Abstract
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.
Highlights
S INCE the length of the pilot sequence must be no less than the number of transmitting antennas, for massive MIMO systems [1], [2] pilot-based channel estimation in the downlink (DL) is very challenging
To benchmark the performance of semi-blind KF-M, KS-M, and expectation propagation (EP), we present the performance of the Kalman filter and smoother in a pure training mode (TM) when the entire frame is composed of known pilot symbols and only channel estimation is performed
To benchmark the performance of KF-M, KS-M, and EP, we present the performance of the Kalman filter and smoother in a pure training mode (TM) when the entire frame is composed of known pilot
Summary
S INCE the length of the pilot sequence must be no less than the number of transmitting antennas, for massive MIMO systems [1], [2] pilot-based channel estimation in the downlink (DL) is very challenging. A semi-blind method is developed for joint channel estimation and data detection in which the users transmit a few pilot symbols (on the order of the number of users) at the beginning of each frame. To benchmark the performance of semi-blind KF-M, KS-M, and EP, we present the performance of the Kalman filter and smoother in a pure training mode (TM) when the entire frame is composed of known pilot symbols and only channel estimation is performed. These two cases, are referred to as KF-TM and KS-TM. To demonstrate that the semi-blind algorithms developed under the assumption of a block-fading channel are not suitable for a time-varying channel model, we compare our results with those from [13] and [15]
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