# Spectral Efficiency of Precoded 5G-NR in Single and Multi-User Scenarios under Imperfect Channel Knowledge: A Comprehensive Guide for Implementation

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## Abstract

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## 1. Introduction

#### 1.1. Related Works

#### 1.2. Motivation

#### 1.3. Contribution

- A detailed description of the 5G-NR precoding matrices implementation covering both Type I and Type II codebook is provided. Each implementation step outlined in the standard is complemented with the corresponding theoretical explanation to improve its understanding, thus providing a comprehensive guide.
- The SE bounds of the 5G-NR precoding matrices are first obtained for a SU-MIMO scenario by using the Type I codebook. These suboptimal precoding matrices are compared with the optimal singular value decomposition (SVD) solution [5] in order to quantify the margin of improvement that could be attained in future precoding designs. It has been found that an increase in the number of parallel layers does not always imply a higher SE and the best choice has been determined in several configurations.Also, the impact on performance of linear or planar arrays is addressed.
- Then, these results are extended to an MU-MIMO system based on the Type II codebook design. The performance achieved with the standardized solution is compared with the theoretical block-diagonalization ZF method described in [37,38]. The saturation effect experienced in SE for high SNR values due to interference is exhibited. It is demonstrated how the usage of Type II codebook is limited to users with low spatial correlation.
- The effect of imperfect channel estimation on system performance is numerically evaluated in both cases, single-user and multi-user.
- Moreover, the simulations are performed for several configurations of antenna arrays, number of antenna ports, and parallel data streams. To guarantee a realistic scenario, a clustered delay line (CDL) channel model defined in the 3GPP technical report (TR) 38-901 is considered.

#### 1.4. Paper Organization

## 2. System Model

## 3. Precoding Matrix Design Based on Type I 5G-NR for SU-MIMO

#### 3.1. Type I Single-Panel

#### 3.2. Type I Multi-Panel

## 4. Precoding Matrix Design Based on Type II 5G-NR for MU-MIMO

## 5. Simulation Results

#### 5.1. SE Bounds Achieved by Type I Codebook

#### 5.2. SE Bounds Achieved by Type II Codebook

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

$\mathbf{W}$ | Precoding matrix |

${\mathbf{W}}_{1}$ | Wideband precoding matrix |

${\mathbf{w}}_{2}$ | Subband precoding vector |

$\mathbf{U}$ | Combining matrix |

$\mathbf{H}$ | Channel matrix |

$\mathbf{s}$ | Data symbols vector |

$\mathbf{n}$ | noise vector |

R | Spectral-efficiency |

K | Number of UEs |

${N}_{s}$ | Number of multiplexed data streams |

${N}_{SB}$ | Number of subbands |

${N}_{sc}$ | Number of subcarriers |

${N}_{f}$ | Number of subcarriers in each subband |

${N}_{sc}^{RB}$ | Number of subcarriers in each physical resource block |

${N}_{PRB}^{SB}$ | Number of physical resource blocks in each subband |

${N}_{t}/{N}_{r}$ | Number of transmit/receive antennas |

${N}_{g}$ | Number of antenna panels |

${N}_{1}/{N}_{2}$ | Number of the dual-polarized antenna elements in the horizontal/vertical dimension |

${O}_{1}/{O}_{2}$ | Oversampling factors in the horizontal/vertical dimension |

## References

- Uwaechia, A.N.; Mahyuddin, N.M. A Comprehensive Survey on Millimeter Wave Communications for Fifth-Generation Wireless Networks: Feasibility and Challenges. IEEE Access
**2020**, 8, 62367–62414. [Google Scholar] [CrossRef] - Zaidi, A.; Athley, F.; Medbo, J.; Gustavsson, U.; Durisi, G.; Chen, X. 5G Physical Layer: Principles, Models and Technology Components, 1st ed.; Academic Press: London, UK, 2018. [Google Scholar]
- Ahmadi, S. 5G NR: Architecture, Technology, Implementation, and Operation of 3GPP New Radio Standards; Academic Press: Cambridge, MA, USA, 2019. [Google Scholar]
- Dahlman, E.; Parkvall, S.; Skold, J. 5G NR: The Next Generation Wireless Access Technology, 2nd ed.; Academic Press: Cambridge, MA, USA, 2020. [Google Scholar]
- Telatar, E. Capacity of Multi-antenna Gaussian Channels. Eur. Trans. Telecommun.
**1999**, 10, 585–595. [Google Scholar] [CrossRef] - Gesbert, D.; Kountouris, M.; Heath, R.W.; Chae, C.b.; Salzer, T. Shifting the MIMO Paradigm. IEEE Signal Process. Mag.
**2007**, 24, 36–46. [Google Scholar] [CrossRef] - Marzetta, T.L. Massive MIMO: An Introduction. Bell Labs Tech. J.
**2015**, 20, 11–22. [Google Scholar] [CrossRef] - Lin, Z.; Niu, H.; An, K.; Wang, Y.; Zheng, G.; Chatzinotas, S.; Hu, Y. Refracting RIS-Aided Hybrid Satellite-Terrestrial Relay Networks: Joint Beamforming Design and Optimization. IEEE Trans. Aerosp. Electron. Syst.
**2022**, 58, 3717–3724. [Google Scholar] [CrossRef] - Niu, H.; Lin, Z.; Chu, Z.; Zhu, Z.; Xiao, P.; Nguyen, H.X.; Lee, I.; Al-Dhahir, N. Joint Beamforming Design for Secure RIS-Assisted IoT Networks. IEEE Internet Things J.
**2022**, 1. [Google Scholar] [CrossRef] - Li, G.; Zeng, M.; Mishra, D.; Hao, L.; Ma, Z.; Dobre, O.A. Energy-Efficient Design for IRS-Empowered Uplink MIMO-NOMA Systems. IEEE Trans. Veh. Technol.
**2022**, 71, 9490–9500. [Google Scholar] [CrossRef] - Zeng, M.; Bedeer, E.; Dobre, O.A.; Fortier, P.; Pham, Q.V.; Hao, W. Energy-Efficient Resource Allocation for IRS-Assisted Multi-Antenna Uplink Systems. IEEE Wirel. Commun. Lett.
**2021**, 10, 1261–1265. [Google Scholar] [CrossRef] - Lin, Z.; Lin, M.; Wang, J.B.; de Cola, T.; Wang, J. Joint Beamforming and Power Allocation for Satellite-Terrestrial Integrated Networks With Non-Orthogonal Multiple Access. IEEE J. Sel. Top. Signal Process.
**2019**, 13, 657–670. [Google Scholar] [CrossRef] [Green Version] - Lin, Z.; An, K.; Niu, H.; Hu, Y.; Chatzinotas, S.; Zheng, G.; Wang, J. SLNR-based Secure Energy Efficient Beamforming in Multibeam Satellite Systems. IEEE Trans. Aerosp. Electron. Syst.
**2022**, 1–4. [Google Scholar] [CrossRef] - Lee, H.H.; Ko, Y.C. Low Complexity Codebook-Based Beamforming for MIMO-OFDM Systems in Millimeter-Wave WPAN. IEEE Trans. Wirel. Commun.
**2011**, 10, 3607–3612. [Google Scholar] [CrossRef] - Wang, J.; Lan, Z.; Woo Pyo, C.; Baykas, T.; Sean Sum, C.; Rahman, M.; Gao, J.; Funada, R.; Kojima, F.; Harada, H.; et al. Beam codebook based beamforming protocol for multi-Gbps millimeter-wave WPAN systems. IEEE J. Sel. Areas Commun.
**2009**, 27, 1390–1399. [Google Scholar] [CrossRef] - Ren, Y.; Wang, Y.; Qi, C.; Liu, Y. Multiple-Beam Selection With Limited Feedback for Hybrid Beamforming in Massive MIMO Systems. IEEE Access
**2017**, 5, 13327–13335. [Google Scholar] [CrossRef] - Castellanos, M.R.; Raghavan, V.; Ryu, J.H.; Koymen, O.H.; Li, J.; Love, D.J.; Peleato, B. Channel-Reconstruction-Based Hybrid Precoding for Millimeter-Wave Multi-User MIMO Systems. IEEE J. Sel. Top. Signal Process.
**2018**, 12, 383–398. [Google Scholar] [CrossRef] [Green Version] - Heath, R.W.; González-Prelcic, N.; Rangan, S.; Roh, W.; Sayeed, A.M. An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems. IEEE J. Sel. Top. Signal Process.
**2016**, 10, 436–453. [Google Scholar] [CrossRef] - Wu, W.; Liu, D.; Hou, X.; Liu, M. Low-Complexity Beam Training for 5G Millimeter-Wave Massive MIMO Systems. IEEE Trans. Veh. Technol.
**2020**, 69, 361–376. [Google Scholar] [CrossRef] - Zhang, R.; Zhang, H.; Xu, W.; You, X. Subarray-Cooperation-Based Multi-Resolution Codebook and Beam Alignment Design for mmWave Backhaul Links. IEEE Access
**2019**, 7, 18319–18331. [Google Scholar] [CrossRef] - Albreem, M.A.; Habbash, A.H.A.; Abu-Hudrouss, A.M.; Ikki, S.S. Overview of Precoding Techniques for Massive MIMO. IEEE Access
**2021**, 9, 60764–60801. [Google Scholar] [CrossRef] - Schulz, B. LTE Transmission Modes and Beamforming; White Paper; Rohde & Schwarz: Munich, Germany, 2015. [Google Scholar]
- 3GPP TS 36.213. LTE Evolved Universal Terrestrial Radio Access (E-UTRA), Physical Layer Procedures. Technical Specification. 2016. Available online: https://itecspec.com/archive/3gpp-specification-ts-36-213/ (accessed on 30 October 2022).
- 3GPP TS 38.211. Physical Channels and Modulation. Technical Specification. 2022. Available online: https://itecspec.com/archive/3gpp-specification-ts-38-211/ (accessed on 30 October 2022).
- 3GPP TS 38.214. Physical Layer Procedures for Data. Technical Specification. 2022. Available online: https://itecspec.com/archive/3gpp-specification-ts-38-214/ (accessed on 30 October 2022).
- Hindy, A.; Mittal, U.; Brown, T. CSI Feedback Overhead Reduction for 5G Massive MIMO Systems. In Proceedings of the 2020 10th Annual Computing and Communication Workshop and Conference (CCWC), Vegas, NV, USA, 6–8 January 2020; pp. 0116–0120. [Google Scholar] [CrossRef]
- Ahmed, R.; Tosato, F.; Maso, M. Overhead Reduction of NR type II CSI for NR Release 16. In Proceedings of the WSA 2019, 23rd International ITG Workshop on Smart Antennas, Vienna, Austria, 24–26 April 2019; pp. 1–5. [Google Scholar]
- Suárez, L.; Ryabov, N.; Lyashev, V.; Sherstobitov, A. DFT Based Beam-Time Delay Sparse Channel Representation for Channel State Information (CSI) Compression in 5G FDD Massive MIMO Systems. In Proceedings of the 2018 IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom), Batumi, Georgia, 4–7 June 2018; pp. 1–5. [Google Scholar] [CrossRef]
- Butovitsch, P.; Chapman, T.; Ghasemzadeh, F.; Hogan, B.; Karlsson, J.; Larsson, E.; Astely, D.; Göransson, B.; Friberg, C.; Jöngren, G.; et al. Massive MIMO Handbook; Ericsson AB. 2022. Available online: https://foryou.ericsson.com/Massive-MIMO-handbook-extended-version-download.html (accessed on 30 October 2022).
- Enescu, M. 5G New Radio: A Beam-Based Air Interface; Wiley & Sons, Limited, John: Hoboken, NJ, USA, 2020. [Google Scholar]
- Asplund, H.; Astely, D.; Butovitsch, P.v. Advanced Antenna Systems for 5G Network Deployments: Bridging the Gap Between Theory and Practice; Academic Press: Cambridge, MA, USA, 2020. [Google Scholar]
- Tang, H.; Yang, N.; Zhang, Z.; Du, Z.; Shen, J. 5G NR and Enhancements: From R15 to R16; Elsevier: Amsterdam, Netherlands, 2021. [Google Scholar]
- Ghosh, A.; Maeder, A.; Baker, M.; Chandramouli, D. 5G Evolution: A View on 5G Cellular Technology Beyond 3GPP Release 15. IEEE Access
**2019**, 7, 127639–127651. [Google Scholar] [CrossRef] - Riviello, D.G.; Di Stasio, F.; Tuninato, R. Performance Analysis of Multi-User MIMO Schemes under Realistic 3GPP 3-D Channel Model for 5G mmWave Cellular Networks. Electronics
**2022**, 11, 330. [Google Scholar] [CrossRef] - Henry, S.; Alsohaily, A.; Sousa, E.S. 5G is Real: Evaluating the Compliance of the 3GPP 5G New Radio System With the ITU IMT-2020 Requirements. IEEE Access
**2020**, 8, 42828–42840. [Google Scholar] [CrossRef] - Urquiza Villalonga, D.A.; OdetAlla, H.; Fernández-Getino García, M.J.; Flizikowski, A. Performance bounds with precoding matrices compliant with standardized 5G-NR for MIMO transmission. In Proceedings of the 2022 IEEE Conference on Standards for Communications and Networking (IEEE-CSCN), Rome, Italy, 20–23 June 2022. [Google Scholar]
- Spencer, Q.; Swindlehurst, A.; Haardt, M. Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels. IEEE Trans. Signal Process.
**2004**, 52, 461–471. [Google Scholar] [CrossRef] - 3GPP TR 38.901. Study on Channel Model for Frequencies from 0.5 to 100 GHz. Technical Specification. 2022. Available online: https://itecspec.com/archive/3gpp-specification-tr-38-901/ (accessed on 30 October 2022).
- 3GPP TS 38.212. Multiplexing and Channel Coding. Technical Specification. 2022. Available online: https://itecspec.com/archive/3gpp-specification-ts-38-212/ (accessed on 30 October 2022).
- Gomadam, K.; Cadambe, V.R.; Jafar, S.A. A Distributed Numerical Approach to Interference Alignment and Applications to Wireless Interference Networks. IEEE Trans. Inf. Theory
**2011**, 57, 3309–3322. [Google Scholar] [CrossRef]

**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. Based on this signal, the channel is estimated at each UE and a CSI is fedback, including the PMI. With this information, the gNB designs the precoding matrix. Finally, the precoded data symbols are transmitted to each UE avoiding interference.

**Figure 2.**Radiation pattern of all the beams obtained with a 5G-NR antenna array designed as a DP single-panel UPA with ${N}_{1}={N}_{2}=2$.

**Figure 3.**Grid of beams of a single-panel UPA with ${N}_{1}=2,{N}_{2}=2$, and ${O}_{1}={O}_{2}=4$. It is assumed that ${N}_{s}=2$, ${i}_{11}=6,{i}_{12}=2$, and ${i}_{13}=2$.

**Figure 4.**Average SE vs. SNR for SU-MIMO systems assuming ${N}_{t}=8,{N}_{r}=4$, and different values of ${N}_{s}$. The gNB is implemented assuming a single-panel ULA with four DP polarized antenna elements in the horizontal dimension (${N}_{1}=4$ and ${N}_{2}=1$).

**Figure 5.**Average SE vs. SNR for SU-MIMO systems assuming ${N}_{t}=8,{N}_{r}=4$, and different values of ${N}_{s}$. The gNB is implemented assuming a single-panel UPA with two DP polarized antenna elements in the horizontal and vertical dimensions (${N}_{1}=2$ and ${N}_{2}=2$).

**Figure 6.**Average SE vs. SNR for SU-MIMO systems assuming ${N}_{t}=8,{N}_{r}=4$, and different values of ${N}_{s}$. The gNB is implemented assuming a multi-panel ULA with ${N}_{g}=2,{N}_{1}=2$, and ${N}_{2}=1$.

**Figure 7.**Average SE vs. SNR for SU-MIMO systems assuming ${N}_{t}=8,{N}_{r}=4$, and ${N}_{s}=3$. The gNB is implemented assuming a single-panel ULA with four DP polarized antenna elements in the horizontal dimension (${N}_{1}=4$ and ${N}_{2}=1$).

**Figure 8.**Average SE vs. SNR for SU-MIMO systems assuming ${N}_{t}=32,{N}_{r}=4$, and ${N}_{s}=3$. The gNB is implemented with different antenna configurations. Imperfect CSI is also assumed with ${\sigma}_{e}^{2}={10}^{-3}$. All the curves in this figure labeled as Type I refer to the proposed 5G-NR case.

**Figure 9.**Average SE vs. SNR for MU-MIMO systems assuming $K=2$, ${N}_{t}=32,{N}_{r}=4$, and different values of ${N}_{s}$. The gNB is implemented assuming an ULA single-panel with ${N}_{1}=16$, and ${N}_{2}=1$. Imperfect CSI is also assumed with ${\sigma}_{e}^{2}={10}^{-3}$.

**Figure 10.**Average SE vs. SNR for MU-MIMO systems assuming $K=2$, ${N}_{t}=32,{N}_{r}=4$, and different values of ${N}_{s}$. The gNB is implemented assuming a single-panel UPA with ${N}_{1}=4$, and ${N}_{2}=4$. Imperfect CSI is also assumed with ${\sigma}_{e}^{2}={10}^{-3}$.

**Figure 11.**Average SE vs. number of users (K) for MU-MIMO systems assuming ${N}_{t}=32,{N}_{r}=4$, ${N}_{s}=1$, and SNR=5dB. The gNB is implemented assuming a single-panel ULA with ${N}_{1}=16$, and ${N}_{2}=1$. Imperfect CSI is also assumed with ${\sigma}_{e}^{2}={10}^{-3}$.

Type | Maximum Number of Layers | Number of Antenna Ports | Number of Antenna Panels | Supported Configurations of $\left({\mathit{N}}_{1},{\mathit{N}}_{2}\right)$ and $\left({\mathit{O}}_{1},{\mathit{O}}_{2}\right)$ |
---|---|---|---|---|

Type I Single-Panel | 8 | 2, 4, 8, 12, 16, 24, 32 | 1 | Table 5.2.2.2.1-2 TS-38.214 |

Type I Multi-panel | 4 | 8, 16, 32 | 2, 4 | Table 5.2.2.2.2-1 TS-38.214 |

Parameters | Value |
---|---|

Size of the bandwidth part | ${N}_{BWP}=52$ PRB |

Number of subcarriers per PRB | ${N}_{sc}^{RB}=12$ |

Number of subcarriers of the OFDM grid | ${N}_{sc}=624$ |

Subcarrier Spacing | ${\Delta}_{f}=15$ kHz |

Subband Size | ${N}_{PRB}^{SB}=4$ PRB |

Number of subbands | ${N}_{SB}=13$ |

Symbols per slot | ${N}_{symb}^{slot}=14$ |

Slots per frame | ${N}_{slot}^{frame}=10$ |

Number of frames | 5 |

CSI-RS period | 4 slots |

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**MDPI and ACS Style**

Urquiza Villalonga, D.A.; OdetAlla, H.; Fernández-Getino García, M.J.; Flizikowski, A.
Spectral Efficiency of Precoded 5G-NR in Single and Multi-User Scenarios under Imperfect Channel Knowledge: A Comprehensive Guide for Implementation. *Electronics* **2022**, *11*, 4237.
https://doi.org/10.3390/electronics11244237

**AMA Style**

Urquiza Villalonga DA, OdetAlla H, Fernández-Getino García MJ, Flizikowski A.
Spectral Efficiency of Precoded 5G-NR in Single and Multi-User Scenarios under Imperfect Channel Knowledge: A Comprehensive Guide for Implementation. *Electronics*. 2022; 11(24):4237.
https://doi.org/10.3390/electronics11244237

**Chicago/Turabian Style**

Urquiza Villalonga, David Alejandro, Hatem OdetAlla, M. Julia Fernández-Getino García, and Adam Flizikowski.
2022. "Spectral Efficiency of Precoded 5G-NR in Single and Multi-User Scenarios under Imperfect Channel Knowledge: A Comprehensive Guide for Implementation" *Electronics* 11, no. 24: 4237.
https://doi.org/10.3390/electronics11244237