How to decide the most possible signal model between two model candidates besed on the received signal vector?
Assume the received signal vector is $y$, the possible signal model candidates could be:
(1) $y = Ax+n$, or
(2) $y = Bx+n$,
in which $x$ is the transmitted signal vector, and $A$ and $B$ are the system matrices for signal model candidate-1 and candidate-2 respectively, and $n$ is the Gaussian noise vector.
If $y$,$A$ and $B$ are all known, and the noise covariance matrix is $E[nn^H] = w^2I$, in which $w^2$ stands for noise power, and $I$ is the identity matrix, how to decide the most possible signal model candidate between the two. What's the optimal solution?
Thanks for any discussions.