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Cyber-physical systems (CPSs) are characterized by integrating computation and physical processes. To cope with the challenges of the application of the CPSs in all kinds of environments, especially the cellular vehicle-to-everything (C-V2X) which needs high quality end-to-end communication, the robustness and reliability for CPSs are very crucial. Aiming at the technical challenges of information transmission caused by the fading effect and the fast time-varying characteristics of the channel for C-V2X communication, an improved Tomlinson–Harashima precoding (THP) algorithm for multiple input multiple output (MIMO) systems is proposed. Channel state information (CSI) and correlation are exploited to compensate instantaneous CSI, which could reflect current real-time channel status exactly. Further, the iterative water filling power allocation algorithm and the multiuser scheduling algorithm based on the greedy algorithm are jointly optimized and applied to the THP, which could improve the system performance. Simulation results show that the proposed algorithm can be efficiently applied to high-speed mobility scenarios and improve bit error ratio (BER) performance as well as spectrum utilization.

In recent years, the construction of global smart city is accelerated, which makes cyber-physical systems (CPSs) develop rapidly [

MIMO can suppress channel fading, with two modes of spatial multiplexing and spatial diversity [

When the vehicle is moving at high-speed, the channel state information (CSI) changes significantly during a symbol transmission period. Therefore, traditional channel estimation is not accurate. The fast time-varying characteristics of the channel cause the feedback CSI cannot accurately describe the real-time channel [

Moreover, if the transmitter adopts the unreasonable transmission power allocation algorithm, it will not be able to obtain communication quality of service (QoS) assurance and better spectrum utilization when the channel has a fast time-varying characteristic [

Precoding design in high-speed mobile scene has become a research hotspot currently. Zhang et al. [

Based on the research and analysis, an improved THP algorithm in high-speed mobility scenarios is proposed. The algorithm combines the statistical information with the space-time correlation characteristics of the MIMO channel to construct a dynamic CSI channel model. At the same time, the iterative water filling power allocation algorithm and the multiuser scheduling algorithm based on the greedy algorithm are jointly designed with THP, which can effectively improve the system transmission reliability and spectrum utilization. The main contributions of this paper are as follows:

In order to suppress the channel fading caused by high-speed vehicle movement, we combine MIMO and IoV to construct a MIMO-V2I communication system. Moreover, since the channel in the high-speed mobile environment of vehicles has fast time-varying characteristics, we adopt the dynamic CSI model that combines the statistical information with the space-time correlation characteristics of the channel, which can reflect the current channel characteristics accurately.

Based on the proposed dynamic CSI model, in order to obtain the diversity gain of the MIMO system, an improved THP algorithm is proposed. In the high-speed vehicle moving environment, the algorithm applies the iterative water filling power allocation and the user scheduling based on the greedy algorithm to the THP algorithm for joint optimization design. Firstly, the user scheduling algorithm aims to maximize spectrum utilization and selects the optimal user set according to the channel information of the dynamic CSI model. Secondly, according to the user scheduling result, the channel matrix based on the dynamic CSI model is selected and reconstructed. And the reconstructed channel matrix is applied to the THP algorithm, which can effectively eliminate multiuser interference. The iterative water filling algorithm allocates power to each user according to the channel characteristics of each user in the system, realizing the redistribution of total power, which can effectively improve the transmission efficiency and maximizing the spectrum utilization of the system.

The rest of this paper is organized as follows. Section

Assuming that in a multiuser MIMO-IoV system, the infrastructure has deployed

The multiuser THP system model is shown in Figure

Multiuser THP system model.

According to (

The precoding symbols

In the high-speed mobility scenarios, the channel response

Since the CSI is dynamically changed, the channel matrix

Assuming that the transmitter has an initial channel measurement

Then, we apply the simplified temporal correlation model (

This paper uses greedy algorithms to select and rank users to maximize spectrum utilization while reducing system bit error ratio (BER). Firstly, a user with the largest spectrum utilization is selected from all

Input: number of transmitting antennas

Output: channel matrix of selected users

Input: system total power

Output: power allocation matrix for each user

The greedy algorithm used in this section determines whether to select the joint channel composed of each user and the selected user by continuously calculating whether it has the maximum spectrum utilization. Compared with the traversal algorithm, the search numbers are greatly reduced, and the result is equal to or close to the optimal solution. When the greedy algorithm selects a user, the joint channel matrix is generated, which means the user is synchronously sorted. It can improve the system performance to a certain extent.

The water filling algorithm is a classic power allocation algorithm [

Figure

Diagram of power allocation for the multiuser precoding system.

To maximize spectrum utilization, we can construct objective function and constrain as follows:

An iterative water filling algorithm suitable for multiuser MIMO systems is designed. Firstly, the power of each user is initialized, and the power is distributed equally after obtaining the precoding matrix. Then, the user power is iteratively updated according to the objective function. In each iteration, the interference is equivalent to noise and processed, and the user power allocation is optimized through the water filling algorithm. When the power allocated by each user basically does not change, the iteration stops and the algorithm ends. The specific process of the iterative water filling power allocation algorithm is as follows.

The iterative water filling algorithm takes full account of the influence of interference and treats it as noise. When there is no spatial correlation in the channel, the singular value distribution of each user channel is relatively average, and the system using the iterative water filling algorithm does not have significant channel capacity. If the channel correlation exists, the channel condition number is large, or even the channel rank is not satisfied, the channel capacity advantage of the iterative water filling algorithm will be more obvious.

The diagram of improved THP based on the iterative water filling algorithm is shown in Figure

Diagram of improved THP based on the iterative water filling algorithm.

According to the MMSE algorithm, we can construct objective functions and constraints as follows:

Substituting (

Let

We perform a LQ decomposition of

This section mainly analyzes the complexity of the proposed algorithm and several other classical precoding algorithms. The simulation is performed by Matlab, and finally the simulation results are analyzed.

We compare the computational complexity of the classical linear precoding algorithm, the THP, and the improved THP algorithm in Table

Complexity comparison.

Algorithm | Complexity |
---|---|

ZF [ | |

MMSE [ | |

ZF-THP (without user scheduling) [ | |

MMSE-THP (without user scheduling) [ | |

ZF-THP (with user scheduling) | |

MMSE-THP (with user scheduling) | |

ZF-THP (dynamic CSI model) | |

MMSE-THP (dynamic CSI model) | |

The proposed algorithm (ZF) | |

The proposed algorithm (MMSE) |

The zero force (ZF) and MMSE algorithms in Table

In order to verify the rationality of the proposed algorithm, we construct a MIMO-V2I communication system to simulate and verify the proposed algorithm in a high-speed mobile scenario. In the simulation, a

Simulation parameters.

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

Carrier frequency | 5.9 GHz |

Moving speed | 30 km/h, 120 km/h |

Transmitting antennas | 4 |

Receiving antennas | 1 |

Total users | 10 |

Target users | 4 |

Modulation | QPSK |

This paper mainly introduces BER and spectrum utilization of linear precoding [

Figures

BER of several precoding algorithms: (a) 120 km/h; (b) 30 km/h.

In high-speed scenarios, the proposed algorithm is the best. The traditional THP algorithm based on the dynamic CSI model is second, and the traditional THP algorithm combined with the user scheduling algorithm is better than the traditional THP. The linear precoding is the worst. This is because the dynamic CSI model compensates for the instantaneous channel through channel correlation, so the CSI model obtained through feedback is closer to the actual channel, thereby improving system performance. The user scheduling algorithm based on the greedy algorithm preferentially selects the user with the highest spectrum utilization rate for priority transmission, which not only improves the spectrum utilization rate of the system but also effectively filters out noise and interference, thereby reducing BER.

In low-speed scenarios, the BER of various precoding algorithms is consistent with the trend of BER in high-speed scenarios. We observe that the precoding algorithm combined with the dynamic CSI model is close to that of the precoding algorithm without the dynamic CSI model. This is because the moving speed is low, there is no strong correlation between channels, and the BER advantage brought by the dynamic CSI model is not obvious.

In summary, the proposed algorithm is suitable for high-speed mobile scenarios.

Figures

Spectrum utilization of several precoding algorithms: (a) 120 km/h; (b) 30 km/h.

In high-speed scenarios, the proposed algorithm has the best spectrum utilization performance. This is because the multiuser scheduling algorithm based on the greedy algorithm optimizes the target by maximizing the channel capacity, thereby improving the spectrum utilization of the system. Moreover, the dynamic CSI model makes the channel closer to the actual channel, and the accurate CSI can design a better precoding matrix and further improve the spectrum utilization.

In low-speed scenarios, the trend of precoding algorithm spectrum utilization is consistent with that in high-speed scenarios. However, in low-speed scenarios, the spectrum utilization of each precoding algorithm is higher than that of similar algorithms in high-speed situations. According to information theory, when the SNR is determined, the spectrum utilization is only related to the channel matrix. In the low-speed scene, the channel is corrected by channel correlation, and the channel gain is improved so that the spectrum utilization is effectively improved to a certain extent.

Figure

Spectrum utilization under different power allocation algorithms.

This paper studies the precoding of the ultra reliable communication for V2I of CPSs. Aiming at the fast time-varying characteristics of the channel in high-speed mobility scenarios, we propose an improved THP algorithm. By constructing a dynamic CSI model based on channel statistic information and related characteristics, the obtained dynamic CSI is closer to the current actual channel. At the same time, the iterative water filling power allocation algorithm and the user scheduling algorithm based on the greedy algorithm are combined with the THP algorithm to carry out joint optimization design. The simulation results show that the proposed algorithm has better BER and spectrum utilization than the traditional THP algorithm and linear precoding algorithm and is more suitable for fast time-varying channel environment in high-speed mobility scenarios.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest regarding the publication of this manuscript.

This work was supported by the National Natural Science Foundation of China (no. 61501066) and Natural Science Foundation of Chongqing (no. cstc2019jcyj-msxmX0017).