} + \left(L-\frac{n_T}{2}\right)\log_2\left(1+\frac{\rho}{n_T}\right) \nonumber.\end{aligned}$$

The same procedure can be pursued for $n_T\geq 2n_R$ resulting in the following general characterization for any $n_T,n_R$ $$\begin{aligned}
\max\left(0,L-\frac{n_T}{2}\right)\log_2\left(1+\frac{\rho}{n_T}\right) \leq C\left(\rho,n_T,n_R\right) &-R_{sA} \nonumber \\
\leq \frac{L_1}{2 \ln(2) }  + \max\left(0,L-\frac{n_T}{2}\right)\log_2\left(1+\frac{\rho}{n_T}\right),\nonumber\end{aligned}$$ which is equal to $$\begin{aligned}
& \left(L-\frac{L_1}{2}\right)\log_2\left(1+\frac{\rho}{n_T}\right) \leq C\left(\rho,n_T,n_R\right) &-R_{sA} \nonumber
\\
& \leq \frac{L_1}{2 \ln(2) }  +
\left(L-\frac{L_1}{2}\right)\log_2\left(1+\frac{\rho}{n_T}\right).\label{eq:AbsLossAllg}\end{aligned}$$ From , we observe that as long as $n_T \geq 2n_R$, the absolute loss is only a constant, which depends only on the number of receive antennas. In case $n_T < 2n_R$ the absolute loss increases linearly with $\left(L-\frac{n_T}{2}\right)$.

Suboptimal detection and condition number {#sec:Schemes}
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In the previous sections, we have shown that the stacked OSTBC achieves significant portions of the ergodic capacity. This does not, however, guarantee good performance in terms of error probability, which will be investigated in this section. Note that in the analysis in the previous sections it was implicitly assumed, that an optimal maximum-likelihood detector is used at the receiver, which performs an exhaustive search over all possible transmit symbols at each detection step. Especially for higher number of transmit antennas, this becomes computationally prohibitive. If additionally high rates are requested, then higher order modulation sizes are necessary which increases 