## 2 System Model Discussion  
We consider a single-cell system, where the BS is equipped with transmit antennas where \(N\gg 1\), which transmits TSs and data for \(K\) single antenna users with \(N\gg K\). Massive MIMO technology is used to improve the performance of wireless communications networks by distributing signals through multiple antennas [45]. This allows for joint beamforming, which enhances the network capacity and improves the overall experience of the users [46]. Instead of using large horizontal linear arrays with hundreds of antennas that would create narrow beams in the azimuth, compact planar panels with limited angular resolution in the azimuth (horizontal) and elevation (vertical) domains are being used. Hence, a UPA is considered in this paper. Due to the closely spaced antenna elements at the BS, the correlation is increased in an m-MIMO system. According to typical wireless networks, the coherence block length that is available for transmission resources consists of time and frequency symbols. These symbols represent the intervals of time and frequency during which the channel responses remain mostly constant [47; 48; 49; 50]. Extension to orthogonal frequency-division multiple (OFDM) could be considered in the future [51; 52]. In this paper, the available CCT denoted by \(\tau_{\rm c}\in\mathbb{Z}^{+}\) is divided into training time period \(\tau_{\rm tr}\) and data transmission period \(\tau_{\rm d}\). The coherence length that can be used for transmission in both the UK and DL is divided between them. The transmit energy can be divided between the TS stage and the data transmission stage. Figure 1 demonstrates the system model with a coherence block length of \(\tau_{\rm c}\in\mathbb{Z}^{+}\), which consists of the DL TS and data transmission in m-MIMO systems with an FDD operation mode. The signal received by the \(k\)th user in the data-transmission stage in the DL can be expressed as [53]  
\[y_{k}=\sqrt{\rho_{\rm d}}\,\mathbf{h}_{k}^{\rm T}\mathbf{Vs}+z_{k}, \tag{1}\]  
where parameter \(\mathbf{s}=[s_{1},\ldots,s_{K}]^{\rm T}\in\mathbb{C}^{K}\) represents independent and identical distribution (iid) of a data signal with a zero-mean circularly symmetric complex-Gaussian (CSCG) with power constraint of \(\mathbb{E}[\mathbf{s}\mathbf{s}^{\rm H}]=\mathbf{I}_{K}\), and \(\mathbf{V}=[\mathbf{v}_{1},\ldots,\mathbf{v}_{K}]\in\mathbb{C}^{N\times K}\) is the precoding matrix. Extension to color noise could be considered in the future [54]. The DL instantaneous channel intended between the BS and the \(k\)th user \(\mathbf{h}_{k}\in\mathbb{C}^{N}\) is given by \(\mathbf{h}_{k}=\mathbf{R}_{k}^{1/2}\mathbf{\tilde{h}}_{k}\), where the elements of \(\mathbf{\tilde{h}}_{k}\in\mathbb{C}^{N}\) are iid with CSCG. The \(k\)th user CCM, \(\mathbf{R}_{k}\) is given by \(\mathbf{R}_{k}=\mathbb{E}\left[\mathbf{h}_{k}\mathbf{h}_{k}^{\rm H}\right]\in \mathbb{C}^{N\times N}\), with \(\mathbf{R}_{k}\succeq\mathbf{0}_{N}\), which represents the transmit correlation matrix. Additive noise \(z_{k}\) is modeled as an iid with CSCG random variable. The received signal to interference and noise ratio SINR, represented by \(\mathbf{f}_{k}\), can be written as \[\mathrm{fl}_{k}=\frac{\left|\,\mathbf{h}_{k}^{\mathrm{T}}\mathbf{v}_{k}\,\right|^{2 }}{\frac{1}{\rho_{\mathrm{d}}}+\sum_{l\
eq k}^{K}|\,\mathbf{h}_{k}^{\mathrm{T}} \mathbf{v}_{l}|^{2}}, \tag{2}\]  
where \(1/\rho_{\mathrm{d}}\) refers to the reciprocal of the SNR. The received signal, i.e., SINR, is influenced by various statistics and the specific precoding technique adopted by the BS, which depends on channel estimation. In terms of information theory, the best precoding strategy for multiuser MIMO systems is achieved by using dirty paper coding (DPC) [55; 56]. Nevertheless, precoding with DPC is still not practically feasible due to its high design complexity [57]. Linear precoding can be utilized instead of DPC to offer a performance that is not optimal but still satisfactory while keeping the design complexity low [58; 59].