Research on Optical Wireless Orbital Angular Momentum Multiplexing System Based on Signal Detection
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摘要: 基于轨道角动量(OAM)的光无线复用通信技术在理想传输条件下能够大幅度提升通信系统性能，然而现实中大气湍流、孔径失配等因素会造成OAM模态间串扰导致误码率(BER)上升。为了降低光无线OAM复用系统在复杂环境中的误码率，该文首先建立了大气湍流、孔径失配场景下基于垂直分层空时码准则(VBLAST)的OAM复用通信系统(VBLAST-OAM)，之后分析对比基于排序干扰连续消除检测算法(OSIC)、基于马尔科夫随机场置信度传播算法(MRF-BP)、基于OAM串扰特性的排序干扰连续消除算法(OAM-OSIC)应用于上述系统时的性能。结果表明：所提信号检测算法均能有效降低OAM复用系统在复杂环境中的误码率，其中，基于MRF-BP算法的系统性能最好；OAM-OSIC虽然属于次优算法，但在算法的运行开销方面具有较大优势。Abstract: The wireless communication technology based on Orbital Angular Momentum (OAM) can greatly improve the performance of the communication system under ideal transmission conditions. However, in the actual environment, atmospheric turbulence and aperture mismatch can cause crosstalk between OAM modes and increase the Bit Error Rate (BER). In order to reduce the BER of the optical wireless OAM multiplexing system in a complex environment, an OAM multiplexing communication system based on the Vertical Bell LAyered Space Time (VBLAST-OAM) code criterion under the scenario of atmospheric turbulence and the aperture mismatch of the transceiver is established firstly. Then, the system performance are analyzed based on the Ordered Successive Interference Cancellation (OSIC), the Markov Random Field Belief Propagation (MRF-BP) algorithm and the algorithm OAM-OSIC. Simulation results show that the algorithm proposed in this paper can reduce the BER of OAM systems effectively in complex environment and the MRF-BP has the best performance. Although OAM-OSIC is a suboptimal algorithm, it has a great advantage in the running cost.
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表 1 OAM在大气湍流中的传播过程
初始化：源端光场$E(r,\phi ,z)$，空间传输函数$H$，相位屏个数N，相位$\varphi (x,y)$ (1) ${\rm{For }}j{\rm{ = 1:}}N$ (2) 傅里叶变换：$U(K,z) = {\rm{FFT}}\left( {E(r,\phi ,z)} \right)$ (3) 真空传播：${U'}(K,z) = {\rm{IFFT}}\left( {U(K,z) \times H} \right)$ (4) 穿过随机相位屏：$E(r,\phi ,z) = {U'}(K,z) \times \exp \left( {{\rm{j}} \times \varphi (x,y)} \right)$ (5) End For 
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表 2 OSIC算法
初始化：复用的OAM数目${ {{N} }_{{t} } }$，串扰信道$H$，接收到的信号r，噪声方差${\sigma ^2}$ (1) ${\rm{For } }j{\rm{ = 1:} }{ {{N} }_{{t} } }$ (2) 加权矢量W: 基于ZF/MMSE准则：$W = {\rm{pinv(} }H{\rm{)/pinv(} }{H^{\rm{H} } }{\rm{ + } }{\sigma ^2} \times {I_{ {N_{\rm{t} } } - j + 1} }{\rm{)} } \times {H^{\rm{H} } }$ (3) 首先对W的每一行求范数，并对范数排序，选取最小范数行k (OSIC) (4) 省略步骤(3) (OAM-OSIC) (5) $y(k) = W(k,:) \times r$ 判决统计量(优化前) (6) $y(k) = W(1,:) \times r$ 判决统计量(优化后) (7) 根据数据判决得到x(k) (8) $r = r{\rm{ - }}x(k) \times H$ 消除前一次检测的数据 (9) $H(:,k) = [\;]$ 将信道矩阵的第k列清除(优化前) $H(:,1) = [\;]$ 将信道矩阵的第1列清除(优化后) (10) 重复步骤(2)，更新W (11) ${\rm{End\; For}}$
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表 3 MRF-BP算法
初始化：$m_{i,j}^0 = b_i^0$, $z,R, p({x_i} = 1) = p({x_i} = - 1), \forall i,j \in $$ (1,2,\cdots,N)$, M是信息迭代次数 (1) ${\rm{For }}\;i{\rm{ = 1:}}N$ 势函数 (2) ${\rm{For }}\;j{\rm{ = 1:}}N$ ${\rm{ }}i \ne j{\rm{ }}$ (3) 根据式(24)计算${\psi _{i,j}}$； (4) ${\rm{End\; For}}$ (5) ${\rm{End\; For}}$ (6) ${\rm{For }}\;i{\rm{ = 1:}}N$ 相容函数 (7) 根据式(25)计算${\phi _i}$； (8) ${\rm{End\; For}}$ (9) ${\rm{For} }\; t = 1:M$ 迭代更新 (10)${\rm{For }}\;i{\rm{ = 1:}}N$ (11) ${\rm{For\; }}j{\rm{ = 1:}}N$ ${\rm{ }}i \ne j{\rm{ }}$ (12) 第t次迭代得到更新的信息$\overline m _{i,j}^t$，利用信息阻尼方式得到新信息$m_{i,j}^t$； (13) ${\rm{End\; For}}$ (14) ${\rm{End\; For}}$ (15) ${\rm{End\; For}}$ (16) ${\rm{For }}\;i{\rm{ = 1:}}N$ 置信度计算 (17) 根据式(20)计算置信度${b_i}$； (18) ${\rm{End\; For}}$
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