Let's the input data vector $X = [X_1, X_2, X_3, X_4, X_5,X_6,X_7,X_8];$ where $[X_7,X_8]$ are well known, and the vector $y = h*X$ where $*$ is the convolution operation and $h = [h_1,h_2]$ is the channel vector. I have a priory information that $[X_7,X_8]$ = $T[X_1,X_2]$ where $T$ is a $2$x$2$ square matrix.
The issue I am trying to solve is can we get the channel vector $h$ based on optimizing $([y_7,y_8]$ - $T[y_1,y_2])$ ? Is there any optimization algorithm we can use to estimate the vector $h$?