## 5 Simulation Results
### SE Bounds Achieved by Type I Codebook  
In this subsection, the performance bounds of the Type I codebook are evaluated for SU-MIMO systems. The SE is obtained averaging over all the subcarriers as \(R=\frac{1}{N_{sc}}\sum_{j=1}^{N_{sc}}R_{j}\), where \(R_{j}\) is the SE per subcarrier defined in (2). Figures 4-6 illustrate the average SE for a range of SNR between \(-5\) and \(15\) dB and assuming different antenna configurations at the gNB. The number of receive and transmit antennas is set to \(N_{r}=4\), and \(N_{t}=8\) (i.e., 8 CSI-RS antenna ports), respectively. Therefore, the maximum number of parallel layers allowed is \(N_{s}=4\). Figures 4 and 5 are obtained for a single-panel antenna array with \(N_{1}=4\), \(N_{2}=1\) (i.e., ULA ), and \(N_{1}=2\), \(N_{2}=2\) (i.e., UPA), respectively. Figure 6 depicts the performance achieved by a multi-panel antenna array with \(N_{g}=2,N_{1}=2,N_{2}=1\). The results obtained with the 5G-NR design are compared with the optimal solution given by the SVD of the channel matrix which serves as a benchmark [5]. It can be noted that for all the configurations shown, the performance of the SVD is better than 5G-NR solution at the cost of perfect knowledge of the channel matrix at both the gNB and UE sides. This is not a practical assumption in real scenarios as it would require an unfeasible overhead. On the contrary, the 5G-NR solution is designed to achieve a trade-off between performance, low overhead, and complexity. Therefore, since the gNB computes the precoding matrix based on a predefined codebook set and using the PMI index transmitted from the UE, the performance is degraded in comparison to the optimal SVD solution. However, the overhead is significantly reduced because only a few bits are required to transmit the PMI. In order to illustrate the complexity and overhead advantages of 5G-NR over SVD, a practical example will be shown. According to TS 38-212 [39] and TS 38-214 [25], in the case of single-panel ULA with \(N_{1}=4\) and \(N_{s}=4\), the PMI requires 6 bits to report the wideband parameters and a single bit per subband to feedback the frequency selective coefficients. Since \(N_{SB}=13\), a total of 19 bits are used to compute the precoding matrix. On the contrary, for the same gNB configuration, the SVD needs to report an \(8\times 4\) matrix with complex coefficients from the UE to the gNB. Assuming an 8-bit quantization, a total of 6656 bits must be fed back. This amount of bits to report the CSI from the UE to the gNB is not affordable in practical applications because it leads to several drawbacks. First, the probability that the CSI will be correctly decoded by the gNB is lower than with smaller report sizes. Therefore, packet segmentation at the UE side might be needed. This means that the report is fed back in different scheduling periods which will introduce more latency and complexity. Moreover, packet retransmission could be a necessity and the delay in the network will be increased. It can be noted that a higher number of parallel layers does not always translate into a higher SE. The value of \(N_{s}\) that achieves the highest performance depends on the channel matrix, antenna configuration, and the value of SNR. Therefore, the UE reports to the gNB the RI of the precoding matrix that corresponds to the value of \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Value** \\ \hline Size of the bandwidth part & \(N_{BWP}=52\) PRB \\ \hline Number of subcarriers per PRB & \(N_{sc}^{RB}=12\) \\ \hline Number of subcarriers of the OFDM grid & \(N_{sc}=624\) \\ \hline Subcarrier Spacing & \(\Delta_{f}=15\,\mathrm{kHz}\) \\ \hline Subband Size & \(N_{PRB}^{SB}=4\) PRB \\ \hline Number of subbands & \(N_{SB}=13\) \\ \hline Symbols per slot & \(N_{symb}^{slot}=14\) \\ \hline Slots per frame & \(N_{slot}^{frame}=10\) \\ \hline Number of frames & 5 \\ \hline CSI-RS period & 4 slots \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. \(N_{s}\) that attains the highest SE.