Alamouti Scheme. MISO. STBC for real constellation I have a real orthogonal design for codeword...

$$
\begin{bmatrix}
    s1 &amp; s2 \\
    -s2 &amp; s1
\end{bmatrix}
$$

$$
s=\begin{bmatrix}
s1\\ 
s2
\end{bmatrix}
$$

$$
Y^T=\sqrt{\frac{P}{Mt}} h^T X + n^T
$$

...and receive signal:

$$
Y1=\begin{bmatrix}
y1\\ 
y2
\end{bmatrix}
$$

So for:

$$
X = \begin{bmatrix}
    x1 &amp; x2 \\
    -x2 &amp; x1
\end{bmatrix}
$$

and 
$$
Y = \begin{bmatrix}
    y1 &amp; y2
\end{bmatrix}
$$

...i have:

$$
Y=\sqrt{\frac{P}{Mt}} \cdot \begin{bmatrix}h1 &amp; h2\\ h2 &amp; -h1\end{bmatrix}\cdot \begin{bmatrix}x1 &amp; x2\end{bmatrix}^T+N
$$

...right?
Your analysis is correct. I would write it as follows: if you define the transmitted matrix as
\begin{equation*}
X = \begin{bmatrix} x_1 &amp; -x_2 \\ x_2 &amp; x_1
\end{bmatrix}
\end{equation*}
with one column transmitted at each symbol interval (that is, first you transmit $[x_1, x_2]$ and then $[-x_2, x_1]$), then the system can be written as $$Y=hX$$ with $h = [h_1, h_2]$, or equivalently it can be written as $$Y = Hx$$ with
\begin{equation*}
H = \begin{bmatrix} h_1 &amp; h_2 \\ -h_2 &amp; h_1
\end{bmatrix}
\end{equation*}
and $x=[x_1, x_2]^T$.

Of course, you can also transpose all vectors and matrices and arrive at equivalent results.