Alamouti Scheme. MISO. STBC for real constellation
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.