Massive MIMO OFDM waveforms help support a large number of users in the same time-frequency resource and also provide significant array gain for uplink reception in cellular systems. However, channel estimation in such large antenna systems can be tricky as pilot assignment for multiple users becomes more challenging with increasing number of users. Additionally, the pilot overhead especially for wideband rapidly changing channels can diminish the system throughput quite significantly. In this paper, we propose an iterative matrix decomposition algorithm for the blind demodulation of massive MIMO OFDM signals without using any pilots. This new decomposition technique provides estimates of both the user symbols and the user channel in the frequency domain simultaneously (to a scaling factor) without any pilots. We discuss methods for finding the appropriate initial points for the algorithm that ensure its convergence in different types of wireless channels. We also propose new methods for resolving the scaling factor in the estimated signal that do not increase pilot overhead. We show how the method can be adapted to both single-user and multi-user systems. Simulation results demonstrate that the lack of pilots does not affect the error performance of the proposed algorithm when compared to the conventional pilot-based channel estimation and equalization methods across a wide range of channels for both single and multi-user cases. We also demonstrate techniques to reduce the complexity of the estimation algorithm over multiple OFDM symbols in a 5G MIMO system by leveraging the temporal correlations in the channel.