How do i modify the code when a=0,a=0.1,...,a=0.9,a=1

I want to calculate the Ps when a=0.1,a=0.2,....,a=0.9,a=1.0 , so i think i should have 11 different Ps number,however,the window always show me 11 same number,it seems that it just calculate 11 times when the "a" is the same number.

How do i modify my code?

I think the PsB value when a=0.1 is not equal to the PsB value when a=0.4,so i think Ps should have 11 different value,why is the value the same? i think i must make a mistake in somewhere

Code :

H_A = 1/sqrt(2)*[randn(5,6) + j*randn(5,6)];
H_AB  = 1/sqrt(2)*[randn(2,6) + j*randn(2,6)];
H_AC  = 1/sqrt(2)*[randn(2,6) + j*randn(2,6)];

[UA,SA,VA]=svd(H_A);
[UAB,SAB,VAB]=svd(H_AB);
[UAC,SAC,VAC]=svd(H_AC);
gamma=10^9;
N0=10^-7;
gN=gamma*N0

%null space of A
null_A=VA((1:6),6);%6*1 vector

%Best beamforming direction of H_AB
BBD_AB=VAB((1:6),1);%6*1 vector

%Best beamforming direction of H_AC
BBD_AC=VAC((1:6),1);%6*1 vector

%BBD_AB has to project on the null_A
AB=null_A*((null_A'*null_A)^(-1))*null_A'*BBD_AB;

%BBD_AC has to project on the null_A
AC=null_A*((null_A'*null_A)^(-1))*null_A'*BBD_AC;

a=0:0.1:1
for i=1:1:length(a)
    f_A=( a(i)*AB+(1-a(i))*AC)/norm( (a(i)*AB+(1-a(i))*AC)    );
    PsB=abs((gN)/(f_A'*H_AB'*H_AB *f_A));
    PsC=abs((gN)/(f_A'*H_AC'*H_AC *f_A));
    
    if PsB > PsC
        Ps(i)=PsB
    else
        Ps(i)=PsC
    end
end

The window show me

Ps =

  Columns 1 through 4

  127.6320  127.6320  127.6320  127.6320

  Columns 5 through 8

  127.6320  127.6320  127.6320  127.6320

  Columns 9 through 11

  127.6320  127.6320  127.6320

Does anyone know where am i wrong?

[Karim]

If you store "f_A" for each iteration, you will see that you get the same result. Irrespective of the value of "a", thus the result of each loop will be the same. (see code below)

If you are trying to compute the weighted average of AB and AC, you don't need the norm etc. The denominator is the sum of the weights (in this case 1 and you can therefore omit the denominator).

H_A = 1/sqrt(2)*[randn(5,6) + i*randn(5,6)];
H_AB  = 1/sqrt(2)*[randn(2,6) + i*randn(2,6)];
H_AC  = 1/sqrt(2)*[randn(2,6) + i*randn(2,6)];
[UA,SA,VA]=svd(H_A);
[UAB,SAB,VAB]=svd(H_AB);
[UAC,SAC,VAC]=svd(H_AC);
gamma=10^9;
N0=10^-7;
gN=gamma*N0;
%null space of A
null_A=VA((1:6),6);%6*1 vector
%Best beamforming direction of H_AB
BBD_AB=VAB((1:6),1);%6*1 vector
%Best beamforming direction of H_AC
BBD_AC=VAC((1:6),1);%6*1 vector
%BBD_AB has to project on the null_A
AB=null_A*((null_A'*null_A)^(-1))*null_A'*BBD_AB;
%BBD_AC has to project on the null_A
AC=null_A*((null_A'*null_A)^(-1))*null_A'*BBD_AC;


a = 0:0.1:1;
Ps = zeros(numel(a),1);
f_A_store = zeros(6,numel(a));

for i=1:length(a)
    
    f_A = ( a(i)*AB + (1-a(i))*AC) / norm( (a(i)*AB+(1-a(i))*AC) );
    
    f_A_store(:,i) = f_A;
    
    PsB = abs((gN)/((f_A')*(H_AB')*H_AB *f_A));
    PsC = abs((gN)/((f_A')*(H_AC')*H_AC *f_A));
    
    if PsB > PsC
        Ps(i)=PsB;
    else
        Ps(i)=PsC;
    end
end

[yang-En Hsiao]

so you mean f_A should modify like this ?

f_A=( a(i)*AB + (1-a(i))*AC) ?

i don't understand why do you think we don't need to norm a(i)*AB + (1-a(i))*AC and The denominator is the sum of the weights,can you explain it more in detail?