complex equation with summation

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Sam
Sam on 2 Jul 2014
Edited: Sam on 3 Jul 2014
I am required to implement this equation in matlab
and here is what i have come up with
i1 = 0;
i1 = ((0.5*(1-(sqrt((g*gamma)/(m+(g*gamma))))))^LM)*s;
s=0;
for k=0:LM-1
s=s+(nchoosek(2*k,k)*(1/((4*((mu^2)+1))^k)));
end
is my code correct?

Answers (2)

Geoff Hayes
Geoff Hayes on 2 Jul 2014
Sam - have you tried executing this equation to see what it will produce, comparing the results against some known input-output pairs?
In the above code, the i1 calculation comes before the s which could have just been a copy and paste ordering mistake but the latter must come before the former since i1 depends on s.
I'm assuming that m, g, LM, and gamma are constants. Note that in MATLAB R2014a, gamma is a built-in function (see http://www.mathworks.com/help/matlab/ref/gamma.html). You should avoid naming variables after built-in functions so please rename gamma to gammaVal.
While the i1 calculation looks correct, the code for s is very different from the equation.
The
nchoosek(2*k,k)
should be
nchoosek(LM-1+k,k)
and the
(1/((4*((mu^2)+1))^k))
should be
(0.5*(1+sqrt(g*gammaVal/(m+g*gammaVal))))^k
Did you perhaps mix up the calculation of s with another equation?

Sam
Sam on 3 Jul 2014
Edited: Sam on 3 Jul 2014
thanks for the corrections, i have made the changes. this is what i am trying to solve
where I1 and I2 are replaced by
and
here is the complete code that i have come up with
function ber = var(gamma)
M = 64;
m = 1;
g = 3/(2*(M-1));
LM = 2;
mu = sqrt((g*gamma)/m);
alpha = sqrt((g*gamma)/(m+(g*gamma)));
beta = sqrt((g*gamma)/(m+(g*gamma)));
s=0;
for k=0:LM-1
s=s+(nchoosek((LM-1+k),k)*((0.5*(1+(sqrt((g*gamma)/(m+(g*gamma))))))^k));
end
i1 = 0;
i1 = ((0.5*(1-(sqrt((g*gamma)/(m+(g*gamma))))))^LM)*s;
s=0;
for k=0:LM-1
s=s+(nchoosek(2*k,k)*(1/((4*((mu^2)+1))^k)));
end
t=0;
for l=1:LM-1
for i=1:l
t=t+(((nchoosek(2*l,l))/((nchoosek(2*(l-i),(l-i)))*((4^i)*(2*(l-i)+1))))/(((mu^2)+1)^l))*((cos(atan(alpha)))^(2*(l-i)+1));
end
end
i2 = 0;
i2 = (1/4)-(beta*(0.5-(atan(alpha)/pi)))*s-((beta*((sin(atan(alpha)))/pi))*t);
p = (4*(1-(1/sqrt(M))))*i1 - (4*(1-(1/sqrt(M))))*i2;
ber = p;
the output should be one of the curves like this
but this is what i get
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