Physical Communication 42 (2020) 101138 Contents lists available at ScienceDirect Physical Communication journal homepage: www.elsevier.com/locate/phycom Full length article Downlink channel estimation of FDD based massive MIMO using spatial partial-common sparsity modeling N. Shalavi a , M. Atashbar a,∗ , M. Mohassel Feghhi b a Department of Electrical Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran b School of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran article info Article history: Received 3 November 2019 Received in revised form 26 May 2020 Accepted 27 May 2020 Available online 29 May 2020 Keywords: Channel estimation Compressive sensing FDD Massive MIMO abstract Downlink channel estimation in FDD massive MIMO systems is a challenge in 5G wireless communi- cation systems. Using orthogonal pilots for downlink channel estimation leads to the pilot overhead problem. To cope with this problem, spatio-temporal common sparsity feature of delay domain beside the compressive sensing algorithm has used for channel estimation. In a practical affair, the spatial common sparsity of the adjacent antennas groups is not entirely separate. In this paper, we model the FDD massive MIMO downlink frequency selective channel estimation problem by a spatial partial- common sparsity, in which it is assumed that the spatial sparsity pattern of antennas in each group has a common part and an uncommon part. For the proposed model, we design a proper pilot sequence, and finally, we propose an estimation method associated with this model to solve the problem. Our proposed method has better NMSE and BER performance than reference methods in the same pilot overhead ratio, which is shown in the simulation results. © 2020 Elsevier B.V. All rights reserved. 1. Introduction There is a growing need for more wireless throughput, while the accessible electromagnetic spectrum not changes. Massive Multiple Input Multiple Output (MIMO) is a hopeful technol- ogy that makes high throughput wireless communication achiev- able [1]. In the massive MIMO, there is a large number of antennas in Base Station (BS), which simultaneously serves users with one or a small number of antennas [2]. Larger antenna arrays can make more focused beams in desired directions. Beam focusing is performed by pre-coding the signals associated with a par- ticular user. To perform pre-coding, channel state information (CSI) must be known in BS [3]. On the other hand, the CSI is required for accurate detection in the receivers of both BS and Mobile Station (MS). So it is essential to estimate CSI with high accuracy. Estimating uplink channel state information is much easier than that of the downlink channel. In the uplink, different users send countable data streams to BS, and BS with powerful computational ability can estimate CSI reliably [4]. In massive MIMO systems with Time Division Duplex (TDD) protocol, down- link channel state information can be obtained using the uplink estimated channel and channel reciprocity property directly [5]. ∗ Corresponding author. E-mail addresses: neda.shalavi@ymail.com (N. Shalavi), atashbar@azaruniv.ac.ir (M. Atashbar), mohasselfeghhi@tabrizu.ac.ir (M. Mohassel Feghhi). Nevertheless, it is shown that hardware impairment can degrade channel estimation accuracy in TDD Massive MIMO systems [6]. In Frequency Division Duplex (FDD) protocol, according to use of different frequencies in uplink and downlink, uplink channel estimation results cannot be used as the downlink channel; thus, downlink channels should be estimated. Since there is a large number of antenna in BS and a small number of antenna (or one antenna) in MS, the downlink channel estimation in FDD massive MIMO systems is a challenge. Orthogonal pilots are commonly used for downlink channel estimation of the classical MIMO sys- tems, in which to estimate downlink channels (in MS) associated with each antenna of BS, at least one pilot is required. On the other hand, in the wireless channels, the value of coherence time (in which the channel between BS and MS is time-invariant) is limited. Thus, both channel estimation and information transmis- sion should be performed in coherence time duration. According to the need for the pilot transmission in channel estimation, we cannot use the total duration of coherence time for transferring the information symbols. Pilot overhead is the ratio of the amount of pilots to all symbols sent from BS. If 10% of symbols sent from BS is pilot and 90% of it is information data, then the pilot over- head is 10%. This also affects the achievable data rate. Since the number of antennas is not large in the classical MIMO systems, pilot overhead will not be a problem in these systems [7]. In massive MIMO, as numerous BS antennas send signals to each user, the pilot overhead grows large. Such a high pilot overhead problem prevents precise channel estimation. https://doi.org/10.1016/j.phycom.2020.101138 1874-4907/© 2020 Elsevier B.V. All rights reserved.