ep1 = .2;
ep2 = .4;
N = 16;
n = (0:N-1);
S1 = sin(pi*(-n+ep1))./(N*sin(pi/N*(ep1-n))).*exp(j*pi*(1-1/N)*(ep1-n));
S2 = sin(pi*(-n+ep2))./(N*sin(pi/N*(ep2-n))).*exp(j*pi*(1-1/N)*(ep2-n));
subplot(2,2,1)
plot(n,abs(S1),'*')
xlabel('Subcarrier index k')
ylabel('|S(l-k)|')
hold on
plot(n,abs(S2),'o')
axis([0 N-1 0 1.1*max([abs(S1) abs(S2)])])
subplot(2,2,2)
plot(n,real(S1),'*')
xlabel('Subcarrier index k')
ylabel('Real(S(l-k))')
hold on
plot(n,real(S2),'o')
axis([0 N-1 1.1*min([real(S1) real(S2)]) 1.1*max([real(S1) real(S2)])])
subplot(2,2,3)
plot(n,imag(S1),'*')
xlabel('Subcarrier index k')
ylabel('Imag(S(l-k))')
hold on
plot(n,imag(S2),'o')
axis([0 N-1 1.1*min([imag(S1) imag(S2)]) 1.1*max([imag(S1) imag(S2)])])
N = 64;
n = (0:N-1);
ep = 0.2;
figure
S = sin(pi*(-n+ep))./(N*sin(pi/N*(ep-n))).*exp(j*pi*(1-1/N)*(ep-n));
Sp1 = sin(pi*(-n+ep+1))./(N*sin(pi/N*(ep-n+1))).*exp(j*pi*(1-1/N)*(ep-n+1));
Sp2 = sin(pi*(-n+ep-1))./(N*sin(pi/N*(ep-n-1))).*exp(j*pi*(1-1/N)*(ep-n-1));
Sp = S - Sp1;
Spp = -Sp2-Sp1+2*S;
plot(n, 10*log10(abs(S)),'-.')
hold on
plot(n, 10*log10(abs(Sp)),'--')
plot(n, 10*log10(abs(Spp)))
axis([0 N-1 -70 0])
legend('|S(l-k)|', '|S^`(l-k)|','|S^`^`(l-k)|')
xlabel('Subcarrier index k')
ylabel('dB')
title('Comparrison of |S(l-k)|, |S^`(l-k)|, and |S^`^`(l-k)| for \epsilon = 0.2 and N = 64');
ep = linspace(0,.5, 100);
for i = 1:100
S = sin(pi*(-n+ep(i)))./(N*sin(pi/N*(ep(i)-n))).*exp(j*pi*(1-1/N)*(ep(i)-n));
CIR(i) = abs(S(1))^2/sum(abs(S(2:N)).^2);
end
for i = 1:100
S_0 = sin(pi*(ep(i)))./(N*sin(pi/N*(ep(i)))).*exp(j*pi*(1-1/N)*(ep(i)));
S_1 = sin(pi*(-1+ep(i)))./(N*sin(pi/N*(ep(i)-1))).*exp(j*pi*(1-1/N)*(ep(i)-1));
S_2 = sin(pi*(1+ep(i)))./(N*sin(pi/N*(ep(i)+1))).*exp(j*pi*(1-1/N)*(ep(i)+1));
Stt = 0;
for l = 2:2:N-1
St = -sin(pi*(l-1+ep(i)))./(N*sin(pi/N*(ep(i)+l-1))).*exp(j*pi*(1-1/N)*(ep(i)+l-
1))+2*sin(pi*(l+ep(i)))./(N*sin(pi/N*(ep(i)+l))).*exp(j*pi*(1-1/N)*(ep(i)+l))-sin(pi*(l+1+ep(i)))./(N*sin(pi/N*(ep(i)+l+1))).*exp(j*pi*(1-
1/N)*(ep(i)+l+1));
Stt = abs(St).^2 + Stt;
end
CIR_SC(i) = abs(-S_1-S_2+2*S_0).^2/Stt;
end
figure
plot(ep, 10*log10(CIR+eps),'--')
hold on
plot(ep, 10*log10(CIR_SC+eps))
xlabel('Normalized Frequency Offset \epsilon')
ylabel('CIR (dB)')
title('CIR versus \epsilon for a standard OFDM system')
legend('Standard OFDM system', 'ICI Theory');