form_e_mat.m

Subspace Projection Based Blind Channel Order Estimation of MIMO Systems m file for a classical

function E_mat = form_E_mat(Rec_Sig,l,w,Q)

%----------------------------
% Step 1: construct Z_Mat
%----------------------------
Mr = size(Rec_Sig,1);
Z_Mat = zeros((2*w+l+1)*Mr,Q-2*w-l);
for row = 1:2*w+l+1
    Z_Mat((row-1)*Mr+1:row*Mr,:) = Rec_Sig(:,2*w+l+2-row:Q+1-row);
end

%----------------------
% Step 2: denoising
%----------------------
[U,S,V] = svd(Z_Mat,'econ');
rank_Z = effective_rank(S);
P = size(S,1);
n_eig = 0;
for i = rank_Z+1:P
    n_eig = n_eig + abs(S(i,i))/(P-rank_Z);
end
S = S - n_eig*eye(P);
Z_Mat = U(:,1:rank_Z)*S(1:rank_Z,1:rank_Z)*V(:,1:rank_Z)';

F_Mat = Z_Mat(1:w*Mr,:);
Y_Mat = Z_Mat(w*Mr+1:(w+l+1)*Mr,:);
P_Mat = Z_Mat((w+l+1)*Mr+1:(2*w+l+1)*Mr,:);
D_Mat = [F_Mat;P_Mat];

%------------------------
% Step 3: Calculate E
%------------------------
V_mat = orth(D_Mat');
E_mat = Y_Mat-Y_Mat*V_mat*V_mat';