The multicarrier code division multiple access (MC-CDMA) technique has received considerable interest for its potential application to future wireless communication systems due to its high data rate. A common problem regarding the blind multiuser detectors used in MC-CDMA systems is that they are extremely sensitive to the complex channel environment. Besides, the perturbation of colored noise may negatively affect the performance of the system. In this paper, a new coherent detection method will be proposed, which utilizes the modified fast independent component analysis (FastICA) algorithm, based on approximate negentropy maximization that is subject to the second-order cone programming (SOCP) constraint. The aim of the proposed coherent detection is to provide robustness against small-to-medium channel estimation mismatch (CEM) that may arise from channel frequency response estimation error in the MC-CDMA system, which is modulated by downlink binary phase-shift keying (BPSK) under colored noise. Noncoherent demodulation schemes are preferable to coherent demodulation schemes, as the latter are difficult to implement over time-varying fading channels. Differential phase-shift keying (DPSK) is therefore the natural choice for an alternative modulation scheme. Furthermore, the new blind differential SOCP-based ICA (SOCP-ICA) detection without channel estimation and compensation will be proposed to combat Doppler spread caused by time-varying fading channels in the DPSK-modulated MC-CDMA system under colored noise. In this paper, numerical simulations are used to illustrate the robustness of the proposed blind coherent SOCP-ICA detector against small-to-medium CEM and to emphasize the advantage of the blind differential SOCP-ICA detector in overcoming Doppler spread.