Why does this code give error?

clear;clc

%%  
fc = 3e8;% Carrier frequency
Nb = 1000;% Number of snapshots
c = 3e8;
wavelength = c/fc;% The wavelength of the received signal 
d = 0.5*wavelength; 
theta = [5 40];
M = length(theta);% Number of signals
N = 10;% Number of antennas

% Wavenumber
beta = 2*pi/wavelength;

% Signal amplitude
A = 1;   

% SNR (dB)
snr = 5;    

% Variance of noise
sigma=sqrt((A^2)/(2*10^(snr/10)));

% Source signal 
D = randi(M,Nb,1);
S =A*(2*D - 1);

% The electrical phase shift from element to element along the array
phi=beta*d*cos(theta*pi/180);  

% Matrix of steering vectors
for i=1:M
  for k=1:N;
    VecteurDirectionnel(k,i)= exp(j*(k-1)*phi(i));
  end
end

% White Gaussien noise
B = (sigma^2)*(randn(N,Nb)+j*randn(N,Nb))/sqrt(2);

% Array output:signal plus noise
X = VecteurDirectionnel*S+B;

Error using *
Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To operate on each element of the matrix individually, use TIMES (.*) for elementwise multiplication.

% Estimation of the spatial correlation matrix of the observed signal
Rxx = X*X'/Nb;

% Eigen decomposition
[Vi,Li] = eig(Rxx);
[L,I] = sort(diag(Li),'descend');
V = Vi(:,I);
Vs = V(:,1:M);
Vs1=Vs(1:N-1,:);
Vs2=Vs(2:N,:);

% Direction Of Arrival
% Least square

xsi=linsolve(Vs(1:N-1,:),Vs(2:N,:));
% DOA estimation
doa=acosd((angle(eig(xsi))/(2*pi*d)))

Answer 1

[Matt J]

As you can see, VecteurDirectionnel and S are the wrong sizes for matrix multiplication,

whos VecteurDirectionnel S

  Name                        Size            Bytes  Class     Attributes

  S                        1000x1              8000  double              
  VecteurDirectionnel        10x2               320  double    complex   

% Array output:signal plus noise
X = VecteurDirectionnel*S+B;

Error using *
Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To operate on each element of the matrix individually, use TIMES (.*) for elementwise multiplication.

[Sadiq Akbar]

@Matt J

Thanks a lot for your kind response. Yes, but how will we correct it?

[Stephen23]

"but how will we correct it?"

We cannot guess what you expect the output of "multiplying" a 1000x1 matrix with a 10x2 matrix to be.

Please tell us the exact size you expect the result of that operation to be.

[Matt J]

@Sadiq Akbar In addition to what Stephen said, you should know what sizes you expect VecteurDirectionnel and S themselves to be. You should be able to tell us what is wrong.

[Sadiq Akbar]

@Matt J

@Stephen23

Thanks to both of you for your kind responses. Actualy the sizes of the matrices VecteurDirectionnel and S should be 10 x 2 and 2 x 1000 respectively. But I don't know how to make size of S as 2 x 1000?

[Matt J]

Well S is Nb x 1 because D is Nb x 1, from this line,

D = randi(M,Nb,1);

Perhaps you meant to have,

D = randi([low, hi] , [M,Nb]);

but we have no way of knowing what you intended the low and hi limits to be.

[Sadiq Akbar]

@Matt J

Thanks a lot for your help. Yes, you are right. It works now.