equation of zero forcing receiver

hi,

can help me in this error , i don't know the solution ?

and i want to sure if this equation is right for zero forcing estimator ?

N_r = 128 ; 
K = 8 ;
H = zeros(N_r, K);
SNR_dB = -12:4:20; 
SNR = 10.^(0.1.*SNR_dB);
for iter = 1:length(SNR) 
S = sqrt((SNR(iter))/K).*dftmtx(K) ;
W_ZF = ((H.^H) .* (H .* (H.^H)).^(-1)) .* S ;  %" error in this line , Arrays have incompatible sizes for this operation"
H_ZF = (W_ZF .^ H) .* y1 ;
end 

Arrays have incompatible sizes for this operation.

[Dyuman Joshi]

What is the size of variables H and S?

[Maha Saif]

edit above

[Dyuman Joshi]

Undefined parameter iter in your code.

Check above.

[Maha Saif]

ok

but the problem of "Arrays have incompatible sizes for this operation"

how can solve?

[Maha Saif]

iter is a for loop

Answer 1

[Maha Saif]

this the right answer of code function

function H_ZF = ZF_receiver ( W_ZF , H , Y , S )

N_r = 128 ;

K = 10 ;

H = zeros (N_r , K) ;

SNR_dB = -12:4:25;

SNR = 10.^(0.1.*SNR_dB);

for iter = 1:length(SNR)

S = sqrt((SNR(iter))/K).*dftmtx(K); % pilot matrix

end

Hh = H' ;

%W_ZF = ((H.^H) .* (H .* (H.^H)).^(-1)) .* S ;

W_ZF = H * pinv(Hh*H) * S ;

H_ZF = W_ZF .* Y ;

%H_ZF = (W_ZF .^ H) .* y1 ;

H_est_zf = reshape (H_ZF , N_r , K );

end

Answer 2

[Walter Roberson]

W_ZF = ((H.^H) .* (H .* (H.^H)).^(-1)) .* S ; 

The first part of that expression results in a 128 x 8 array that is all infinity -- with H being all 0, the H .* gives all 0 and all-zero ^-1 is going to be all infinity.

S is 8 x 8.

You cannot use element-by-element multiplication between a 128 x 8 matrix and an 8 x 8 matrix.

You could potentially use * matrix-multiplication between a 128 x 8 matrix and an 8 x 8 matrix, giving a 128 x 8 result. Which will probably be entirely complex-NaN due to the infinities in the left-hand side...

[Maha Saif]

so , what can i do ?

how solve it ?

and the values of N and K are variables

[Walter Roberson]

I do not have any idea what the equations are for zero forcing receiver.

[Maha Saif]

i mean how i can do multiplication in this case

[Walter Roberson]

N_r = 128 ; 
K = 8 ;
H = zeros(N_r, K);
SNR_dB = -12:4:20; 
SNR = 10.^(0.1.*SNR_dB);
numSNR = length(SNR);
W_ZF = cell(numSNR,1);
H_ZF = cell(numSNR,1);
for iter = 1:numSNR 
    S = sqrt((SNR(iter))/K).*dftmtx(K) ;
    W_ZF{iter} = ((H.^H) .* (H .* (H.^H)).^(-1)) * S ;
    H_ZF{iter} = (W_ZF{iter} .^ H) .* y1 ;
end 

Unrecognized function or variable 'y1'.

However, I have no idea whether the modified expression is a correct expression for zero forcing receiver.

And it's still going to be all complex nan and inf anyhows. The matrix of zeros raised to power -1 is going to produce all infinities, and when you start manipulating infinities nan are a very common result.

Answer 3

[Maha Saif]

Does it make any difference if the H matrix is complex or has zeros or ones ?

[Walter Roberson]

I had to guess about the size and values of y1 and about what might be reasonable "complex" entries.

If you have even a single zero entry in H then you get a NaN output -- at least for the corresponding row.

N_r = 128 ; 
K = 8 ;

y1 = randi([0 1], N_r, K);

SNR_dB = -12:4:20; 
SNR = 10.^(0.1.*SNR_dB);
numSNR = length(SNR);
H_ZF0 = cell(numSNR,1);
H_ZF1 = cell(numSNR,1);
H_ZFc = cell(numSNR,1);

H0 = zeros(N_r, K);
H1 = ones(N_r, K);
Hc = ones(N_r, K) * (1+1i); Hc(1,1) = 0;

for iter = 1:numSNR 
    S = sqrt((SNR(iter))/K).*dftmtx(K) ;
    
    W_ZF = ((H0.^H0) .* (H0 .* (H0.^H0)).^(-1)) * S ;
    H_ZF0{iter} = (W_ZF .^ H0) .* y1 ;
    
    W_ZF = ((H1.^H1) .* (H1 .* (H1.^H1)).^(-1)) * S ;
    H_ZF1{iter} = (W_ZF .^ H1) .* y1 ;

    W_ZF = ((Hc.^Hc) .* (Hc .* (Hc.^Hc)).^(-1)) * S ;
    H_ZFc{iter} = (W_ZF .^ Hc) .* y1 ;

end

H_ZF0{1}(1:5,:)

ans = 
      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi
      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi
      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi
      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi
      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi

H_ZF1{1}(1:5,:)

ans = 5×8

0.7105 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.7105 0 0 0 0 0 0 0 0.7105 0 0 0 0 0 0 0

H_ZFc{1}(1:5,:)

ans = 
      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi      NaN +    NaNi
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i  -0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 - 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i  -0.0000 + 0.0000i
   0.1067 - 1.0967i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i  -0.0000 + 0.0000i   0.0000 + 0.0000i  -0.0000 + 0.0000i
   0.1067 - 1.0967i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i