order to further decrease the complexity of this layered space-time architecture, [@A.F.Naguib1998; @N.Prasad2001; @N.Prasad2003] used the Alamouti scheme as component code for each group in combination with a suboptimal successive group interference suppression detection strategy. The outage probability of this scheme was analyzed in [@SezginJorsCapHighRate] for $n_T>n_R$ and an upper bound was derived. An asymptotic analysis of the rate achievable with this scheme is performed in [@LiYeCapStackedAlamou]. For $n=2$, this transmission scheme is also referred to as double-space-time transmit diversity (DSTTD) and was proposed as one possible candidate for high speed downlink packet access (HSDPA) in 3GPP and beyond [@TexasInstrum].

It is obvious that reducing the computational complexity of the detector without sacrificing much performance is an important issue. There is a huge amount of suboptimal detectors with low complexity in the literature, linear detectors like zero-forcing (ZF) or minimum mean square error (MMSE) and nonlinear detectors like e.g. VBLAST [@WolnianskyFoschiniGoldenValen98]. Unfortunately, these detectors significantly sacrifice performance in terms of bit-error-rate (BER). Recently, lattice reduction (LR) aided detection in combination with suboptimal detectors was proposed by Yao and Wornell in order to improve the performance of multi antenna systems [@YaoWornell]. The lattice reduction algorithm proposed in [@YaoWornell] is optimal, but 