# Signal model classification between two possbile candidates

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.

-