the computational complexity even more. Thus, suboptimal detection schemes have to be employed reducing the detection complexity and thereby achieving reasonable error rate performance results. Therefore, in this section the impact of the suboptimal LR-aided linear ZF-detector on the performance of the stacked OSTBC is analyzed and compared to SM and QSTBC by resorting the equivalent channel representation. In order to apply the LR algorithm, the system model has to rewritten, which is done in the following subsections for the different transmission schemes. Afterwards, the LR-aided linear ZF-detection is described briefly.

Spatial Multiplexing (SM)
-------------------------

For SM, the transmit matrix $\mathbf{G}_{n_T}$ is reduced to $\mathbf{x}$, since $T=1$. In order to apply the suboptimal LR for SM, the system model in (\[eq:System\]) has to be rewritten as a real model [@WindpassingerLLL] of the form $$\nonumber
 \mathbf{y}_E = \left[%
\begin{array}{cc}
  \Re\{\mathbf{x}\} \\
  \Im\{\mathbf{x}\} \\
\end{array}%
\right]^T\mathbf{H}^{SM}_E+  \mathbf{n}_E\;,$$ where $$\nonumber
 \mathbf{y}_E=\left[%
\begin{array}{c}
  \Re\{\mathbf{y}\} \\
  \Im\{\mathbf{y}\} \\
\end{array}%
\right]^T\;,\mathbf{n}_E=\left[%
\begin{array}{c}
  \Re\{\mathbf{n}\} \\
  \Im\{\mathbf{n}\} \\
\end{array}%
\right]^T\;,$$ and $$\nonumber
\mathbf{H}^{SM}_E=\left[%
\begin{array}{rr}
  \Re\{\mathbf{H}\} & \Im\{\mathbf{H}\} \\
  -\Im\{\mathbf{H}\} & \Re\{\mathbf{H}\} \\
\end{array}%
\right]\;.$$ In the following, we refer to $\mathbf{H}^{SM}_E$ as the equivalent channel for the SM scheme.

QSTBC
-----

Without loss of generality, in this subsection 