A low-complexity 3D massive MIMO scheme jointly using statistical and instantaneous CSIT

Fan et al. EURASIP Journal on Wireless Communications and Networking (2016) 2016:235 DOI 10.1186/s13638-016-0723-0 R ES EA R CH Open Access A low-complexity 3D massive MIMO scheme jointly using statistical and instantaneous CSIT Lixing Fan1,2 , Shiwen He1,2 , Yongming Huang1,2 and Luxi Yang1,2* Abstract In this paper, we propose a three-dimensional (3D) beamforming scheme for the massive multiple-input multiple-output (MIMO) system where the base station (BS) employs a uniform rectangular array (URA). In order to avoid the high computational complexity involving large-dimensional channel matrices, a two-stage beamforming method is applied where the second-stage beamforming is a Kronecker product of azimuth and elevation discrete Fourier transform (DFT) beamforming. These DFT prebeamformers are used for cell splitting and form effective channels with lower dimension for first-stage precoding. We develop a low-complexity user grouping algorithm based on the statistical channel state information at the transmitter (CSIT) to partition users. Each group of users is served by the signal-to-leakage-and-noise ratio (SLNR) precoding aiming at suppressing the intra-group and adjacent-group interferences, which is a good balance between performance and complexity. We derive the approximate signal-to-interference-plus-noise ratio (SINR) of our proposed scheme. Numerical results validate that the SINR approximations are tight and indicate the significance of the proposed 3D beamforming scheme. Keywords: Massive MIMO, 3D MIMO, Deterministic equivalent 1 Introduction In order to meet the demand of explosively increasing data services, the massive multiple-input multiple-output (MIMO) system has emerged as a promising technology for the next generation of cellular systems [1–3]. The basic premise behind massive MIMO is to reap all the benefits of conventional MIMO on a much greater scale, by deploying a few hundred antennas at the base station (BS) to serve a multiplicity of users simultaneously in the same time-frequency resource [4–7]. However, in practice, it is infeasible to place a large number of antennas only in the azimuth direction at the BS. To cope with this limitation, three-dimensional (3D) MIMO has been introduced, where antennas are deployed in a two-dimensional (2D) grid at the BS to enable the multiplexing of many users in a multi-user MIMO (MU-MIMO) fashion [8–12]. *Correspondence: School of Information Science and Engineering, Southeast University, 2 Sipailou, 210096 Nanjing, People’s Republic of China 2 Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education, Southeast University, Nanjing 210096, China 1 In 3D MIMO, elevation antennas are exploited to design 3D beamforming. More users can thus be served by the 3D beamformer with the same azimuth but different elevation angles [13]. A practical method for performing per-user adaptation of the elevation direction is presented in [14], which is transparent to the Long-Term Evolution (LTE) standard and requires no changes to the existing mobiles. But no performance analysis is given. The achievable sum rate is analyzed for uplink 3D MIMO systems with zero-forcing (ZF) receivers in [15, 16]. In [17], 3D beamforming is developed which consists of azimuth two-stage beamforming and one elevation prebeamformer. This scheme takes advantage of cell splitting by prebeamformers and functions efficiently when users in the same group have identical angle of arrival (AoA) intervals but have nonoverlapping AoA intervals in the different groups. However, users are usually randomly distributed and the angle requirements cannot be guaranteed. Besides, elevation groups are designated by orthogonal time-frequency slots to assure near orthogonality, which does not exploit the full use of resources. © 2016 The Author(s). Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Fan et al. EURASIP Journal on Wireless Communications and Networking (2016) 2016:235 And the specific user grouping algorithm for 3D massive MIMO is not developed. In this paper, a low-complexity 3D beamforming scheme is proposed for the massive MIMO system where the BS deploys a uniform rectangular array (URA). We apply two-stage beamforming to avoid the high complexity involving the large-dimensional channel matrices. The second-stage beamforming is a Kronecker product of azimuth and elevation discrete Fourier transform (DFT) prebeamformers, since the 3D channel covariance can be approximated by a Kronecker product of azimuth and elevation correlations and it is possible to separate the 3D channel into azimuth and elevation directions which are respectively served by uniform linear arrays (ULAs) in associated directions at the BS [18]. Considering the one-ring scattering model, the azimuth and elevation correlations are characterized by Toeplitz matrices, and the eigenvector matrices of these Toeplitz matrices are approximated by submatrices of DFT matrix when the number of antennas is large [19, 20]. So, we apply the DFT beamforming as the azimuth and elevation prebeamformers, and their Kronecker product constructs the 3D prebeamformer. These DFT prebeamformers are used for cell splitting, and all groups are all working in the same time-frequency resource. We develop a low-complexity user grouping algorithm to partition users into groups using statistical channel state information at the transmitter (CSIT). The first-stage precoding is designed based on the effective channels formed by large-dimensional instantaneous channels and DFT prebeamformers, which has low complexity. We employ the signal-to-leakage-and-noise ratio (SLNR) precoding considering the intra-group and adjacent-group interferences which dominate the intergroup interferences. The SLNR precoding is designed based on the signal-to-leakage-and-noise ratio as the optimization metric, where leakage is a measure which quantifies the interference power caused by the desired user on the signal received by others [21]. It is a good balance between eliminating co-channel interference (CCI) and noise, while zero forcing (ZF) design considers the CCI only and suffers from noise enhancement. Moreover, the ZF precoding imposes a restriction on the number of antennas, while for SLNR precoding there is no requirement on the relation between the number of transmit and receive antennas. Compared to the signal-to-interferenceplus-noise ratio (SINR) precoding which is obtained iteratively due to the coupled optimization problem [22], the SLNR precoding admits a closed-form solution, since the SLNR metric results in a decoupled optimizati (...truncated)