NOMA using intelligent reflecting surfaces with adaptive transmit power and multi-antennas energy harvesting

Abstract

In this paper, we propose the use of Intelligent Reflecting Surfaces (IRS) between the secondary source and K secondary users. The secondary source transmits the combination of K symbols dedicated to K secondary Non Orthogonal Multiple Access (NOMA) users. A set $I_i$ of IRS reflectors are dedicated to user $U_i$ so that all reflections are in phase at $U_i$. We derive the throughput when the secondary source harvests energy using $n_r$ antennas and transmits with an adaptive transmit power to generate low interference at primary destination. We show that the use of IRS with 32 reflectors per user offers up to 45 and 50 dB gain with respect to NOMA and Orthogonal Multiple Access (OMA) without IRS.

Appendix 1: Matlab codes

• function NOMAR(NN)

• NN is the number of Reflectors

• x=0.1:0.01:10000;

• Q=4;Constellation size

• a1=0.9;

• a2=0.1;

• $\begin{aligned} g & = 1 - (1 - 2*(1 - 1/sqrt(Q)) \\ & *erfc(sqrt(3*log2(Q)/2/(Q - 1)*x))).^{2} 00; \\ \end{aligned}$

• w0=sum(g)*.01;

• alpha=1/2;

• dspr=2;

• dh=1;

• $lamdahs=dh^3;$

• $rauspr=1/dspr^3$;

• dsr=1/3;

• $rausr=1/dsr^3$;

• d1=1.1;

• $rau1=1/d1^3$;

• $rau2=1/d2^3;$

• d2=1;

• $lamdasr1=d1^3;$

• $lamdasr2=d2^3;$

• drpr=2;

• $raurpr=1/drpr^3;$

• i=1

• T=10

• plage=-30:2:30

• for ebnodb=plage

• $ebno=10^(ebnodb/10);$

• N0=1/ebno

• esno=log2(Q)*ebno;

• lamda=max(w0*N0/(a1-a2*w0),N0*w0/a2);

• betaa=max(w0*N0/(a1-a2*w0),0)

• alpha=0.5;

• $\begin{gathered} [FY2(i)FY2s(i)] = outageRISATPEHFinal \hfill \\ (lamda,NN,1/d1^{3} ,alpha); \hfill \\ \end{gathered}$

• $\begin{gathered} [FY1(i)FY1s(i)] = outageRISATPEHFinal \hfill \\ (betaa,NN,1./d2^{3} ,alpha); \hfill \\ \end{gathered}$

• i=i+1;

• end

• PEP1=FY1

• PEP2=FY2;

• PEP1s=FY1s;

• PEP2s=FY2s;

• $Th1=log2(Q)*(1-PEP1)*(1-alpha);$

• $Th1s=log2(Q)*(1-PEP1s)*(1-alpha);$

• $Th2=log2(Q)*(1-PEP2)*(1-alpha);$

• $Th2s=log2(Q)*(1-PEP2s)*(1-alpha);$

• $Th=Th1+Th2;$

• $Ths=Th1s+Th2s;$

• plot(plage,Th1,’k-’)

• hold on

• plot(plage,Th1s,’kp’)

• figure

• plot(plage,Th2,’r–’)

• hold on

• plot(plage,Th2s,’rs’)

• figure

• plot(plage,Th,’-.’)

• hold on

• plot(plage,Ths,’o’)

• function [F Fs]=outageRISATPEH(x,NN,asnr,alpha)

• ple=3;

• D=1;

• $Delta=1/D^ple;$

• m=NN*pi/4;

• $sig=sqrt(NN*(1-pi^2/16));$

• N0=1/asnr;

• K=10000;

• a=1;

• n=2;

• gAS=(randn(n,K)+j*randn(n,K))*sqrt(a/2);

• mu=0.5*alpha/(1-alpha);

• $Emax=mu*sum(abs(gAS).^2,1);$

• T=1;dspr=1;

• $aspr=dspr^ple;$

• $hSPR=(randn(1,K)+j*randn(1,K))*sqrt(aspr/2);$

• $E=min(Emax,T./abs(hSPR).^2);$

• A=m+randn(1,K)*sig;

• $SNR=A.^2.*E/N0;$

• $Fs=length(find(SNR!`x))/K;$

• pas=.01;

• y=.0001:pas:1000;

• JJ=zeros(1,length(y));

• for pp=0:n-1

• $JJ=JJ+(x*N0./y).^pp/factorial(pp)/mu^pp/a^(2*pp);$

• end

• $\begin{aligned} {\text{F3}} & {\text{ = 1 - 1/a*exp( - 1/a*x*N0}}{\text{./y/mu)}}{\text{.*JJ + 1/a*1/aspr}} \\ & {\text{*exp( - 1/a*x*N0}}{\text{./y/mu)}}{\text{.*exp( - 1/aspr*T*y/x/N0)}}{\text{.*JJ;}} \\ \end{aligned}$

• $\begin{aligned} f2 & = 1./sqrt(8*pi*sig^{2} *asnr*y*Delta). \\ & *exp( - (sqrt(y/asnr/Delta) - m).^{2} /2/sig^{2} ) \\ & + 1./sqrt(8*pi*sig^{2} *asnr*y*Delta). \\ & *exp( - (sqrt(y/asnr/Delta) + m).^{2} /2/sig^{2} ); \\ \end{aligned}$

• F=sum(f2.*F3)*pas;