works only for MIMO systems with two transmit and two receive antennas. The impact of receive antenna correlation on the performance of LR-aided detection was analyzed in [@MengPanYouKimLLLforVLBAST]. In [@WindpassingerLLL], the work of [@YaoWornell] was extended to systems with more transmit and receive antennas, using the sub-optimal LLL [@LLL] lattice reduction algorithm. In [@WuebbenLLL], the LR-aided schemes in [@WindpassingerLLL] were adopted to the MMSE criterion. Note that the error rate curves of all these LR detectors are parallel to those for maximum likelihood (ML) detection with only some penalty in power efficiency.

In this work, we show that the stacked Alamouti scheme is capable to achieve the capacity in combination with the optimal maximum likelihood detector for the case of $n_T=2n$ transmit antennas and $n_R=1$ receive antennas. This was also shown for the basic Alamouti scheme with $n_T=2$ and $n_R=1$ [@HassibiHoch2002]. Our result may therefore be regarded as an extension of the Alamouti scheme to $n_T>2$. Furthermore, we show that in the case of more than one receive antenna and if $n_T>n_R$ the stacked Alamouti scheme is capable to achieve a significant portion of the capacity and approaches the capacity if $n_T\gg n_R$. For any $n_T$, $n_R$, we show that 