Semi-blind Channel Estimation and Data Detection for Multi-cell Massive MIMO Systems on Time-Varying Channels

We study the problem of semi-blind channel estimation and symbol detection in the uplink of multi-cell massive MIMO systems with spatially correlated time-varying channels. An algorithm based on expectation propagation (EP) is developed to iteratively approximate the joint a posteriori distribution of the unknown channel matrix and the transmitted data symbols with a distribution from an exponential family. This distribution is then used for direct estimation of the channel matrix and detection of data symbols. A modified version of the popular Kalman filtering algorithm referred to as KF-M emerges from our EP derivation and it is used to initialize the EP-based algorithm. Performance of the Kalman smoothing algorithm followed by KF-M is also examined. Simulation results demonstrate that channel estimation error and the symbol error rate (SER) of the semi-blind KF-M, KS-M, and EP-based algorithms improve with the increase in the number of base station antennas and the length of the transmitted frame. It is shown that the EP-based algorithm significantly outperforms KF-M and KS-M algorithms in channel estimation and symbol detection. Finally, our results show that when applied to time-varying channels, these algorithms outperform the algorithms that are developed for block-fading channel models.Comment: 28 pages, 13 figures, Submitted to IEEE Trans. on Vehicular Technolog

Channel Estimation in Multi-user Massive MIMO Systems by Expectation Propagation based Algorithms

Massive multiple input multiple output (MIMO) technology uses large antenna arrays with tens or hundreds of antennas at the base station (BS) to achieve high spectral efficiency, high diversity, and high capacity. These benefits, however, rely on obtaining accurate channel state information (CSI) at the receiver for both uplink and downlink channels. Traditionally, pilot sequences are transmitted and used at the receiver to estimate the CSI. Since the length of the pilot sequences scale with the number of transmit antennas, for massive MIMO systems downlink channel estimation requires long pilot sequences resulting in reduced spectral efficiency and the so-called pilot contamination due to sharing of the pilots in adjacent cells. In this dissertation we first review the problem of channel estimation in massive MIMO systems. Next, we study the problem of semi-blind channel estimation in the uplink in the case of spatially correlated time-varying channels. The proposed method uses the transmitted data symbols as virtual pilots to enhance channel estimation. An expectation propagation (EP) algorithm is developed to iteratively approximate the joint a posterior distribution of the unknown channel matrix and the transmitted data symbols with a distribution from an exponential family. The distribution is then used for direct estimation of the channel matrix and detection of the data symbols. A modified version of Kalman filtering algorithm referred to as KF-M emerges from our EP derivation and it is used to initialize our algorithm. Simulation results demonstrate that channel estimation error and the symbol error rate of the proposed algorithm improve with the increase in the number of BS antennas or the number of data symbols in the transmitted frame. Moreover, the proposed algorithms can mitigate the effects of pilot contamination as well as time-variations of the channel. Next, we study the problem of downlink channel estimation in multi-user massive MIMO systems. Our approach is based on Bayesian compressive sensing in which the clustered sparse structure of the channel in the angular domain is exploited to reduce the pilot overhead. To capture the clustered structure, we employ a conditionally independent identically distributed Bernoulli-Gaussian prior on the sparse vector representing the channel, and a Markov prior on its support vector. An EP algorithm is developed to approximate the intractable joint distribution on the sparse vector and its support with a distribution from an exponential family. This distribution is then used for direct estimation of the channel. The EP algorithm requires the model parameters which are unknown. We estimate these parameters using the expectation maximization (EM) algorithm. Simulation results show that the proposed combination of EM and EP referred to as EM-EP algorithm outperforms several recently-proposed algorithms in the literature