we shortly describe the QSTBC for $n_T=4$ transmit antennas [@SharmaPapadias02]. To generalization to higher number of transmit antennas is straightforward [@A.Sezgin2004]. The transmit matrix for $n_T=4$ transmit antennas is then given [@SharmaPapadias02; @A.Sezgin2004]. $$\begin{aligned}
\mathbf{G}_{4}({\mathbf{x}}) = \left[
\begin{array}{*{4}{r}}
          x_1 & x_2 & x_3 & x_4 \\
        x_2^* & -x_1^* & x_4^* & -x_3^* \\
        x_3 & -x_4 & -x_1 & x_2 \\
       x_4^* & x_3^* & -x_2^* & -x_1^* \\
        \end{array}\nonumber
\right]\;.\end{aligned}$$ After rewriting (\[eq:System\]), we arrive at (similar to the proposed scheme, (cf. ) $$\label{eq:EQ_SysModQSTBC}
    \mathbf{y}^Q=\mathbf{H}^Q\mathbf{x}+ \mathbf{n}^Q\;,$$ where $\mathbf{H}^Q=[(\mathbf{H}_1^Q)^T,\dots,(\mathbf{H}_i^Q)^T,\dots,(\mathbf{H}_{n_R}^Q)^T]^T$ and $(\mathbf{H}_i^Q)$ is given as $$\mathbf{H}_i^Q=\left[%
\begin{array}{rrrr}
   h_{1i}   &  h_{2i}   &   h_{3i}   &  h_{4i}   \\
  -h_{2i}^* &  h_{1i}^* &  -h_{4i}^* &  h_{3i}^* \\
  -h_{3i}   &  h_{4i}   &   h_{1i}   & -h_{2i}   \\
  -h_{4i}^* & -h_{3i}^* &   h_{2i}^* &  h_{1i}^* \\
\end{array}%
\right] \nonumber \;.$$ For general $n_T$, we have to rewrite the system model in  as a real model similar to SM. For $n_T=4$, however, it is not necessary to resort to the real system model. Here, the system model can be decomposed such that the iterative optimal algorithm in [@YaoWornell] for a system with $n_T=2$ transmit antennas can be applied. For this we first perform channel-matched filtering as the first 