Orthogonal frequency division multiplexing modulation techniques in visible light communication
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摘要:可见光通信（VLC）由于可以弥补射频通信的不足而成为研究热点，正交频分复用（OFDM）技术因其高数据速率和抗频率选择性衰落被广泛应用在VLC中。本文从能量效率、频谱效率、误码率、计算复杂度等方面对可见光通信系统中OFDM调制技术进行研究和比较，主要包括基于离散傅立叶变换的单极性方案、改进或增强型方案和混合型方案，基于哈特莱变换的光OFDM，以及基于LED索引调制的光OFDM。文中介绍了多种光OFDM调制技术的工作原理综合对比了频谱效率等性能；研究了光OFDM系统接收机改进方案；总结了可见光OFDM系统存在的问题和未来研究方向。本文对可见光OFDM系统进行归纳和总结，为提出更加高效的单极化调制技术、进一步提高系统频谱效率及可靠性提供了参考。Abstract:With its unique advantages, Visible Light Communication (VLC) can compensate for limitations in radio frequency communication, allowing it to become a recent avid topic of research. Orthogonal Frequency Division Multiplexing (OFDM) has been widely used in VLC due to its high rate of data transfer and frequency selective fading resistance. We compare the performance of several OFDM modulation techniques in VLC, including unipolar schemes, enhanced schemes and hybrid schemes based on discrete Fourier transformation, as well as optical OFDM systems based on Hartley transform and LED index modulation. We perform these comparisons in terms of energy efficiency, spectral efficiency, bit error rate, and algorithm complexity. The principles of some kinds of optical OFDM systems are firstly illustrated and their spectrum efficiencies are theoretically analyzed and compared. We also research and analysis the improved design of receivers in optical OFDM systems. The challenges and upcoming research of OFDM systems in VLC are summarized. The research in this paper can provide a research reference and propose more efficient unipolar modulation schemes to further improve the spectral efficiency and reliability of optical OFDM systems.
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图 1基于离散傅立叶变换的光OFDM系统框图
Figure 1.Block diagram of an optical OFDM system based on discrete Fourier transformation
图 2光OFDM系统BER=10−3时光功耗与频带利用率的关系
Figure 2.The relationship between optical power and spectral efficiency in the optical OFDM system underBER=10−3
表 1典型单极性光OFDM调制原理对比
Table 1.Comparison of modulation principles of typical optical OFDM
典型单极性光OFDM 频域子载波设置 时域信号极性 单极化处理 DCO-OFDM[10] $ {X}_{k}={X}_{N-k}^{\ast },0 双极性实数 添加直流偏置 ACO-OFDM[11] ${{X} }=\left(0,{X}_{1},0,{X}_{3},\cdots,{X}_{\frac{N}{2}-1},0,{X}_{\frac{N}{2}-1}^{\ast },\cdots,{X}_{3}^{\ast },0,{X}_{1}^{\ast }\right)$ 双极性实数，具有特殊对称性：${x}_{n}=-{x}_{n+\frac{N}{2} }\left(0{\text{≤} } n < N/2\right)$ 负值限幅 U-OFDM[12] $ {X}_{k}={X}_{N-k}^{\ast },0 双极性实数 极性编码 Flip-OFDM[13] $ {X}_{k}={X}_{N-k}^{\ast },0 双极性实数 “正”、“负”模块分别传输 PAM-DMT[14] $\begin{array}{l}{{X} }=(0,{\rm{j} }{X}_{\rm{PAM},1},{\rm{j} }{X}_{\rm{PAM,2} },\cdots,{\rm{j} }{X}_{ { {\rm{PAM} } },\frac{N}{2}-1},0,\\-{\rm{j} }{X}_{ {\rm{PAM} },\frac{N}{2}-1},\cdots,-{\rm{j} }{X}_{\rm{PAM},2},-{\rm{j} }{X}_{\rm{PAM},1})\end{array}$ 双极性实数，具有特殊对称性：${x}_{N-n}=-{x}_{n},1{\text{≤} } n{\text{≤} } \dfrac{N}{2}-1$ 负值限幅 MACO-OFDM[15] ${{X} }=\left(0,{X}_{1},0,{X}_{3},\cdots,{X}_{\frac{N}{2}-1},0,{X}_{\frac{N}{2}-1 }^{\ast },\cdots,{X}_{3}^{\ast },0,{X}_{1}^{\ast }\right)$ 双极性实数具有特殊对称性：${x}_{n}=-{x}_{n+\frac{N}{2} }\left(0{\text{≤} } n < \dfrac{N}{2}\right)$ 极性编码 
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表 2光OFDM性能比较
Table 2.Performance comparison of optical OFDM schemes
光OFDM 频谱效率（bits·s−1·Hz−1） 功率效率 接收机复杂度 DCO-OFDM[10] $\displaystyle \frac{N-2}{2N}{\rm{log} }_{2}\; M$ 低 $ O\left(N{\rm{log}}_{2}\; N\right)$ ACO-OFDM[11] $\displaystyle \frac{1}{4}{\rm{log} }_{2}\; M$ 高 $ O\left(N{\rm{log}}_{2}\; N\right)$ U-OFDM[12] $\displaystyle \frac{N-2}{4N}{\rm{log} }_{2}\; M$ 高 $ O\left(N{\rm{log}}_{2}\; N\right)$ Flip-OFDM[13] $\displaystyle \frac{N-2}{4N}{\rm{log} }_{2}\; M$ 高 $ O\left(N{\rm{log}}_{2}\; N\right)$ PAM-DMT[14] $\displaystyle\frac{N-2}{2N}{\rm{log} }_{2}\; M$ 低 $ O\left(N{\rm{log}}_{2}\; N\right)$ MACO-OFDM[15] $\displaystyle\frac{1}{8}{\rm{log} }_{2}\; M$ 高 $ O\left(N{\rm{log}}_{2}\; N\right)$ eU-OFDM[16] $\left(1-\displaystyle\frac{1}{ {2}^{D} }\right)\displaystyle\frac{N-2}{2N}{\rm{log} }_{2}\; M$ 高 $ {O}\left[\left(2D-1\right)\left(N{\rm{log}}_{2}\; N\right)\right]$ GREENER-OFDM[32] $\displaystyle\frac{N-2}{4N}{\displaystyle \sum _{d=1}^{D}\displaystyle\frac{ {\rm{log} }_{2}\; {M}_{d} }{ {2}^{d-1} } }$ 高 $ {O}\left[\left(2D-1\right)\left(N{\rm{log}}_{2}\; N\right)\right]$ ePAM-DMT[33] $ {\displaystyle \sum _{d=1}^{D}\frac{\left(N-2d\right){\rm{log}}_{2}{M}_{d}}{{2}^{d}N}}$ 高 ${O}\left({2\displaystyle \sum _{d=1}^{D}{N}_{d}{\rm{log} }_{2}{N}_{d} }-{N}_{D}{\rm{log} }_{2}{N}_{D}\right)$ eACO-OFDM[34] $ {\displaystyle \sum _{d=1}^{D}\frac{{\rm{log}}_{2}{M}_{d}}{{2}^{d+1}}}$ 高 ${ O }\left({\displaystyle \sum _{l=1}^{L}\displaystyle\frac{N}{ {2}^{l-2} } }{\rm{log} }_{2}\left(\displaystyle\frac{N}{ {2}^{l-1} }\right)-\displaystyle\frac{N}{ {2}^{L-1} }{\rm{log} }_{2}\left(\displaystyle\frac{N}{ {2}^{L-1} }\right)\right)$ LACO-OFDM[17] $\left(\displaystyle\frac{1}{2}-\displaystyle\frac{1}{ {2}^{L+1} }\right){\rm{log} }_{2}\; M$ 高 ${O}\left({\displaystyle \sum _{l=1}^{L}\displaystyle\frac{N}{ {2}^{l-2} } }{\rm{log} }_{2}\left(\displaystyle\frac{N}{ {2}^{l-1} }\right)-\displaystyle\frac{N}{ {2}^{L-1} }{\rm{log} }_{2}\left(\displaystyle\frac{N}{ {2}^{L-1} }\right)\right)$ THO-OFDM[35] $\displaystyle\frac{1}{4}{\rm{log} }_{2}\; {M}_{\rm{ACO} }^{1}+\frac{1}{8}{\rm{log} }_{2}\; {M}_{\rm{ACO} }^{2}+\left(\frac{1}{8}-\frac{1}{N}\right){\rm{log} }_{2}\; {M}_{\rm{PAM} }$ 高 $\begin{array}{l}{\rm{TD} }:{O}\left[N\left({\rm{log} }_{2}N+{\rm{log} }_{2}\left(\displaystyle\frac{N}{2}\right)\right)\right]\\ {\rm{FD} }:{O}\left[N\left(3{\rm{log} }_{2}N+{\rm{log} }_{2}\left(\displaystyle\frac{N}{2}\right)\right)\right]\end{array}$ ADO-OFDM[18] $\displaystyle \frac{1}{4}{\rm{log} }_{2}\; {M}_{\rm{ACO} }+\left(\frac{1}{4}-\frac{1}{N}\right){\rm{log} }_{2}\; {M}_{\rm{DCO} }$ 中 $ {O}\left(4N{\rm{log}}_{2}\; N\right)$ HACO-OFDM[19] $\displaystyle \frac{1}{4}{\rm{log} }_{2}\; {M}_{\rm{ACO} }+\left(\frac{1}{4}-\frac{1}{N}\right){\rm{log} }_{2}\; {M}_{\rm{PAM} }$ 高 $ {O}\left(3N{\rm{log}}_{2}\; N\right)$ EHACO-OFDM[20] $\displaystyle\frac{1}{4}{\rm{log} }_{2}\; {M}_{\rm{ACO} }+\left(\frac{1}{4}-\frac{1}{N}\right)\left({\rm{log} }_{2}\; {M}_{\rm{DCO} }+{\rm{log} }_{2}\; {M}_{\rm{PAM} }\right)$ 高 $ {O}\left(5N{\rm{log}}_{2}\; N\right)$ AAO-OFDM[21] $\displaystyle\frac{1}{4}\left({\rm{log} }_{2}\; {M}_{\rm{AVO} }+{\rm{log} }_{2}\; {M}_{\rm{ACO} }\right)-\frac{1}{N}{\rm{log} }_{2}\; {M}_{\rm{AVO} }-\frac{1}{2}$ 高 $ {O}\left(4N{\rm{log}}_{2}\; N\right)$ PM-OFDM[22] $\displaystyle\frac{1}{4}{\rm{log} }_{2}\; M$ 高 $ \begin{array}{l}{\rm{PM}}-1:{O}\left(N{\rm{log}}_{2}\; N\right)\\ {\rm{PM}}-2:{O}\left(9N{\rm{log}}_{2}\; N\right)\end{array}$ P-OFDM[23] $\displaystyle \frac{1}{2}{\rm{log} }_{2}\; M$ 高 $ O\left(N{\rm{log}}_{2}\; N\right)$ 下载:
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表 3基于FFT与FHT的光OFDM对比
Table 3.Comparison of optical OFDM with FFT and FHT
FFT-OFDM FHT-OFDM 定义式 $\begin{array}{l}{\rm{FFT} }: X(k)={\displaystyle \sum _{n=0}^{N-1}x(n){\rm{exp} }\;\left(-{\rm{j} }\frac{2{\text{π} } nk}{N}\right)},0{\text{≤} } k{\text{≤} } N-1\\ {\rm{IFFT} }: x(n)={\displaystyle \sum _{k=0}^{N-1}X(k){\rm{exp} }\;\left({\rm{j} }\frac{2{\text{π} }nk}{N}\right)},0{\text{≤} } n{\text{≤} } N-1\end{array}$ $\begin{array}{l}{\rm{FHT} }: X(k)={\displaystyle \sum _{n=0}^{N-1}x(n)}{\rm{cas} }\;(2{\text{π} } kn/N),0{\text{≤} } k{\text{≤} } N-1\\ {\rm{IFHT} }:x(n)={\displaystyle \sum _{k=0}^{N-1}X(k)}{\rm{cas} }(2{\text{π} } kn/N),0{\text{≤} } n{\text{≤} } N-1\\{\rm{cas} }(2{\text{π} }kn/N)={\rm{cos} }(2{\text{π} }kn/N)+{\rm{sin} }(2{\text{π} }kn/N)\end{array}$ 调制方式 复星座（m-QAM） 实星座（BPSK，M-PAM） 星座尺寸 m $ M=\sqrt{m}$ 厄米特对称 需要 不需要 计算复杂度 有复数计算附加共轭运算 无复数计算无附加共轭运算 有用载波 N/2 N 下载:
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