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Corollary 2

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

${\mathcal{X}}_{U}\left(\mathit{SNR}\right)$

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

is DMT-optimal for the quasi-static Rayleigh faded ${n}_{t}×{n}_{r}$ MIMO channel ...

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