Distributed Channel Estimation and Pilot Contamination Analysis for Massive MIMO-OFDM Systems

Massive MIMO communication systems, by virtue of utilizing very large number of antennas, have a potential to yield higher spectral and energy efficiency in comparison with the conventional MIMO systems. In this paper, we consider uplink channel estimation in massive MIMO-OFDM systems with frequency selective channels. With increased number of antennas, the channel estimation problem becomes very challenging as exceptionally large number of channel parameters have to be estimated. We propose an efficient distributed linear minimum mean square error (LMMSE) algorithm that can achieve near optimal channel estimates at very low complexity by exploiting the strong spatial correlations and symmetry of large antenna array elements. The proposed method involves solving a (fixed) reduced dimensional LMMSE problem at each antenna followed by a repetitive sharing of information through collaboration among neighboring antenna elements. To further enhance the channel estimates and/or reduce the number of reserved pilot tones, we propose a data-aided estimation technique that relies on finding a set of most reliable data carriers. We also analyse the effect of pilot contamination on the mean square error (MSE) performance of different channel estimation techniques. Unlike the conventional approaches, we use stochastic geometry to obtain analytical expression for interference variance (or power) across OFDM frequency tones and use it to derive the MSE expressions for different algorithms under both noise and pilot contaminated regimes. Simulation results validate our analysis and the near optimal MSE performance of proposed estimation algorithms.