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A Noisy Independent Component Analysis (ICA) based method for detection in the compound system MIMO-OFDM and in the context of CDMA is proposed. Noisy-ICA algorithm is used as a post processor attached to a subspace based CDMA receiver in the presence of Gaussian noise. The proposed architecture of the detector reduces the bias caused by the channel noise and further decreases the noise by dimensionality reduction. An uplink CDMA based MIMO-OFDM channel is investigated given that only the code of the desired user is known in a blind symbol separation situation. The proposed receiver is compared to the conventional matched filter MF, the well-known linear MMSE detector, the ZF multi-user detector and the detection based on the ordinary ICA. The obtained simulation results for the AWGN channel demonstrate that the proposed scheme achieves significant bit error rate performance and appears to be suitable for CDMA based MIMO-OFDM system.