A massive multiple-input multiple-output system with pilot contamination is considered. In order to improve channel estimation we propose a blind data-aided method based on complex independent component analysis (cICA) with the aid of mutual information rate as contrast function. In this approach, interference and the noise are first suppressed by subspace projection, then the uplink data is extracted blindly. Finally, based on the estimated uplink data of all the users in the cell of interest, the least square estimate of the channel is obtained. Simulation results confirm that 1) the pilot contamination effect decays, as the number of receive antennas and the data length increase; and 2) that the proposed approach outperforms both kurtosis-based cICA and pure subspace projection for the considered scenarios.