the mutual information achievable with certain schemes such as the stacked OSTBC. After comparing the first two expansion coefficients (the linear term and the second order coefficients) it is shown that the stacked OSTBC reaches second-order capacity for $n_R=1$, i.e. the second-order coefficient of the mutual information of the stacked OSTBC is equal to the second-order coefficient of the capacity. Although essential features of the mutual information can be already seen from the first and second-order coefficients (especially at low SNR), our result above may regarded as more general, since the exact capacity and mutual information expressions are analyzed. Further note that the result above may be regarded as an extension of the results in [@HassibiHoch2002]. There it was shown, that the basic Alamouti scheme with $n_T=2$ and $n_R=1$ achieves the capacity.

### Case of $n_T=4$ and $n_R=2$ (DSTTD)

In the case of $n_T=4$ transmit and $n_R=2$ receive antennas, the equivalent channel is given by $$\nonumber
   \mathbf{H}'= \left[%
\begin{array}{cccc}
  h_{11} & h_{12} & h_{13} & h_{14} \\
  -h^*_{12} & h^*_{11} &-h^*_{14} & h^*_{13} \\
  h_{21} & h_{22} & h_{23} & h_{24} \\
  -h^*_{22} & h^*_{21} &-h^*_{24} & h^*_{23} \\
\end{array}%
\right].$$ The achievable rate in this case is given as 