time-domain channel estimation based on two vectors optimization
You specify that $T$ is known and invertible, so you know $X_1, X_2$, and then it's really trivial: $y[3]=[X_1,X_2]*[h_1, h_2]$, and $y[9]=[X_7, X_8] *[h_1,h_2]$; write that down as matrix system
$$\begin{pmatrix}y[3]\\y[9]\end{pmatrix}=\begin{pmatrix}X_1&amp;X_2\\X_7&amp;X_8\end{pmatrix}\begin{pmatrix}h_2\\h_1\end{pmatrix}$$
and solve it.