## 2 System Definition  
### System and Channel Model  
This paper examines the downlink transmission of a single cell multiuser massive MIMO system. BS with an \(Nt\) element uniform planar array (UPA) serves \(Nu\) UEs with \(Nr\) element UPA where each UE is assigned \(N\)s signal streams. To ensure the LoS environment and reduce the probability of human blockage [22], BS is assumed to be located on the ceiling and UEs are facing straight up, as shown in Figure 1.  
Assuming orthogonal frequency division multiplexing (OFDM) transmission, we define the channel matrix per subcarrier, \(\mathbf{H}\in^{NuNr\times Nt}\), as follows:  
\[\mathbf{H}=\ \ \left[ \begin{array}{cccc}\mathbf{H}_{1}^{T}&\cdots&\mathbf{H}_ {i}^{T}&\cdots&\mathbf{H}_{Nu}^{T}\end{array} \right]^{T} \tag{1}\]  
Figure 1: System model: (**a**) Multistream transmission per user equipment (UE): \(Nu=4\) and \(Ns=4\); and (**b**) 1 st eigenmode transmission per UE: \(Nu=16\) and \(Ns=1\). where \(\mathbf{H}_{i}\in{}^{N\times Nt}\) denotes the channel sub matrix between the \(i\)-th UE and BS. Note these expressions are per subcarrier so indices are omitted. A Rician fading channel is considered so \(\mathbf{H}_{i}\) is expressed using Rician \(K\)-factor as:  
\[\mathbf{H}_{i}=\sqrt{\frac{K}{K+1}}\ \mathbf{H}_{LoS,i}+\sqrt{\frac{1}{K+1}}\ \mathbf{H}_{NLoS,i} \tag{2}\]  
\(\mathbf{H}_{LoS,i}\) is determined by the spatial relationship of the \(i\)-th UE and BS:  
\[H_{LoS,i}=\left[ \begin{array}{cccc}e^{-2\pi\frac{d_{1N}}{\lambda}}&\cdots&e^ {-2\pi\frac{d_{1N}}{\lambda}}\\ \vdots&\ddots&\vdots\\ e^{-2\pi\frac{d_{1N}}{\lambda}}&\cdots&e^{-2\pi\frac{d_{1N}}{\lambda}}\\ \end{array} \right] \tag{3}\]  
where \(d_{mn}\) is the distance between the \(m\)-th UE antenna element and the \(n\)-th BS antenna element. \(\lambda\) is the carrier wavelength. Path loss component is omitted here. The channel time variation of \(\mathbf{H}_{LoS,i}\) is simulated by the spatial relationships between the UEs and the BSs determined by UE movement. \(\mathbf{H}_{NLoS,i}\) is the non-line-of-sight (NLoS) component from the scatters, which are uniformly sited around the UEs. To consider the spatial correlation between BS antenna elements, independent identically distributed (i.i.d.) Rayleigh fading channels are converted into correlated channels using the Kronecker model [23]. \[\mathbf{H}_{NLoS,i}=\mathbf{R}_{rx,i}^{1/2}\mathbf{H}_{id,i}\left(\mathbf{R}_ {rx,i}^{1/2}\right)^{T} \tag{4}\]  
where correlation matrices \(\mathbf{R}_{tx,i}\in{}^{Nt\times Nt}\) and \(\mathbf{R}_{rx,i}\in{}^{Nr\times Nr}\) are expressed as,  
\[\mathbf{R}_{tx,i}=\left( \begin{array}{cccc}1&\rho_{rx1,rx2}^{(i)}&\cdots& \rho_{rx1,rxNr}^{(i)}\\ \rho_{rx2,rx1}^{(i)}&1&\cdots&\rho_{rx2,rxNr}^{(i)}\\ \vdots&\vdots&\ddots&\vdots\\ \rho_{rxNr,rx1}^{(i)}&\rho_{rxNr,rx2}^{(i)}&\cdots&1\\ \end{array} \right) \tag{5}\]  
\[\mathbf{R}_{rx,i}=\left( \begin{array}{cccc}1&\rho_{rx1,rx2}^{(i)}&\cdots& \rho_{rx1,rxNr}^{(i)}\\ \rho_{rx2,rx1}^{(i)}&1&\cdots&\rho_{rx2,rxNr}^{(i)}\\ \vdots&\vdots&\ddots&\vdots\\ \rho_{rxNr,rx1}^{(i)}&\rho_{rxNr,rx2}^{(i)}&\cdots&1\\ \end{array} \right) \tag{6}\]  
Spatial correlation coefficient between the \(p\)-th and the \(q\)-th antenna elements is derived as [24]:  
\[\rho_{p,q}=\frac{\int_{\omega}^{\pi}\int_{-\pi}^{\pi}A_{p}(\psi,\theta)A_{q}( \psi,\theta)\,G(\psi,\theta)\,e^{-jW_{p,q}(\psi,\theta)}d\psi d\theta}{\int_{ \omega}^{\pi}\int_{-\pi}^{\pi}A_{p}(\psi,\theta)A_{q}(\psi,\theta)\,G(\psi, \theta)\,d\psi d\theta} \tag{7}\]  
UPA is arranged on \(xy\) plane, \(\psi\) [rad] is the AoA or angle of departure (AoD) from the \(x\)-axis toward the positive \(z\)-axis, and \(\theta\) [rad] is the angle from the positive \(y\)-axis toward the \(xz\) plane. \(A_{p}(\psi,\theta)\) [dB] is radiation pattern of the \(p\)-th antenna element.