## 2 System Model  
In this section, a general MU-MIMO setting composed of \(K\) UEs is considered as shown in Figure 1. At each symbol period, the gNB sends \(N_{s}\) data streams spatially multiplexed to \(K\) UEs. An OFDM transmission with \(N_{sc}\) subcarriers in the frequency domain is assumed. The complex symbols transmitted at the \(j\)th subcarrier are denoted as \(\mathbf{s}_{j}=\left[\mathbf{s}_{j}^{[1]},...,\mathbf{s}_{j}^{[K]}\right]^{T }\in\mathbb{C}^{N_{s}K\times 1},\forall j\in\{1,2,...,N_{sc}\},\forall k\in\{1,2,...,K\}\). In this equation, \(\mathbf{s}_{j}^{[k]}\in\mathbb{C}^{N_{s}\times 1}\) represents the \(N_{s}\) data streams transmitted to the \(k\)th UE. It is assumed that \(\mathbb{E}\left[\mathbf{s}_{j}^{[k]}\left(\mathbf{s}_{j}^{[k]}\right)^{H} \right]=\mathbf{I}_{N_{s}}\). The gNB and each UE are equipped with \(N_{t}\) and \(N_{r}\) antennas, respectively. The OFDM symbols are precoded in the gNB to avoid interference between the UEs. The precoding matrix is designed according to the 5G-NR standard. To avoid large overhead, contiguous subcarriers are grouped in a subband since they are likely to experience a comparable channel effect. The number of subcarriers in each subband is given by \(N_{f}=N_{sc}^{RB}N_{PRB}^{SB}\), where \(N_{sc}^{RB}\) is the number of subcarriers in each physical resource block (PRB) and \(N_{PRB}^{SB}\) is the number of PRB in each subband. Let \(\mathbb{A}=\{\mathcal{A}_{1},...,\mathcal{A}_{n},...,\mathcal{A}_{N_{SB}}\}\) denote the set of subbands, where \(\mathcal{A}_{n}\) contains the subcarriers that are in the \(n\)th subband. The total number of subbands \(N_{SB}\), given by the cardinality of the set \(N_{SB}=|\mathbb{A}|\), is defined according to the TS 38-214 [25]. The subcarriers inside the \(n\)th subband (i.e., \(\forall j\in\mathcal{A}_{n}\)) are precoded with the same matrix \(\mathbf{W}_{n}\) computed according to the 5G-NR standard. For simplicity, it is assumed that the number of physical transmit antennas is the same as that of virtual antenna ports. Therefore, the precoding matrix is given by \(\mathbf{W}_{n}=\left[\mathbf{W}_{n}^{[1]},...,\mathbf{W}_{n}^{[K]}\right]\in \mathbb{C}^{N_{i}\times N_{i}\times}\), where \(\mathbf{W}_{n}^{[k]}\in\mathbb{C}^{N_{i}\times N_{i}}\) is the precoder related to the \(k\)th UE. A codebook-based beamforming is considered, according to 5G-NR specifications. Therefore, the precoding matrix is selected from a set of predefined codebooks based on the knowledge that the gNB can acquire from the CSI. Therefore, a codebook-based CSI acquisition procedure is applied [2]. As illustrated in Figure 1, the channel is estimated at the UE by measuring known reference signals transmitted from the gNB called CSI reference signal (CSI-RS). A quantized version of the estimated CSI is reported from the UE to the gNB including information about the precoding matrix indicator (PMI) and rank indicator (RI), which identify the best precoding matrix according to the UE measurements. This information is used by the gNB as a recommendation to select the precoding matrix. CSI feedback has been designed in the 5G-NR standard to cover both Type I and Type II codebooks, for SU-MIMO and MU-MIMO, respectively [25; 39]. The received signal at the \(k\)th UE side is multiplied by the combining matrix \(\mathbf{U}_{j}^{[k]}\in\mathbb{C}^{N_{i}\times N_{s}}\) to maximize the signal to interference and noise ratio (SINR). With these considerations, the received symbol vector is expressed as [6]  
\[\hat{\mathbf{s}}_{j}^{[k]}=\left(\mathbf{U}_{j}^{[k]}\right)^{H}\mathbf{H}_{ j}^{[k]}\mathbf{W}_{n}^{[k]}\mathbf{s}_{j}^{[k]}+\left(\mathbf{U}_{j}^{[k]} \right)^{H}\mathbf{H}_{j}^{[k]}\sum_{i=1,j\
eq k}^{K}\mathbf{W}_{n}^{[i]} \mathbf{s}_{j}^{[i]}+\left(\mathbf{U}_{j}^{[k]}\right)^{H}\mathbf{n}_{j}^{[k]},\forall j\in\mathcal{A}_{n}, \tag{1}\]  
Figure 1: Block diagram of an MU-MIMO downlink transmission in 5G-NR composed of several stages. First, the gNB sends the CSI-RS to each UE.