Channel Coding: Theory, Algorithms, and Applications

Corollary 2

An LSTBC-scheme $\mathcal{X}$, whose LSTBCs are given by ${\mathcal{X}}_L(\mathit{SNR})=\{\mu \mathbf{X}\mid \mathbf{X}\in {\mathcal{X}}_U(\mathit{SNR})\}$ with ${\mu }^2\doteq \mathit{SNR}{\left(1-\frac{r}{n_{\text{min}}}\right)}^{}$ and

${\mathcal{X}}_U(\mathit{SNR})$

$=\left\{\left.{\displaystyle \sum _{i=1}^{n_{\text{min}}T}}(s_{\mathit{iI}}{\mathbf{A}}_{\mathit{iI}}+s_{\mathit{iQ}}{\mathbf{A}}_{\mathit{iQ}})\right|\begin{array}{c}{s}_{\mathit{iI}}\text{,}{s}_{\mathit{iQ}}\in {\mathcal{A}}_{M-\text{PAM}}\text{,}\hfill \\ i=1\text{,}2\text{,}\dots \text{,}{n}_{\text{min}}T\text{,}\hfill \\ M\doteq {\mathit{SNR}}^{\frac{r}{2n_{\text{min}}}}\hfill \end{array}\right\}\text{,}$

is DMT-optimal for the quasi-static Rayleigh faded $n_t\times n_r$ MIMO channel ...