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Downlink transmission techniques for multiuser (MU) multiple-input multiple-output (MIMO) systems have been comprehensively studied during the last two decades. The well-known low complexity linear precoding schemes are currently deployed in long-term evolution (LTE) networks. However, these schemes exhibit serious shortcomings in scenarios when users’ channels are strongly correlated. The nonlinear precoding schemes show better performance, but their complexity is prohibitively high for a real-time implementation. Two-stage precoding schemes, proposed in the standardization process for 5G new radio (5G NR), combine these two approaches and present a reasonable trade-off between computational complexity and performance degradation. Before applying the precoding procedure, users should be properly allocated into beamforming subgroups. Yet, the optimal solution for user selection problem requires an exhaustive search which is infeasible in practical scenarios. Suboptimal user grouping approaches have been mostly focused on capacity maximization through greedy user selection. Recently, overlapping user grouping concept was introduced. It ensures that each user is scheduled in at least one beamforming subgroup. To the best of our knowledge, the existing two-stage precoding schemes proposed in literature have not considered overlapping user grouping strategy that solves user selection, ordering, and coverage problem simultaneously. In this paper, we present a two-stage precoding technique for MU-MIMO based on the overlapping user grouping approach and assess its computational complexity and performance in IoT-oriented 5G environment. The proposed solution deploys two-stage precoding in which linear zero forcing (ZF) precoding suppresses interference between the beamforming subgroups and nonlinear Tomlinson-Harashima precoding (THP) mitigates interuser interference within subgroups. The overlapping user grouping approach enables additional capacity improvement, while ZF-THP precoding attains balance between the capacity gains and suffered computational complexity. The proposed algorithm achieves up to 45% higher MU-MIMO system capacity with lower complexity order in comparison with two-stage precoding schemes based on legacy user grouping strategies.

Cellular Internet of things (IoT) has been recognized as a key enabler for digital transformation and automation of almost all industries. Before 5G New Radio (5G NR), cellular networks have been mainly designed and implemented for human-type communications. Hence, the connectivity needs of industry 4.0 can be addressed only with the implementation of massive machine type communication (mMTC) 5G NR use cases. Based on current predictions, around 5 billion cellular IoT connections are expected by 2025 [

The performance of MU-MIMO system design is largely dependent on deployed user grouping method [

The joint decoding at the receiver side is not feasible in MU-MIMO system since users cannot cooperate due to their random geographic location. Hence, the successful data transmission is extremely dependent on the precoding technique deployed at the base station, i.e., the ability to simultaneously send independent signals and suppress interference between users as much as possible. When channel state information (CSI) is considered known at the transmitter side (i.e., reliably estimated), the nonlinear dirty paper coding (DPC) technique [

Conversely, the linear precoding schemes with the reduced complexity are also proposed for MU-MIMO systems, such as zero forcing (ZF) and block diagonalization (BD) [

In [

In this paper, we propose an approach in which the existing hybrid two-stage precoding scheme is extended with the overlapping user grouping strategy. Also, the comprehensive analysis on its computational complexity throughput and BER performance has been conducted for mMTC 5G NR use case. Instead of further modification of

The rest of the paper is organized as follows. System model is introduced and user grouping problem is formulated in Section

The downlink of a single-cell MU-MIMO system is considered, in which a base station with a uniform rectangular antenna array of

In many urban mMTC 5G NR use cases, IoT devices are located indoor, whereas macrobase station is located outdoor. Hence, we here consider that base station communicates with users over the spatially correlated Rayleigh channels characterized with the non-line-of-sight (NLOS) propagation [

In the considered scenario, base station is elevated and free of local scattering, which results in high correlation among the transmit antennas. We model spatial correlation matrix at the transmitter

One-ring MIMO channel scattering model.

From Equation (

IoT devices located indoor usually experience fluctuation of the received signal power due to the obstacles on the transmission path, i.e., shadow fading. The channels of geographically proximate devices are significantly correlated when affected by the same shadowing. Spatial correlation of the channels between users

The performance of MU-MIMO system largely depends on the channel correlation among the users included in the same beamforming subgroup. Hence, the proper user grouping is necessary in order to suppress interuser interference and maximize system capacity.

Let

Different user selections for beamforming subgroups

The system model for the proposed two-stage precoding scheme based on overlapping user grouping strategy is depicted in Figure

System model for two-stage precoding with overlapping user grouping approach.

User grouping is achieved by employing the overlapping method from OUG-Greedy algorithm introduced in [

Once users are grouped according to the OUG-Greedy algorithm, linear ZF precoding scheme is applied to suppress interference between already formed beamforming subgroups. For this purpose, precoder

In order to cancel intergroup interference, the effective ZF channel matrix from Equation (

Hence, the user data in each beamforming subgroup is ideally transmitted in the null space of the channel matrix made of channel vectors related to users from all other subgroups. However, it should be noticed that it is not necessary to determine previous Equation (

After the ZF precoding technique is performed, remaining interuser interference in each beamforming subgroup is mitigated by using the nonlinear THP precoding scheme. THP precoded signal for beamforming subgroup

System model for THP scheme.

As can be seen, the proposed hybrid mechanism is based on two-stage precoding. The first stage consists of the linear precoder used to eliminate intergroup interference. To suppress interference inside every group, the nonlinear precoding is employed in the second stage. In other words, beamforming matrix

The achievable sum rate of the proposed algorithm is calculated as

Computational complexity is an important design parameter, especially in implementation of IoT-oriented 5G systems where a massive number of IoT devices have limited battery lifetime. This section covers complexity analysis of the proposed scheme with two-stage ZF-THP precoding based on overlapping user grouping approach (marked as OUG ZF-THP algorithm). In order to achieve this, the computational complexity for deployed overlapping user grouping method and two-stage ZF-THP precoding is derived. The total computational capacity is defined as the sum of these two parts (excluding the calculations from the prior steps that can be reused in the former steps). Also, in order to compare computational complexity for the proposed and the referent algorithms, the complexity for these algorithms is given. As the referent algorithms, we here observed previously introduced OUG-Greedy grouping with the linear ZF precoding (marked as OUG-Greedy ZF algorithm) proposed in [

The complexity for all the observed algorithms is quantified by the number of floating-point operations (FLOPs) [

First, we consider complexity of the overlapping user grouping method. For the sake of brevity, it was assumed that each beamforming subgroup has

Hence, the computational complexity of the overlapping user grouping strategy is no more than

Computational complexity of user grouping algorithms.

User grouping algorithm | Number of FLOPs |
---|---|

Capacity-based ZFS | |

ZFS with SWF | |

OUG-Greedy | |

Optimized |

Next, we derive the computational complexity of two-stage ZF-THP precoding scheme. Matrix-matrix multiplication is executed in order to obtain diagonal elements of the effective channel matrix

Finally,

Application of the corresponding substitution

As summarized in Table

Computational complexity of precoding schemes.

Precoding scheme | Number of FLOPs |
---|---|

ZF | |

THP | |

BD-THP | |

ZF-THP |

Moreover, two-stage ZF-THP technique has the lowest complexity among conventional linear and nonlinear precoding schemes. The computational complexity required to generate one two-stage precoded data vector in the case of 32 antennas and IoT devices grouped in 4 beamforming subgroups is illustrated in Figure

Computational complexity of precoding schemes.

Based on the previously defined computational complexity for different user grouping and precoding schemes, the total complexity for all observed algorithms is presented in Table

Computational complexity of all observed algorithms comprising the user grouping and precoding.

Algorithm | Number of FLOPs |
---|---|

ZFS | |

OUG-Greedy ZF | |

OUG ZF-THP | |

OUG THP |

As evident in Table

On the other hand, OUG ZF-THP algorithm has lower computational complexity than OUG THP and

Also, it is worth mentioning that in

To evaluate the performance of the proposed two-stage ZF-THP precoding based on overlapping user grouping approach (OUG ZF-THP algorithm), we compared the MU-MIMO system capacity for this algorithm with the linear OUG-Greedy ZF algorithm [

We assumed a single-cell MU-MIMO system with a base station located at the center of the cell and equipped with 128 omnidirectional antennas which represent the typical configuration of the commercial massive MIMO antenna. It simultaneously transmits data in 3.5 GHz band to 300 single-antenna IoT devices. This frequency band has been identified as a global International Mobile Telecommunications-2020 (IMT-2020) band for 5G NR deployment by International Telecommunication Union Radiocommunication Sector (ITU-R) [

Parameter values for both correlation models were taken from [

System parameter configuration.

Parameter | Value | Parameter | Value |
---|---|---|---|

[-180°, 180°] | 128 | ||

[5°, 15°] | 300 | ||

20 m | 0.5 | ||

30 m | 0.4 | ||

3.5 GHz | 16 |

In [

First, we have evaluated the proposed algorithm performance in the case of the environment with uncorrelated Rayleigh fading where users’ channels are mutually independent. Equivalent channel-based received signal-to-noise ratio (SNR) to throughput mapping method adopted by 3GPP [

Sum rate comparison under uncorrelated MIMO channels.

It can be seen that proposed OUG ZF-THP algorithm achieves approximately the same capacity as OUG THP and OUG-Greedy ZF algorithms. The same finding holds for the conventional ZFS and

Next, we consider more realistic scenario with correlated shadow fading which imposes dependency between user channels. Results in Figure

Sum rate comparison under correlated MIMO channels.

Obtained large performance gain of OUG ZF-THP algorithm is the result of the proposed combination of more advanced two-stage signal processing and overlapping among beamforming subgroups. Linear OUG-Greedy ZF algorithm achieves lower sum rate due to the correlation of user channel vectors, whereas the poor performance of

In order to give further performance comparison for the observed algorithms which comprise user grouping and precoding procedures, we considered the average uncoded bit error rate (BER) as the performance metric (i.e., achieved BER prior to forward error correction decoding at the receiver), where averaging is performed over a sufficient number of channel realizations and over all users. The uncoded BER is calculated as in [

The comparison of the estimated average uncoded BER for all the observed algorithms is presented in Figures

Average uncoded BER comparison under uncorrelated MIMO channels.

Average uncoded BER comparison under correlated MIMO channels.

Previous findings are summarized in Table

Performance of all observed algorithms in good radio conditions.

Algorithm | Achievable sum rate (bps/Hz) | Average BER |
---|---|---|

ZFS | ||

OUG-Greedy ZF | ||

OUG ZF-THP | ||

OUG THP |

When the number of users

In this paper, we have studied user grouping and scheduling problem in IoT-oriented 5G MU-MIMO systems. We have proposed two-stage hybrid precoding scheme based on overlapping user grouping strategy for mMTC 5G NR use case. In this framework, user grouping is performed using the greedy approach that allows users with favorable channel conditions to be scheduled into the multiple beamforming subgroups simultaneously. Two-stage hybrid precoding scheme is then applied on created beamforming subgroups in order to minimize the interference in MU-MIMO system. Linear ZF precoding cancels interference among beamforming subgroups while the nonlinear THP precoding reduces remaining interference between scheduled users within each beamforming subgroup. Comparative analysis with other precoding schemes based on different user grouping methods has been presented. Numerical results demonstrate that proposed algorithm achieves much higher MU-MIMO system capacity in comparison to the existing two-stage precoding schemes based on legacy user grouping strategies, especially in large SNR regime (from 30% at 4 dB to 45% at 20 dB). Also, thorough complexity analysis has shown that despite its good throughput performance, the proposed approach has lower computational complexity as the existing algorithms that employ user grouping methods and two-stage precoding schemes. Also, the proposed OUG ZF-THP algorithm achieves very good BER performance in the observed application scenario.

Obtained numerical results encourage further research in the area of user grouping and scheduling in 5G MU-MIMO systems. Future work will include evaluation of the proposed two-stage precoding based on overlapping user grouping approach in heterogeneous 5G network consisting of both IoT devices and legacy users with different quality of service (QoS) requirements and assessment of its performance in more realistic radio environment which imposes channel imperfections. In order to support given QoS requirements for the observed users, a deployment of adaptive modulation mechanism might be necessary. In that case, the low complexity VP precoding techniques could be observed as a promising solution, instead of here considered THP schemes.

The data generated from Monte-Carlo simulations to support the findings of this study are available from the corresponding author upon request.

The authors declare that there is no conflict of interest regarding the publication of this paper.

This work has been supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia.