complex equation with summation

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?

Answer 1

[Geoff Hayes]

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?

Answer 2

[Sam]

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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