Regular paper Blind downlink channel estimation of multi-user multi-cell massive MIMO system in presence of the pilot contamination Parisa Pasangi a , Mahmoud Atashbar a,⇑ , Mahmood Mohassel Feghhi b a Department of Electrical Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran b Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran article info Article history: Received 8 July 2019 Accepted 27 January 2020 Keywords: Downlink channel Massive MIMO Multi-cell Pilot contamination TDD abstract The pilot contamination is a challenge of channel estimation in multi-user multi-cell massive Multiple Input Multiple Output (MIMO) system. In the Time Division Duplexing (TDD) technique, the uplink estimated channel is used for pre-coding the downlink signals, which leads to converting the downlink channel estimation to channel gain estimation. The classical method for the channel gain estimation is pilot-based estimation, which has several problems such as low spectral efficiency. In this paper, we pro- pose a blind method for estimating the downlink channel gain in the TDD based multi-cell multi-user massive MIMO system in the presence of the pilot contamination. In the proposed method, we show that the average energy of the downlink received signal to each user is a function of the channel gain, thus by calculating this average energy using samples of the received signal, the channel gain is estimated. The convergence of the proposed method is analyzed theoretically, and the performance of the proposed method is evaluated with simulation results. Ó 2020 Elsevier GmbH. All rights reserved. 1. Introduction The massive MIMO system is equipped with a large number of antennas at the Base Station (BS) and a single antenna (or a few numbers of antennas) in Mobile Station (MS). The massive MIMO system has many advantages over a typical MIMO system, includ- ing spectral efficiency [1], improved link reliability [2], reduced interference between users [2]. Recently, the focus has shifted to Multi-User (MU) massive MIMO systems, in which a BS simultane- ously serves multiple mobile stations. Lower equipment costs and higher multi-user diversity are some advantages of the MU mas- sive MIMO systems [3]. Channel estimation is a key issue in MU massive MIMO system. Due to the existence of a large number of receiver antennas in the uplink, the channel estimation is simple in this direction. But, in the downlink, each user should estimate several channel coeffi- cients between the MS antenna and all antennas of the BS using received signal, which leads to some problems in the downlink channel estimation of massive MIMO such as pilot overhead [4]. One way to solve this problem is the use of the TDD technique [3], in which the uplink estimated channel is used in the downlink for signal detection. This scenario accompanies with some errors, such as uplink channel estimation error and time variation of the channel, which leads to corruption in the system performance [4,5]. To solve this problem, in the TDD technique, in addition to estimating the uplink channel, the downlink channel also is esti- mated to ensure accurate signal detection in MS. The classical method for this purpose is pilot-based channel estimation [4–6], which leads to problems such as pilot overhead and low spectral efficiency [7]. To solve these problems, a blind channel estimation method is used. In most cases, the blind channel estimation methods are used for estimating the uplink channels, such as Independent Compo- nent Analysis (ICA) based method [8], subspace-based method [9,10], and the method based on the reduction of the order of received signal covariance matrix [11], which cannot be used to blind estimation of downlink massive MIMO channels. On the other hand, in the TDD based MU massive MIMO system, by applying the proper pre-coding, the downlink channel estima- tion problem is reduced to downlink channel gain estimation. A common method for estimating the downlink channel gain is the average channel gain, which leads to some problems such as a lot of estimation error and needing to knowledge of some statistics of the channel [12–14]. To solve these problems, Ngo et al. [12] presented a blind method for estimating the downlink channel https://doi.org/10.1016/j.aeue.2020.153099 1434-8411/Ó 2020 Elsevier GmbH. All rights reserved. ⇑ Corresponding author at: Department of Electrical Engineering, Azarbaijan Shahid Madani University, Tabriz 53714-161, Iran. E-mail addresses: p.pasangi@azaruniv.ac.ir (P. Pasangi), atashbar@azaruniv.ac.ir (M. Atashbar), mohasselfeghhi@tabrizu.ac.ir (M. Mohassel Feghhi). Int. J. Electron. Commun. (AEÜ) 117 (2020) 153099 Contents lists available at ScienceDirect International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue