Digital precoding techniques have been widely applied in multiple-input multiple-output (MIMO) systems to enhance spectral efficiency (SE) which is crucial in 5G New Radio (NR). Therefore, the 3rd Generation Partnership Project (3GPP) has developed codebook-based MIMO precoding strategies to achieve a good trade-off between performance, complexity, and signal overhead. This paper aims to evaluate the performance bounds in SE achieved by the 5G-NR precoding matrices in single-user (SU) and multi-user (MU) MIMO systems, namely Type I and Type II, respectively. The implementation of these codebooks is covered providing a comprehensive guide with a detailed analysis. The performance of the 5G-NR precoder is compared with theoretical precoding techniques such as singular value decomposition (SVD) and block-diagonalization to quantify the margin of improvement of the standardized methods. Several configurations of antenna arrays, number of antenna ports, and parallel data streams are considered for simulations. Moreover, the effect of channel estimation errors on the system performance is analyzed in both SU and MU-MIMO cases. For a realistic framework, the SE values are obtained for a practical deployment based on a clustered delay line (CDL) channel model. These results provide valuable insights for system designers about the implementation and performance of the 5G-NR precoding matrices.

Advanced multiple-input multiple-output (MIMO) beamforming techniques are crucial in 5G New Radio (NR) to achieve the expected data rate values. Therefore, the 3rd Generation Partnership Project (3GPP) has proposed a codebook-based MIMO precoding strategy to provide high diversity, array gain, and spatial multiplexing. The main goal is to obtain a tradeoff between performance, signal overhead, and complexity. The precoding matrix is selected from a set of predefined codebooks based on the knowledge that the 5G-NR base station (gNB) acquires about the channel status. In this work, a detailed study of the precoding matrix design is provided following the guidelines reported in the technical specifications 38-211 and 38-214 of the 3GPP. An analysis of the performance in terms of spectral efficiency (SE) achieved by the 5G-NR precoding matrices is illustrated for a single-user MIMO scenario. These results are contrasted against the optimal singular value decomposition (SVD) solution in order to explore the gap between the standardized precoding proposal and the optimal one. Several values of signal-to-noise ratio (SNR) and different antenna array configurations are considered. Moreover, the multiplexing gain for a different number of parallel data streams is evaluated. Numerical results show the SE bounds that can be obtained with the 5G-NR precoding matrices. These insights are of key importance for practical implementation of precoding strategies in 5G-NR systems and beyond.