To support high data rate wireless communications, in this paper, based on the linearly constrained constant modulus (LCCM) criterion, the reverse link performance of the multi-carrier code division multiple access (MC-CDMA) receiver, with frequency combiner, and having smart antenna arrays beamformer in base station, has been investigated over the Rayleigh fading channel. By using the Kronecker product an equivalent direct formulation, which integrates the information of spatial-domain as well as temporal-domain, with constraint matrix could be obtained. In consequence, the modified normalized LCCM-gradient algorithm is devised to adaptively implement the direct constrained optimal weights solution of the fully space-time MC-CDMA detector. We show that the proposed method outperforms the constrained minimum output energy (CMOE) algorithm and is more robust against to the signal mismatch, due to imperfect channel and direction-of-arrival estimation used in the array beamformer.