wireless exmple

8/12/2019 wireless exmple

1/22

August 5, 2013

Lab-4

Prepared By-Nilay Vithani and Sameer Patel

Common Function for Periodic Correlation and Periodic Autocorrelation:-

function x = disi(s1,s2)

if s1 == s2

m1=s1';

m2=m1;

for j=1:25

m2=circshift(m2,1);

m=m1.*m2;

s=0;

for i=1:length(m)

s=s+m(i);

end

x(j)=s;

end

else

m1=s1';

m2=s2';

for j=1:25

m=m1.*m2;

m2=circshift(m2,1);

s=0;

for i=1:length(m)

s=s+m(i);

end

x(j)=s;

end

end


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Q1) For Autocorrelation

Code:-

clear all;

clc;

s1=[+1 -1 +1 +1 +1 -1 -1 -1 +1 -1]%input('Enter Sequence 1: ');


plot(disi(s1,s2));

xlabel('f(x)');

ylabel('x');

title('Periodic cross or auto correlation function');

legend('Auto correlation');

Figure:-

Figure For Q1-Autocorrelation

For Cross Correlation

Code:-

clear all;

clc;


s2=[1 -1 -1 +1 -1 1 -1 1 -1 -1]%input('Enter Sequence 2: ');


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plot(disi(s1,s2));

xlabel('f(x)');

ylabel('x');

title('Periodic cross or auto correlation function');

legend('Auto correlation');

Figure:-

Figure For Q1-Cross Correlation


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Q2)

Code:-

clear all;

clc;

N=16;

k=2;

H = hadamard(16);

k1 = randperm(size(H,1));

k2 = randperm(size(H,1));

s1 = H(k1(1:1),:);

s2 = H(k2(1:1),:);

Rc=disi(s1,s2);

Ra=disi(s1,s1);

Rmax=max(max(Rc,Ra))

figure;

s_2=disi(s1,s1);

s_2=[-s_2 s_2];

subplot(211);

plot(s_2);

title('Hadamard Walsh code set of length 16 Auto corr periodic');

s_1=disi(s1,s2);

s_1=[-s_1 s_1];

subplot(212);

plot(s_1,'g');

title('Hadamard Walsh code set of length 16 Cross corr periodic');

figure;

Rc=[-Rc Rc];

subplot(211);

plot(Rc);

title('Hadamard Walsh code set of length 16 Cross corr periodic');

welch=N*sqrt((k-1)/(k*N-1))


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Cxy=xcorr(s1,s2);

subplot(212);

plot(Cxy,'r');

title('Hadamard Walsh code set of length 16 Cross corr Aperiodic');

for n=1:N-1;

Rxy(n)= Cxy(n) + Cxy(N-n);

end

figure;

subplot(211);

plot(Rxy);

title('Even cross correlation function');

subplot(212);

plot(Cxy,'black');

title('Aperiodic cross correlation function');

Output:-

Rmax =

16

welch =

2.8737

Conclusion:-

This shows that >

Note:-The value of Rmax will change on every run of the code because of the coding taking two random rows from the Hadamard

matrix for the purpose of auto and cross-correlation

Figure:-


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Figures For Q2


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Q3)

Code:-

clear all;

clc;;

N=31;

%uncoded_bits = round(rand(1,N));

%b = -2*(uncoded_bits-0.5)

% Primitive polynomial here taken: x^5 + x^2 + 1

%initial sequance is 00001

a=[1; 0; 0; 0; 0];

for i=1:31

b(i)=a(5);

c=xor(a(5),a(2));

a=circshift(a,1);

a(1)=c;

end

d=b';

for i=1:31

m1(i,:)=circshift(d,i);

end

% Reciprocal polynomial of above is: x^5 + x^3 + 1

a=[1; 0; 0; 0; 0];

for i=1:31

b(i)=a(5);

c=xor(a(5),a(3));

a=circshift(a,1);

a(1)=c;

end

e=b';

for i=1:31

m2(i,:)=circshift(e,i);


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end

matrix1=m1

matrix2=m2

Output:-

matrix1 =

Columns 1 through 22

1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1

0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1

0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1

1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1

0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0

1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0

1 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0

0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1

0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1

1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0

1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1

1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1

1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1

1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 0

0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1

0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0

0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1

1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0

1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0

0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0

1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0

1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1

1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0


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0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0

1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1

0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0

1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1

0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1

0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0

0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0

0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1


1 0 0 1 1 0 1 0 0

1 1 0 0 1 1 0 1 0

1 1 1 0 0 1 1 0 1

1 1 1 1 0 0 1 1 0

1 1 1 1 1 0 0 1 1

0 1 1 1 1 1 0 0 1

0 0 1 1 1 1 1 0 0

0 0 0 1 1 1 1 1 0

1 0 0 0 1 1 1 1 1

1 1 0 0 0 1 1 1 1

0 1 1 0 0 0 1 1 1

1 0 1 1 0 0 0 1 1

1 1 0 1 1 0 0 0 1

1 1 1 0 1 1 0 0 0

0 1 1 1 0 1 1 0 0

1 0 1 1 1 0 1 1 0

0 1 0 1 1 1 0 1 1

1 0 1 0 1 1 1 0 1

0 1 0 1 0 1 1 1 0

0 0 1 0 1 0 1 1 1

0 0 0 1 0 1 0 1 1

0 0 0 0 1 0 1 0 1


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1 0 0 0 0 1 0 1 0

0 1 0 0 0 0 1 0 1

0 0 1 0 0 0 0 1 0

1 0 0 1 0 0 0 0 1

0 1 0 0 1 0 0 0 0

1 0 1 0 0 1 0 0 0

1 1 0 1 0 0 1 0 0

0 1 1 0 1 0 0 1 0

0 0 1 1 0 1 0 0 1

matrix2 =


1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0

0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0

1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0

0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1

1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1

1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1

1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1

0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1

1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0

1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0

0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1

0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1

0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0

1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1

1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0

1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0

1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1

1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0


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0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0

0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0

1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0

1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1

0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0

1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1

0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0

0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1

1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1

0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1

0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0

0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1

0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1


1 1 0 1 1 1 0 1 0

0 1 1 0 1 1 1 0 1

0 0 1 1 0 1 1 1 0

0 0 0 1 1 0 1 1 1

1 0 0 0 1 1 0 1 1

1 1 0 0 0 1 1 0 1

1 1 1 0 0 0 1 1 0

1 1 1 1 0 0 0 1 1

1 1 1 1 1 0 0 0 1

0 1 1 1 1 1 0 0 0

0 0 1 1 1 1 1 0 0

1 0 0 1 1 1 1 1 0

1 1 0 0 1 1 1 1 1

0 1 1 0 0 1 1 1 1

1 0 1 1 0 0 1 1 1

0 1 0 1 1 0 0 1 1

0 0 1 0 1 1 0 0 1


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1 0 0 1 0 1 1 0 0

0 1 0 0 1 0 1 1 0

0 0 1 0 0 1 0 1 1

0 0 0 1 0 0 1 0 1

0 0 0 0 1 0 0 1 0

1 0 0 0 0 1 0 0 1

0 1 0 0 0 0 1 0 0

1 0 1 0 0 0 0 1 0

0 1 0 1 0 0 0 0 1

1 0 1 0 1 0 0 0 0

1 1 0 1 0 1 0 0 0

1 1 1 0 1 0 1 0 0

0 1 1 1 0 1 0 1 0

1 0 1 1 1 0 1 0 1

Theory:-

The primitive polynomial used is: 5 + 2 + 1

Reciprocal polynomial is: 3 + 2 + 1

What wed obtained was a single sequence of length 31.

The entire matrix of sequences (31x31) can be obtained by circularly shifting the single sequence 31 times.


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Q4)

Code:-

x=[1;0;0;0;0;1;0;1;0;1;1;1;0;1;1;0;0;0;1;1;1;1;1;0;0;1;1;0;1;0;0];

y=[1;0;0;0;0;1;1;0;1;0;1;0;0;1;0;0;0;1;0;1;1;1;1;1;0;1;1;0;0;1;1];

Ty=y;

for j=1:31

Ty=circshift(Ty,1);

a(j,:)=Ty;

end

gold=[x,y,xor(x, y),xor(x, a(:,1)),xor(x, a(:,2)),xor(x, a(:,3)),xor(x, a(:,4)),xor(x, a(:,5)),xor(x, a(:,6)),xor(x, a(:,7)),xor(x, a(:,8)),xor(x,

a(:,9)),xor(x, a(:,10)),xor(x, a(:,11)),xor(x, a(:,12)),xor(x, a(:,13)),xor(x, a(:,14)),xor(x, a(:,15)),xor(x, a(:,16)),xor(x, a(:,17)),xor(x,

a(:,18)),xor(x, a(:,19)),xor(x, a(:,20)),xor(x, a(:,21)),xor(x, a(:,22)),xor(x, a(:,23)),xor(x, a(:,24)),xor(x, a(:,25)),xor(x, a(:,26)),xor(x,

a(:,27)),xor(x, a(:,28)),xor(x, a(:,29)),xor(x, a(:,30))]

gold=gold';

k1 = randperm(size(gold,1));

k2 = randperm(size(gold,1));

s1 = gold(k1(1:1),:);

s2 = gold(k2(1:1),:);

seq1=s1;

seq2=s2;

crosscorrel=disi(seq1,seq2);

Rc=max(crosscorrel);

seq1=s1;

seq2=s1;

autocorrel=disi(seq1,seq1);

Ra=max(autocorrel);

Rmax=max(Ra,Rc);

N=31;


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k=N+2;

Welch_bound=N*sqrt((k-1)/(k*N-1));

Rmax

Welch_bound

subplot(211)

title('Cross Correlation')

plot(crosscorrel,'black')

subplot(212)

plot(autocorrel,'b');

title('Auto Correlation')

Output:-

gold =


1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0

0 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0

0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0

0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0

0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1

1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1

0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0

1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0

0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0

1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0

1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1

1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0

0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1

1 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1

1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1

0 0 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0

0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0


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0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1

1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0

1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0 0 1 1 0

1 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0 0 1 1

1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0 0 1

1 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0 0

0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1

0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 0

1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0

1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0

0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1

1 0 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 0

0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1

0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0


1 0 0 0 0 0 1 0 0 1 1

1 0 1 1 1 1 1 0 1 1 0

0 1 0 1 1 1 1 1 0 1 1

0 0 1 0 1 1 1 1 1 0 1

0 0 0 1 0 1 1 1 1 1 0

0 1 1 1 0 1 0 0 0 0 0

0 1 0 0 0 1 0 1 1 1 1

1 1 0 1 1 1 0 1 0 0 0

1 0 0 1 0 0 0 1 0 1 1

1 0 1 1 0 1 1 1 0 1 0

0 1 0 1 1 0 1 1 1 0 1

1 0 1 0 1 1 0 1 1 1 0

1 0 1 0 1 0 0 1 0 0 0

0 0 1 0 1 0 1 1 0 1 1

1 0 0 1 0 1 0 1 1 0 1

0 0 1 1 0 1 0 1 0 0 1


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0 0 0 1 1 0 1 0 1 0 0

0 0 0 0 1 1 0 1 0 1 0

0 1 1 1 1 0 0 1 0 1 0

0 0 1 1 1 1 0 0 1 0 1

0 0 0 1 1 1 1 0 0 1 0

1 0 0 0 1 1 1 1 0 0 1

1 1 0 0 0 1 1 1 1 0 0

1 0 0 1 1 1 0 0 0 0 1

1 1 0 0 1 1 1 0 0 0 0

1 0 0 1 1 0 0 0 1 1 1

0 1 0 0 1 1 0 0 0 1 1

1 1 0 1 1 0 0 1 1 1 0

0 0 0 1 0 0 1 1 0 0 0

1 1 1 1 0 1 1 0 0 1 1

1 1 1 1 1 0 1 1 0 0 1

Rmax =

10

Welch_bound =

5.4854

Conclusion:-

This shows that >

Note:- The value of Rmax will change on every run of the code because of the coding taking two random rows from the Gold

sequence matrix for the purpose of auto and cross-correlation.


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Figure:-

Figure For Q4


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Q5)

Code:-

clear all;

clc;

N=7;

M=6;

M1=7;

%CI

for k=1:N

s1(k)=exp(i.*((2*pi./N)) .*(k-1).*(M-1));

s2(k)=exp(i.*((2*pi./N)) .*(k-1).*(M1-1));

end

auto=abs(disi(s1,s1));

cross=abs(disi(s1,s2));

Rmax_CI=max(max(abs(auto),abs(cross)))

subplot(221);

plot(auto);

xlabel('f(x)');

ylabel('x');

title('CI Auto correlation function');

subplot(222);

plot(cross,'g');

xlabel('f(x)');

ylabel('x');

title('CI Cross correlation function');

%FZC

for k=1:N

s3(k)=(-1)^(M*k).*(exp(i*(pi.*M .*M.*k/N)));

s4(k)=(-1)^(M1*k).*(exp(i*(pi.*M1 .*M1.*k/N)));

end


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auto1=abs(disi(s3,s3));

cross1=abs(disi(s3,s4));

Rmax_FZC=max(max(abs(auto1),abs(cross1)))

subplot(223);

plot(auto1,'r');

xlabel('f(x)');

ylabel('x');

title('FZC Auto correlation function');

subplot(224);

plot(cross1,'black');

xlabel('f(x)');

ylabel('x');

title('FZC Cross correlation function');

Output:-

Rmax_CI =

1.5906e-15

Rmax_FZC =

1.0150e-14


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Figure:-

Figure For Q5


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Q6)

Code:-

clc;

clear all;

N=8;

k=8;

i=1/(k*(k-1)*N*N);

sumci=0;

sumhad=0;

h=hadamard(N);

for k=1:N

for j=1:N

ci(k,j)=exp((1i*2*pi*(k-1).*(j-1))./N);

end

end

for x=1:N

for y=1:N

for l=1:(2*N)-1

if(x~=y)

crossci=xcorr(ci(x,:),ci(y,:)); %CI cross-correlation

sumci=sumci+(abs(crossci(l)).^2);

crosshad=xcorr(h(x,:),h(y,:)); %Hadamard Walsh cross-correlation

sumhad=sumhad+(abs(crosshad(l)).^2);

end

end

end

end

Rccci=i.*sumci;

display(Rccci);

Rcchad=i.*sumhad;

display(Rcchad);

Output:-


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Rccci =

0.3750

Rcchad =

0.6607

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