## 1 Introduction
Their computation costs will be significant with a massive array. As the effective solutions, hybrid analog/digital beamforming approaches have been studied [8; 16; 17; 18; 19]. Analog beamforming can reduce costly RF chains and the computation costs associated with digital processing. It requires beam training or search with the use of pre-determined beam patterns, and so causes an overhead. Exploiting the LoS dominant (i.e., sparse) nature of millimeter wave communication, compressed sensing based simplified CSI estimation schemes has also been investigated [18]. Though these studies also address CSI for supporting multiple stream transmission, evaluations have been limited to the single user MIMO scenario. As indicated above, there remains the possibility of further enhancing the system capacity in millimeter wave channels via multiuser MIMO. From the implementations viewpoint, multiuser MIMO transmission with multistream per UE requires SVD operation and block diagonalization (BD). It causes difficulty in hardware implementation. The equipment, which requires high speed and large amount of computation, should be operated as simple as possible. Assuming that we assign single stream to each UE, such signal processing include CSI estimation can be significantly simplified even though full digital processing and it is expected to save the hardware resource with optimized design. System capacity can be enlarged by spatially multiplexing a number of UEs. Given the above features, we focus on multiuser massive MIMO with only 1 st eigenmode transmission to each UE to achieve stable and high transmission capacity, even in high mobility situations. This paper proposes an approximate beamforming scheme based on highly efficient CSI estimation. It is based on frequency domain CSI interpolation schemes using sparsely arranged training subcarriers, on which power density is concentrated. Although numerous interpolation schemes have been investigated [20; 21], our proposal only extracts phase components with simple linear least squares regression, by using quite limited number of subcarriers. Furthermore, training subcarriers are dispersed on plural antenna elements to further reduce peak-to-average power ratio (PAPR) per antenna element. It reduces the burden of complexity and additive noise effect by roughly estimating the CSI from the LoS component. The two key contributions of this paper are: (1) the robustness of 1 st eigenmode transmission is validated by comparisons of the achievable throughput with the parameter of the stream number allocated per UE; and (2) a simplified beamforming scheme based on highly efficient CSI estimation is introduced and verified. The rest of this paper is organized as follows. Section 2 defines the system model and presents the methodology of multiuser massive MIMO eigenmode transmission. Section 3 describes the proposed scheme: simplified beamforming based on highly efficient CSI estimation. Computer simulation results are shown in Section 4. Finally, Section 5 concludes the paper. Throughout the paper, normal letters represent scalar quantities, bold lowercase letters indicate vectors and uppercase letters indicate matrices. \(|.,|1.|,|.|,(. )^{T}\), and \((. )^{H}\) represent absolute values, Frobenius norm, transpose and conjugate transpose, respectively.