The spectral efficiency of multi-cell multi-user distributed antenna system with imperfect channel state information (CSI) is studied in this paper. First, considering the pilot contamination and minimum mean-squared-error (MMSE) channel estimation, the equivalent channel model is presented and the sum-rate of the uplink transmission is derived. Under a physical channel model, the equivalent channel model can be seen as a special case of the joint correlated MIMO channel model proposed by Gao [1]. Then, the closed-form approximation of the spectral efficiency is derived. The spectral efficiency of the system with large number of antennas is also studied. Finally, the theoretical results are compared with Monte-Carlo simulation, and the performances of DAS and co-located massive MIMO are also compared. It is shown that similar to the systems with perfect CSIs, DAS still has large performance gains compared with massive MIMO.
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