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In order to hold fine spectral efficiency, it is meaningful to investigate multicarrier code-division multiple access (MC-CDMA) systems without cyclic prefix (CP), which are unavoidably corrupted by the hostile intersymbol interference (ISI) so that we can call them as ISI-corrupted MC-CDMA systems. Moreover, combining multiple antennas with ISI-corrupted MC-CDMA systems is advantageous in suppressing cochannel interference. Hence, this paper applies multiple antennas to the base station of ISI-corrupted MC-CDMA systems over frequency-selective fading channels. A joint spatio-temporal estimation method of uplink vector channel is then derived based on the singular value decomposition (SVD) technique. Computer simulations illustrate that our algorithm is more robust against noise and can well mitigate multiple access interference (MAI) in multiuser scenarios.