% Decision Feedback Dectection
function X_receive = DF_decode(H11, H12, H21, H22, X_odd, X_even, Ncarr)

% prepare for normalization
H1 = H11.*conj(H12) + H21.*conj(H22);              % H_ZF
H2 = abs(H12).^2 + abs(H21).^2;                    % H_SML
H  = H11.*conj(H21) - H12.*conj(H22);

% linear combining for x1
X_est1  = (conj(H12).*X_odd.' + H21.*X_even')./H1; % conj(h11)*R1 + h22*conj(R2) = (|h11|^2 + |h22|.^2)*X1
X_sink1 = (1 + sign(real(X_est1)))/2;

% x2
X_est2 = (conj(H21).*X_odd.' - H12.*X_even' - H.*(2*X_sink1-1))./H2;
X_sink2 =  (1 + sign(real(X_est2)))/2;

% equlization in frequence domain
X_receive(1:2:Ncarr) = X_sink1;                    % the received symbols
X_receive(2:2:Ncarr) = X_sink2;