%some parameters
% No=1;%the PSD(power spectrum density) of the noise, the units is W/Hz
vr=0.01;
hsr=1;%the path loss of the source and relay
hrd=1;%the path loss of the relay and destination
hsd=0.1;%the path loss of the source and destination
prmax=10;
Gsr=abs(hsr)^2;
clc;
%at the time t=6s
a1=zeros(1,100);a2=zeros(1,100);a3=zeros(1,100);
b1=zeros(1,100);b2=zeros(1,100);b3=zeros(1,100);
c1=zeros(1,100);c2=zeros(1,100);c3=zeros(1,100);
d1=zeros(1,100);d2=zeros(1,100);d3=zeros(1,100);
i=0;
B=0;Bth=0;
for ps=0.1:1:100
i=i+1;
% t==0
Es0=5; Er0=10;
ps0=1;pr=2;
if (ps0<=ps)
beta=prmax/(ps*Gsr+vr^2);
r=1/2*log2(1+ps0*abs(hsd)^2/vr^2+beta*ps0*abs(hrd)^2*abs(hsr)^2/(beta*abs(hrd)^2*vr^2+vr^2))+1/2*log2(1+pr*abs(hrd)^2/vr^2);
K=(ps0*abs(hsr)^2+vr^2)*(ps0*abs(hsd)^2+ps0*abs(hsr)^2+vr^2);
betath=(-1)/abs(hrd)^2+abs(hsr)*sqrt(ps0*K*(ps0*abs(hsr)^2+prmax*abs(hrd)^2+2*vr^2))/abs(hrd)^2*K;
rth=1/2*log2(1+ps0*abs(hsd)^2/vr^2+betath*ps0*abs(hrd)^2*abs(hsr)^2/(betath*abs(hrd)^2*vr^2+vr^2))+1/2*log2(1+pr*abs(hrd)^2/vr^2);
B=r*5;Bth=rth*5;
end
% t==5
Es5=1;Er5=10;
ps5=Es5;pr=Er5;
if (ps5<=ps)
beta=prmax/(ps*Gsr+vr^2);
r=1/2*log2(1+ps5*abs(hsd)^2/vr^2+beta*ps5*abs(hrd)^2*abs(hsr)^2/(beta*abs(hrd)^2*vr^2+vr^2))+1/2*log2(1+pr*abs(hrd)^2/vr^2);
K=(ps5*abs(hsr)^2+vr^2)*(ps5*abs(hsd)^2+ps5*abs(hsr)^2+vr^2);
betath=(-1)/abs(hrd)^2+abs(hsr)*sqrt(ps5*K*(ps5*abs(hsr)^2+prmax*abs(hrd)^2+2*vr^2))/abs(hrd)^2*K;
rth=1/2*log2(1+ps5*abs(hsd)^2/vr^2+betath*ps5*abs(hrd)^2*abs(hsr)^2/(betath*abs(hrd)^2*vr^2+vr^2))+1/2*log2(1+pr*abs(hrd)^2/vr^2);
B=B+r;Bth=Bth+rth;
end
a1(i)=B;a2(i)=ps;a3(i)=Bth;
% t==6
Es6=2;Er6=4;
ps6=Es6/2;pr=Er6/2;
if (ps6<=ps)
beta=prmax/(ps*Gsr+vr^2);
r=1/2*log2(1+ps6*abs(hsd)^2/vr^2+beta*ps6*abs(hrd)^2*abs(hsr)^2/(beta*abs(hrd)^2*vr^2+vr^2))+1/2*log2(1+pr*abs(hrd)^2/vr^2);
K=(ps6*abs(hsr)^2+vr^2)*(ps6*abs(hsd)^2+ps6*abs(hsr)^2+vr^2);
betath=(-1)/abs(hrd)^2+abs(hsr)*sqrt(ps6*K*(ps6*abs(hsr)^2+prmax*abs(hrd)^2+2*vr^2))/abs(hrd)^2*K;
rth=1/2*log2(1+ps6*abs(hsd)^2/vr^2+betath*ps6*abs(hrd)^2*abs(hsr)^2/(betath*abs(hrd)^2*vr^2+vr^2))+1/2*log2(1+pr*abs(hrd)^2/vr^2);
B=B+r*2; Bth=Bth+rth*2;
end
b1(i)=B;b2(i)=ps;b3(i)=Bth;
% t==8
Es8=1;Er8=0;
ps8=Es8;pr=Er8;
if (ps8<=ps)
beta=prmax/(ps*Gsr+vr^2);
r=1/2*log2(1+ps8*abs(hsd)^2/vr^2+beta*ps8*abs(hrd)^2*abs(hsr)^2/(beta*abs(hrd)^2*vr^2+vr^2))+1/2*log2(1+pr*abs(hrd)^2/vr^2);
K=(ps8*abs(hsr)^2+vr^2)*(ps8*abs(hsd)^2+ps8*abs(hsr)^2+vr^2);
betath=(-1)/abs(hrd)^2+abs(hsr)*sqrt(ps8*K*(ps8*abs(hsr)^2+prmax*abs(hrd)^2+2*vr^2))/abs(hrd)^2*K;
rth=1/2*log2(1+ps8*abs(hsd)^2/vr^2+betath*ps8*abs(hrd)^2*abs(hsr)^2/(betath*abs(hrd)^2*vr^2+vr^2))+1/2*log2(1+pr*abs(hrd)^2/vr^2);
B=B+r;Bth=Bth+rth;
end
c1(i)=B;c2(i)=ps;c3(i)=Bth;
% t==9
Es9=5;Er9=10;
ps9=Es9;pr=Er9;
if (ps9<=ps)
beta=prmax/(ps*Gsr+vr^2);
r=1/2*log2(1+ps9*abs(hsd)^2/vr^2+beta*ps9*abs(hrd)^2*abs(hsr)^2/(beta*abs(hrd)^2*vr^2+vr^2))+1/2*log2(1+pr*abs(hrd)^2/vr^2);
K=(ps9*abs(hsr)^2+vr^2)*(ps9*abs(hsd)^2+ps9*abs(hsr)^2+vr^2);
betath=(-1)/abs(hrd)^2+abs(hsr)*sqrt(ps9*K*(ps9*abs(hsr)^2+prmax*abs(hrd)^2+2*vr^2))/abs(hrd)^2*K;
rth=1/2*log2(1+ps9*abs(hsd)^2/vr^2+betath*ps9*abs(hrd)^2*abs(hsr)^2/(betath*abs(hrd)^2*vr^2+vr^2))+1/2*log2(1+pr*abs(hrd)^2/vr^2);
B=B+r;Bth=Bth+rth;
end
d1(i)=B;d2(i)=ps;d3(i)=Bth;
end
plot(a2,a1,'b-.');hold on;
plot(b2,b1,'m:');
plot(c2,c1,'k--');
plot(d2,d1,'g-');
plot(a2,a3,'r-.');
plot(b2,b3,'r-.');
plot(c2,c3,'r-.');
plot(d2,d3,'r-.');
xlabel('Ps(W)');
ylabel('B(bits)');
legend('T=6s','T=8s','T=9s','T=10s','Bthmax');
grid on;
hold off;
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