## 2 System Description  
### Massive MIMO Model  
We consider a downlink massive MIMO system with \(N_{t}\) TX antennas, and \(K\) single antenna UEs and/or IoT devices/sensors. The received signal vector at UEs can be represented as follows:  
\[\mathbf{y} = \sqrt{\rho_{t}}\mathbf{G}\mathbf{s}+\mathbf{n}, \tag{1}\]  
where \(\mathbf{y}\) is the \(K\times 1\) received signal vector for \(K\) UEs, \(\rho_{t}\) is the total TX power for forward link, \(\mathbf{G}\) is the \(K\times N_{t}\) channel matrix between the transmitter with \(N_{t}\) TX antennas and \(K\) UEs, \(\mathbf{s}\) is the \(N_{t}\times 1\) TX signal vector, and \(\mathbf{n}\) is the \(K\times 1\) additive white Gaussian noise (AWGN) vector at the UEs (i.e., \(\mathbf{n}\sim CN(\mathbf{0}_{K},\sigma_{d}^{2}\mathbf{I}_{K})\)) where \(\sigma_{d}^{2}\) is the variance of AWGN. \(\mathbf{G}\) consists of both a small scale fading channel matrix, \(\mathbf{H}\) and large scale fading channel matrix, \(\mathbf{B}\), i.e., \(\mathbf{G}=\mathbf{H}\circ\mathbf{B}\) where \(\circ\) indicates the componentwise product. \(\mathbf{H}\) is the independent and identically distributed (i.i.d) Rayleigh fading channel matrix with zero mean and unit variance which can be represented as:  
\[\mathbf{H}=\left( \begin{array}{cccc}h_{1,1}&h_{1,2}&\cdots&h_{1,N_{t}}\\ h_{2,1}&h_{2,2}&\cdots&h_{2,N_{t}}\\ \vdots&\vdots&\vdots&\vdots\\ h_{K,1}&h_{K,2}&\cdots&h_{K,N_{t}}\end{array} \right), \tag{2}\]  
\(\mathbf{B}\) is the large scale fading channel matrix which can be represented as:  
\[\mathbf{B}=\left( \begin{array}{cccc}\sqrt{\beta_{1,1}}&\sqrt{\beta_{1,2}}& \cdots&\sqrt{\beta_{1,N_{t}}}\\ \sqrt{\beta_{2,1}}&\sqrt{\beta_{2,2}}&\cdots&\sqrt{\beta_{2,N_{t}}}\\ \vdots&\vdots&\vdots&\vdots\\ \sqrt{\beta_{K,1}}&\sqrt{\beta_{K,2}}&\cdots&\sqrt{\beta_{K,N_{t}}}\end{array}  \right), \tag{3}\]  
where \(\beta_{i,j}\) is the path loss component from \(j\)th antennas in BS to \(i\)th UE. Then, the combined channel matrix \(\mathbf{G}=\mathbf{H}\circ\mathbf{B}\) can be represented as:  
\[\mathbf{G}=\left(\begin{array}{cccc}h_{1,1}\sqrt{\beta_{1,1}}&h_{1,2}\sqrt {\beta_{1,2}}&\cdots&h_{1,N_{t}}\sqrt{\beta_{1,N_{t}}}\\ h_{2,1}\sqrt{\beta_{2,1}}&h_{2,2}\sqrt{\beta_{2,2}}&\cdots&h_{2,N_{t}}\sqrt{ \beta_{2,N_{t}}}\\ \vdots&\vdots&\vdots&\vdots\\ h_{K,1}\sqrt{\beta_{K,1}}&h_{K,2}\sqrt{\beta_{K,2}}&\cdots&h_Since the path loss components from 1 th, 2 nd, \(\cdots\), \(N_{t}\)th antenna in BS to antenna in \(i\)th UE are almost the same, for the path loss component from BS to \(i\)th UE, \(\beta_{i}\), we can represent as follows:  
\[\beta_{i}=\beta_{i,1}=\beta_{i,2},\cdots,\beta_{i,N_{t}}. \tag{5}\]  
where \(i=1,2,\cdots,K\). Note that, to get the benefit of channel hardening effect, usually the massive MIMO antenna systems should satisfy the condition of \(N_{t}>10K\)[26; 27]. There is no strict criterion to get the channel hardening effect, but we can asymptotically observe the effect when \(N_{t}\) is larger than \(10K\). Figure 1 presents the simulation to show the channel hardening effect. The x-axis of the figure represents the ordered eigenvalue of \(\mathbf{HH}^{H}\), and y-axis represents the cumulative distribution function (CDF). The figure shows the case in which the number of UEs is fix to \(K=4\), and the number of TX antennas increases as \(N_{t}=4,\,40\), and \(400\). As \(N_{t}\) increases, the randomness of the channel significantly reduces. Likewise, due to the law of large numbers, as \(N_{t}\) increases, the level of interference also converges to a certain constant. Figure 2 presents the normalized interference power versus number of trials. Figure 2 is the result when we use the matched filtering (MF) precoding which will be introduced in the next subsection. As observed, as \(N_{t}\) increases, the variation of interference reduces. It is very close to a constant when \(N_{t}=10K\).