflectors per user. We optimized NOMA powers in Fig. 7. We observe that optimal sensing and harvesting durations ζ and μ offers a better throughput than (μ = 1/3, ζ = 1/2), (μ = 1/3, optimal ζ) and (optimal μ, ζ = 1/2).

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Figure 7: Total throughput for three users, 16QAM and M = 16

Fig. 8 shows the total throughput for the same parameters as Fig. 6. We have studied the effect of m-fading figure. For m = 3, we observe up to 8 and 2 dB gain vs. m = 1 and m = 2 that corresponds to Rayleigh channels.

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Figure 8: Total throughput for three users, 16QAM and M = 16

In Fig. 9, we plotted the total throughput for K = 3 users and 16QAM modulation. The parameters are the same as Fig. 6. We have plotted the throughput when a energy harvesting uses IRS. The parameters are dAIRS1 = 1.1 and dIRS1SS = 1.3. The use P = 8 reflectors for energy harvesting and M = Mi = 8 reflectors per user for data communications offers 7 and 38 dB gain vs. one IRS M = Mi = 8 and without IRS [29]. The use of P = 16 reflectors for energy harvesting and M = Mi = 8 reflectors per user for data communications offers 9 and 42 dB gain vs. one IRS M = Mi = 8 and without IRS [29].

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Figure 9: Total throughput using two IRS: three users, 16QAM

5  Conclusion

In this article, we optimized the powers of NOMA users, sensing and harvesting duration for CRN. Secondary source senses the channel over (1−μ)ζT s to detect primary activity. If no activity is detected, SS broadcasts a signal during (1−μ)(1−ζ)T s to NOMA users. The signal is reflected by Intelligent Reflecting Surfaces (IRS) towards K users. A set Ii of reflectors is associated to user Ui. The use of M = Mi = 512, 256, 128, 64, 32, 16, 8 reflectors per user offers 45, 42, 39, 36, 33, 30, 27 dB gain vs. wireless systems without IRS [29]. We also suggest the use of IRS in energy harvesting. The use P = 8 reflectors for energy harvesting and M = Mi = 8 reflectors per user for data communications offers 7 and 38 dB gain vs. one IRS M = Mi = 8 and without IRS [29]. The use of P = 16 reflectors for energy harvesting and M = Mi = 8 reflectors per user for data communications offers 9 and 42 dB gain vs. one IRS M = Mi = 8 and without IRS [29].

Funding Statement: The authors received no specific funding for this study.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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