In this paper we have investigated the performance of generalized layered space time codes (GLST) under the assumption of spatial correlated fading channels, where the architecture of distributed antenna system (DAS) has been considered. Motivated by previous study, here we have used basis vector from null space instead of orthogonal set to obtain the same system performance but with lower complexity. In the mean time OSTBC-Sphere algorithms have been utilized to further improve the system performance. Moreover we share a common framework in deducing the numeric expression of correlated coefficients according to series of Bessel function, and lift the range restriction of incident angle. Furthermore, in order to maximize the capacity, Gerschgorin circles antenna selection algorithms have been considered including a discussion of those simulation results.