## 2 System Definition
### MU-MIMO Eigenmode Transmittion  
When the number of UE antenna elements is larger than that of the transmission stream, i.e., \(Nr>Ns\), BS performs space division multiplexing (SDM) or beamforming in beam space [28]. The \(i\)-th UE obtains channel matrix \(\mathbf{H}_{i}\) and computes the SVD.  
\[\mathbf{H}_{i}=[\mathbf{U}_{i}\ \overline{\mathbf{U}}_{i}]\mathbf{\Sigma}_{i} \mathbf{V}_{i}^{H} \tag{13}\]  
where \(\mathbf{U}_{i}\in{}^{Nr\timesNs}\), \(\mathbf{\Sigma}_{i}\in{}^{Nr\times Nt}\), and \(\mathbf{V}_{i}\in{}^{Nt\times Nt}\) represent left singular matrix, singular value matrix whose diagonal elements are arranged in descending order, and right singular matrix, respectively. Using \(\mathbf{U}_{i}^{H}\) for the \(i\)-th UE provides effective MIMO channel matrix for BS, \(\mathbf{H^{\prime}}\in{}^{NuNs\times Nt}\);  
\[\mathbf{H^{\prime}}=\left[\ \ \left(\mathbf{U}_{1}^{H}\mathbf{H}_{1}\right)^{T} \ \ \cdots\ \ \left(\mathbf{U}_{i}^{H}\mathbf{H}_{i}\right)^{T}\ \ \cdots\ \ \ \left(\mathbf{U}_{Nu}^{H}\mathbf{H}_{Nu}\ \ \right)^{T}\right]\ ^{T} \tag{14}\]  
BS calculates the precoding weight via BD [28]. Here, the transmission/reception weight for the 1 st eigenmode steers the beam so as to obtain large gain. It extracts the path for the stable LoS component and, by comparison, suppresses NLoS components that have extremely strong time variation characteristics. Since massive MIMO enhances beamforming efficacy, it can be expected to further improve system robustness to the time varying channels. This fundamental characteristic is verified here. Figure 2 shows the normalized correlation of the effective channel vector defined as:  
\[C_{j}(t)=\ \frac{\left|\left\{\ \mathbf{u}_{ij}^{H}\mathbf{H}_{i}(0)\right\} \ \left\{\ \mathbf{u}_{ij}^{H}\mathbf{H}_{i}(t)\right\}^{H}\right|}{\left|\ \mathbf{u}_{ij}^{H}\mathbf{H}_{i}(0)\right|\ \left|\ \left|\ \mathbf{u}_{ij}^{H}\mathbf{H}_{i}(t)\right|\ \right|} \tag{15}\]  
where \(\mathbf{H}_{i}(t)\) represents the channel matrix for the \(i\)-th UE at instant \(t\); it is composed of the channel coefficient between \(Nr\) UE antenna and \(Nt\)(=256) BS antenna elements. \(\mathbf{u}_{ij}\in{}^{Nr\times 1}\) is singular vector for the \(j\)-th eigenmode, i.e., \(\mathbf{U}_{i}=[\mathbf{u}_{i1},\ldots,\mathbf{u}_{ij},\ldots,\mathbf{u}_{iNs}]\). Note that \(\mathbf{U}_{i}\) is obtained from the CSI at \(t=0\). UE speed is assumed to be 10 km/h and Rician \(K\) factor is 10 dB. Figure 2(a) plots channel correlation fluctuation of four eigenmodes when \(Nr=16\). As shown, the correlations of the 2 nd-4 th eigenmodes rapidly decrease and fluctuate at a lower value while that of the 1 st eigenmode is almost always 1. Multistream transmission per UE is considered to be severely affected by the channel time variation, especially in the 2 nd and higher order eigenmodes. Figure 2(b) depicts channel correlation of the 1 st eigenmode over time with the number of UE antenna elements, \(Nr\), as the parameter. Increasing \(Nr\) can suppress the channel fluctuation impact. These fundamental results yield the expectation that 1 st eigenmode transmission with large antenna arrays can achieve quite stable multiuser SDM performance.