In this paper we have investigated the performance of downlink generalized distributed antenna system (GDAS). Under the assumption of spatial correlated fading conditions, we have derived the numeric expression of correlated coefficients according to series of Bessel function, and have lifted the range restriction of the mean angle of incident. Moreover, the architecture of distributed generalized layered space time codes (GLST) has been considered in order to achieve both multiplexing gain and diversity gain while we have used basis vector from null space instead of orthogonal set to obtain the same system performance but with lower complexity. Furthermore, in order to maximize the capacity, Gerschgorin circles based fast antenna selection algorithms have been evaluated including a discussion of those simulation results.