張 穎，高 悅，柯熙政

預編碼室內MIMO可見光通信系統空間相關性分析

張 穎1,2，高 悅1*，柯熙政1,2

1西安理工大學自動化與信息工程學院，陜西 西安 710048；2陜西省智能協同網絡軍民共建重點實驗室，陜西 西安 710048

為了解決多用戶MIMO(MU-MIMO)室內可見光通信中存在用戶間干擾問題及對角化(BD)算法所產生的子信道強弱的問題，利用子流選擇BD算法，對室內MU-MIMO 可見光通信系統的誤碼率進行優(yōu)化。建立了MU-MIMO室內可見光通信的信道模型，利用控制變量法并采用不同LED與PD距離的參數，對比了在4′4 MIMO與8′8 MIMO兩種不同的室內系統布局方式下的信道空間相關性，分析對比子流選擇BD算法及BD算法的系統容量及誤碼率性能。結果表明，隨著空間相關的不斷增強，誤碼率性能下降，子流選擇BD算法相對于BD算法可以帶來4 dB以上的增益。

可見光通信；子流選擇；信道相關性；塊對角化

1 引 言

可見光通信(Visible light communication，VLC)已影響著人們的生活，為達到實際照明標準以及避免通信中斷，將多輸入多輸出(multi-input multi-output，MIMO)技術應用于室內VLC系統中形成可見光MIMO技術[1]，不僅擴大信號的到達范圍，還提高數據傳輸速率[2]。

針對MIMO VLC系統的研究很多，主要集中在優(yōu)化室內的光源布局、信號調制方式、分集接收等方面。趙黎等[3]設計了一種優(yōu)化的環(huán)形光源布局；Ishikawa等[4]使用空間調制技術對功率不平衡MIMO系統的容量進行最大化；薛家豪等[5]利用分集接收技術設計了光電二極管的布局及數據選擇接收裝置，保證通信質量。Huang等[6]設計了一種改進型規(guī)整晶格解碼技術的MIMO VLC系統的收發(fā)器；Narmanlioglu等[7]采用非順序光線跟蹤對各種實際布線和布線拓撲進行MIMO VLC信道建模。然而，接收端通常會接收到來自于其他用戶數據的干擾，從而造成系統性能下降。線性預編碼算法可以有效地降低來自于其他用戶的數據干擾及接收端的復雜度[8]，其中塊對角化(block diagonalization，BD)算法是一種典型的線性預編碼技術，但BD算法的研究主要用于降低用戶間的干擾及提高系統性能方面[9]，在室內MIMO VLC系統的空間相關性研究較少。由于室內MIMO VLC系統中LED光源與光電檢測器(photoelectric detector，PD)的不同位置組合會出現不同的子信道，同時影響MIMO信道的空間相關性及系統性能[10]，因此研究預編碼技術的室內MIMO VLC系統信道的空間相關性具有重要意義。

論文將無線通信中的子流選擇BD技術[11]應用到室內多用戶MIMO(multipleuser MIMO，MU-MIMO)VLC系統中，討論了室內MIMO VLC系統的空間相關性，同時解決了BD算法中因等效信道矩陣經奇異值分解(singular value decomposition，SVD)后子信道強弱不均衡的問題，實現降低多用戶干擾的目的，提高系統傳輸速率。仿真分析驗證了該方法的可行性。

2 系統模型

式中：hij為第i個LED陣列和用戶j的PD之間的信道直流增益，即：

式中：R為第個LED陣列與用戶的檢測器間信道的等效直流增益。

經第個用戶的探測器的光電轉換和濾除直流分量后，最后輸出為

第個用戶輸出端的信噪比(signal to noise ratio，SNR)及系統誤碼率(bit error rate，BER)分別定義為

式中函數定義為

3 預編碼和解碼方案

3.1 子流選擇BD算法的預編碼方案

用戶的預編碼矩陣為

在接收端，用戶接收到的信號為

由式(4)和子流選擇BD預編碼矩陣可得系統和容量為

3.2 子流選擇BD算法的解碼方案

4 系統仿真結果

圖2 室內MIMO VLC系統4′4的空間分布。(a) LED的空間分布；(b) PD的空間分布

圖3 室內MIMO VLC系統8′8的空間分布。(a) 8個LED的空間分布；(b) 8個PD的空間分布

表1 仿真參數

取LED=2且PD=2時，分別求得4′4及8′8信道增益矩陣的條件數(1)=8.4274，(2)=1.1755E+017，8′8的信道相關性強于4′4。取LED=1.5且PD=1.5時，兩種信道矩陣的條件數分別為(3)=13.8906，(4)=3.2784E+017。取LED=1.0且PD=1.0時，兩種信道矩陣的條件數分別為(5)=33.2971，(6)=5.6754E+017。因此，LED、PD間隔的縮小，信道的相關性增強。

通過在信道空間相關性的四種取值下，信道容量與SNR的仿真如圖4所示?？梢奓ED、PD取值越小，隨著信道相關性的增強，信道容量上升的斜率變大。在4′4 MIMO的信道下，BD算法的信道容量受信道相關性影響小于子流選擇BD算法，但在8′8 MIMO的信道下，相關性對兩種算法信道容量的影響區(qū)別不大。

圖5為不同信道相關性下，系統的SNR與BER關系曲線?？梢缘玫?，子流選擇BD算法的BER性能較BD來說有4 dB以上增益，這是子流選擇BD算法在奇異值大的子流信道用于數據通信而獲得的。同時，隨著信道相關性的變強，系統的BER提升。在圖5(a)，8′8 信道的子流選擇BD算法室內VLC系統中BER取10-3時所需SNR約為15.5 dB，而圖5(b)約為19.5 dB，圖5(c)則需要更大的信噪比。因此，可以看出，在8′8的MIMO信道中，不同相關性的BD算法與子流選擇BD算法的信道容量曲線趨勢大致相同；但在相同的系統BER性能下，子流選擇BD算法所需SNR的值比BD算法小，且空間相關性與系統的BER性能呈反比關系。

圖4 四種空間相關性下SNR與信道容量的曲線。

(a)LED=2，PD=2；(b)LED=1.5，PD=1.5；(c)LED=1.0，PD=1.0；(d)LED=0.5，PD=0.5

Fig. 4 Curve between SNR and channel capacity under four spatial correlation.

(a)LED=2，PD=2; (b)LED=1.5，PD=1.5; (c)LED=1.0，PD=1.0; (d)LED=0.5，PD=0.5

圖5 不同信道相關性下SNR與BER的曲線。

(a)LED=2，PD=2；(b)LED=1.5，PD=1.5；(c)LED=1.0，PD=1.0；(d)LED=0.5，PD=0.5

Fig. 5 Curve between SNR and BER under different channel correlation.

(a)LED=2，PD=2; (b)LED=1.5，PD=1.5; (c)LED=1.0，PD=1.0; (d)LED=0.5，PD=0.5

5 結 論

本文利用子流選擇BD算法，討論了在MU-MIMO室內VLC系統中不同的空間相關性下對系統信道容量及BER的影響。結果表明：隨著空間相關性的不斷增大，信道容量上升的斜率隨之變大，同時在8′8的MIMO布局中，在不同信道空間相關性中，BD算法和子流選擇BD算法的信道容量區(qū)別不大；子流選擇BD算法的BER相對于BD算法可以帶來4 dB以上的增益。

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Analysis of spatial correlation of precoding indoor MIMO visible light communication system

Zhang Ying1,2, Gao Yue1*, Ke Xizheng1,2

1School of Automation and Information Engineering, Xi￠an University of Technology, Xi￠an, Shaanxi 710048, China;2Shaanxi Civil-Military Integration Key Laboratory of Intelligence Collaborative Networks, Xi￠an, Shannxi 710048, China

Substream selected BD algorithm MU-MIMO indoor VLC system model

Overview:Visible light communication is a kind of wireless communication, which can solve the problem of serious electromagnetic radiation or limited spectrum resources in hospitals, mines, military, etc. It’s a new communication technology with green, high efficiency and energy saving. In the actual application scenario, there are multiple users and multiple sets of LEDs in the room, which can effectively reduce the communication link interruption caused by indoor displays and personnel walking. There are many researches on indoor MIMO visible light communication, most of which are mainly to solve the problem of indoor layout, diversity reception and so on. However, the receiver can receive interference from others. Precoding technology is mainly used to reduce the inter-user interference now, but the spatial correlation research of precoding for visible light communication is relatively rare. In this paper, two indoor MIMO visible light communication system models are established, namely 4′4 and 8′8. The substream selected BD algorithm is applied to the indoor MIMO visible light communication system. By optimizing the singular value of the singular value decomposition caused by the BD algorithm in the equivalent channel matrix, the purpose of reducing inter-user interference is realized. At the same time, under different indoor system models and the distribution of LED and PD, the channel capacity and bit error rate performance of BD algorithm and substream selected BD algorithm are studied. The indoor MIMO visible light communication system with substream selected BD algorithm in the above figure mainly includes three parts: the transmitter, the receiver and channel. The transmitter mainly performs serial-to-parallel conversion of data, controls the parallel data modulation by on-off keying modulation and processes substream selected BD algorithm, and to add the DC offset and use the high frequency flickering characteristic of the LED to perform data transmission; at the receiver, the received signal is decoded and demodulated by the optical detector to restore the original data and complete the information transmission. The simulation results show that in terms of channel capacity, the spatial correlation of the channel is stronger and the channel capacity is increased. Meanwhile, under the indoor channel of 4′4, the channel capacity of the BD algorithm is higher than the substream selected BD algorithm under different spatial correlations, but under the indoor 8′8 channel, BD algorithm and substream selected BD algorithm have little difference in capacity under different spatial correlation; in terms of the bit error rate of the system, the bit error rate of the substream selected BD algorithm can bring a gain of more than 4 dB compared with the BD algorithm, the spatial correlation is continuously enhanced, and the system error rate performance is degraded.

Citation: Zhang Y, Gao Y, Ke X ZAnalysis of spatial correlation of precoding indoor MIMO visible light communication system[J]., 2020, 47(3): 190666

Analysis of spatial correlation of precoding indoor MIMO visible light communication system

Zhang Ying1,2, Gao Yue1*, Ke Xizheng1,2

1School of Automation and Information Engineering, Xi￠an University of Technology, Xi￠an, Shaanxi 710048, China;2Shaanxi Civil-Military Integration Key Laboratory of Intelligence Collaborative Networks, Xi￠an, Shannxi 710048, China

In order to solve the problem of multi-user interference and the subchannel strength generated by the block diagonalization (BD) algorithm in multi-user MIMO (MU-MIMO) indoor visible light communication, the bit error rate of the indoor MU-MIMO visible light communication system is optimized by using the substream selected BD algorithm. This paper establishes the channel model for MU-MIMO indoor visible light communication and compares the channel spatial correlation between the 4′4 MIMO and 8′8 MIMO in different indoor system layout modes by using the control variable method and taking different parameters of LED and PD distance, the system capacity and bit error rate performance of substream selected BD algorithm and BD algorithm are compared and analyzed. The results show that with the continuous enhancement of spatial correlation, the bit error rate performance decreases, and the substream selected BD algorithm can bring a gain of more than 4 dB compared with BD algorithm.

visible light communication; substream selected; channel correlation; block diagonalization

TN929.1

A

10.12086/oee.2020.190666

: Zhang Y, Gao Y, Ke X Z. Analysis of spatial correlation of precoding indoor MIMO visible light communication system[J]., 2020,47(3): 190666

2019-11-02；

2019-11-29

陜西省重點產業(yè)創(chuàng)新鏈工程(2017ZDCXL-GY-06-01)；陜西省教育廳自然科學基金(17JK0569)；陜西省教育廳科研計劃項目(18JK0341)；西安市科技創(chuàng)新引導項目(201805030YD8CG14(12))

張穎(1982-)，女，博士，講師，主要從事可見光通信及Ad Hoc網絡拓撲的研究。E-mail：zhangying@xaut.edu.cn

高悅(1993-)，女，碩士研究生，主要從事可見光通信多用戶預編碼技術的研究。E-mail：yuegao56510@163.com

張穎，高悅，柯熙政. 預編碼室內MIMO可見光通信系統空間相關性分析[J]. 光電工程，2020，47(3): 190666

Supported by Key Industry Innovation Chain Project of Shaanxi Province (2017ZDCXL-GY-06-01), Natural Science Foundation of Shaanxi Provincial Department of Education (17JK0569), Scientific Research Project of Education Department of Shaanxi Province (18JK0341), and Xi'an Science and Technology Innovation Guidance Project (201805030YD8CG14(12))

* E-mail: yuegao56510@163.com