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经过相干接收机输出理想的I路和Q路两路信号是完全正交的。但在实际系统中, 由于:(1)I, Q两路偏置点、相位控制的偏置点与理论值存在偏差;(2)90°光混频器因共轭不对称造成相位偏置不是90°;(3)光电二极管的响应度不匹配等原因,造成I路和Q路的幅度不能保持一致,相位不完全正交[16]。幅度不一致造成信噪比降低,不影响信号的解调,而相位不正交就会造成不能正确的解调信号及星座图旋转[17],造成系统误比特率增加,系统性能下降。
常用以下几种补偿算法来消除其影响:施密特正交化[7]、对称正交化(简称Löwdin正交化)[12]、椭圆拟合算法[8]、恒模算法[9]。这3种算法的原理图如图 2所示。
Figure 2. a—Gram-Schmidt orthogonalization b—symmetric orthogonalization c—ellipse fitting algorithm
由图 2可知,GSOP算法由于计算复杂度较低而广泛地应用于解决QI补偿。其实现原理如下式所示:
$ \left[\begin{array}{l}{\boldsymbol{I}(t)} \\ {\boldsymbol{Q}(t)}\end{array}\right]=\left[\begin{array}{cc}{1} & {0} \\ {-m} & {n}\end{array}\right]\left[\begin{array}{l}{\boldsymbol{I}^{\prime}(t)} \\ {\boldsymbol{Q}^{\prime}(t)}\end{array}\right] $
(1) 即I(t)=I′(t),Q(t)=nQ′(t)-mI′(t)。其中,m,n为校正系数,I′(t)和Q′(t)分别是已调输出的相位不完全正交的I路和Q路信号,I(t)和Q(t)是经过QI补偿的I路和Q路信号。
若相干接收机输出的两路电信号为:
$ \boldsymbol{I}^{\prime}(t)=\alpha A_{\mathrm{s}} A_{1} \cos \left(\omega_{\mathrm{IF}} t+\theta\right) $
(2) $ \boldsymbol{Q}^{\prime}(t)=\alpha A_{\mathrm{s}} A_{1} \sin \left(\omega_{\mathrm{IF}} t+\theta+\psi\right) $
(3) 式中,α为光电探测器的灵敏度;ωIF, As, Al分别是中频信号的频率、信号光和本振光的幅度;θ和θ+ψ分别是相干接收机输出的两路中频信号的相位。
当m, n的值分别为m=tanψ, n=1/cosψ时,可得中频信号经过GSOP补偿后的两路信号为:
$ \boldsymbol{I}(t)=\alpha A_{\mathrm{s}} A_{1} \cos \left(\omega_{\mathrm{IF}} t+\theta\right) $
(4) $ \boldsymbol{Q}(t)=\alpha A_{{\rm s}} A_{1} \sin \left(\omega_{\mathrm{IF}} t+\theta\right) $
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本文中采用松尾环实现载频的跟踪、捕获。松尾环的鉴相特性是矩形特性,通过矩形振荡状态来分析锁相环的锁定状态。锁相环由数字下变频、数字鉴相器(PD)、环路滤波器三部分组成,下面对这部分实现原理进行分析[18]。
假定由直接数字频率合成器(direct digital synthesizer,DDS)产生的本地载波信号为:
$ \mathit{\boldsymbol{S}} = 2\frac{1}{{\alpha {A_{\rm{s}}}{A_1}}}\cos \left( {{\omega _{{\rm{IF}}}}t + \phi } \right) $
(6) 式中, ϕ是本地载波信号的初始相位,经过乘法器相乘后得到的两路信号为:
$ \begin{array}{*{20}{c}} {{\mathit{\boldsymbol{I}}_1}(t) = \mathit{\boldsymbol{I}}(t) \cdot \mathit{\boldsymbol{S}} = }\\ {\cos \left( {2{\omega _{IF}}t + \theta + \phi } \right) + \cos (\theta - \phi )} \end{array} $
(7) $ \begin{array}{*{20}{c}} {{\mathit{\boldsymbol{Q}}_1}(t) = \mathit{\boldsymbol{Q}}(t) \cdot \mathit{\boldsymbol{S}} = }\\ {\sin \left( {2{\omega _{{\rm{IF}}}}t + \theta + \phi } \right) + \sin (\theta - \phi )} \end{array} $
(8) 再通过低通滤波器滤除二倍频后,得到的两路基带信号为:
$ \mathit{\boldsymbol{I}}_0^\prime (t) = \cos (\theta - \phi ) $
(9) $ \boldsymbol{Q}_{0}^{\prime}(t)=\sin (\theta-\phi) $
(10) 输出的两路信号通过鉴相器得到相位误差信号ud(t),其反映的是环路跟踪相位的程度,鉴相器的设计原理如图 3所示。
由鉴相器的原理可知,基带信号I0′(t), Q0′(t)经鉴相输出相位误差信号为[19]:
$ \begin{aligned} u_{\mathrm{d}}(t)=u_{1} & \oplus u_{2} \oplus u_{5} \oplus u_{6}=\operatorname{sgn}\left(u_{1} u_{2} u_{5} u_{6}\right)=\\ & \operatorname{sgn}\left[\boldsymbol{I}_{0}^{\prime}(t) \boldsymbol{Q}_{0}^{\prime}(t) u_{3} u_{4}\right] \end{aligned} $
(11) 式中,u1=sgn[I0′(t)],u2=sgn[Q0′(t)],u3=I0′(t)+Q0′(t),u4=I0′(t)-Q0′(t),u5=sgn(u3),u6=sgn(u4)。⊕的运算规则如下式所示:
$ \begin{array}{c} {\mathop{\rm sgn}} A \oplus {\mathop{\rm sgn}} B = {\mathop{\rm sgn}} (AB) = \\ \left\{ {\begin{array}{*{20}{l}} { + 1, (A, B符号相同)}\\ { - 1, (A, B符号不同)} \end{array}} \right. \end{array} $
(12) 式中, A和B是两个变量。则将(9)式、(10)式、(12)式带入(11)式可得鉴相器输出的误差信号ud(t)为下式所示:
$ \begin{array}{l}{u_{\mathrm{d}}(t)=\boldsymbol{I}_{0}^{\prime}(t) \boldsymbol{Q}_{0}^{\prime}(t)\left[\boldsymbol{I}_{0}^{\prime}(t)+\boldsymbol{Q}_{0}^{\prime}(t)\right] \times} \\ {\left[\boldsymbol{I}_{0}^{\prime}(t)-\boldsymbol{Q}_{0}^{\prime}(t)\right]=\frac{1}{4} \operatorname{sgn}\{\sin [4(\theta-\phi)]\}}\end{array} $
(13) 误差信号ud(t)再通过环路滤波器,一方面抑制输入噪声,另一方面还能通过环路参量调节环路的校正速度[20]。这里使用常用的二阶理想环路滤波器,其结构图如图 4所示。
其对应的数字化系统函数为:
$ F(z)=c_{1}+\frac{c_{2} z^{-1}}{1-z^{-1}} $
(14) 环路系数c1和c2分别为:$c_{1}=\frac{2 \xi \omega}{K}, c_{2}=\frac{\omega^{2} T}{K} $。其中,ξ为阻尼系数,取值为0.707;K=2πfs(fs=10G sample/s)为环路增益,T为采样周期,Tclk为环路更新周期,ω为环路自然角频率;对于理想二阶环路滤波器,环路等效噪声带宽为:$B_{1}=\frac{\omega}{8 \xi}\left(1+4 \xi^{2}\right) $。其中,Bl取小于10倍的数据速率:Bl=0.1R,R是波特率,代入可得Bl=0.53ω,则可得:c1=3.397×10-5,c2=3.626×10-9。
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在相干解调中,要正确地解调出初始码元,位同步是不可或缺的。要正确地恢复出基带信号,就需要知道接收码元的起止时刻,进行正确地抽样判决,以恢复出正确的基带信号,这里采用直接抽样判决的方法来实现位同步。在经过滤波的基带信号中确定码元的起始位置,在每个码元的中间时刻进行抽样并对其进行判决。根据调制编码原理分析,恢复信号的判决规则如下:若I0′(t)>0,判决结果为I0(t)=1;若I0′(t) < 0,判决结果为I0(t)=0;Q路判决规则同I路。
通过松尾环正确的追踪、捕获,再经过正确的抽样判决,I, Q两路信号得到正确解调。
相干光通信系统中QPSK调制解调实验研究
Experimental study about QPSK modulation and demodulation in coherent optical communication systems
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摘要: 为了使相干接收机输出的两路信号相位正交, 正确地解调信号, 采用施密特正交化算法对两路信号进行了理论分析和实验验证, 经正交失衡算法补偿后, 星座图的性能得到改善; 通过松尾环实现载频的跟踪、捕获以达到载波恢复, 实现了基带信号正确解调。结果表明, 经施密特正交化算法补偿后, 旋转的星座图得到了修正, 星座点间的欧几里德距离不相等问题得到修正, 基带信号畸变得到了改善; 当频偏在-300kHz~300kHz范围内, 松尾环可以实现载频的跟踪、捕获, 基带信号实现正确解调。该方案实现复杂度低, 切实可行, 适用于相干光通信系统的研究。Abstract: In order to make the received two signals orthogonal to each other and correctly demodulate the signal, Schmitt orthogonalization algorithm was used to theoretically analyze and experimentally verify the two signals. The performance of constellation was improved after orthogonal imbalance compensation. The carrier frequency was tracked and captured by the loose tail ring to achieve carrier recovery, and the baseband signal was demodulated correctly. The experimental results show that, after compensation by Schmidt orthogonalization algorithm, the rotated constellation is corrected and the problem of unequal Euclidean distance between constellation points is improved. The baseband signal distortion becomes corrected. When the frequency offset is in the range of -300kHz~300kHz, the loose tail loop can track and capture carrier frequency and baseband signal can be correctly demodulated. The scheme is low complexity and practical, and is suitable for the study of coherent optical communication systems.
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[1] YOSHIDA T, SUGIHARA T, SAWADA K, et al. Polar coordinate transformation based dual binary-drive QPSK modulation[C]//Optical Fiber Communication. New York, USA: IEEE, 2010: OMK4. [2] YAN S, WENG X, GAO Y, et al. Generation of square or hexagonal 16-QAM signals using a dual-drive IQ modulator driven by binary signals[J]. Optics Express, 2012, 20(27):29023-29034. doi: 10.1364/OE.20.029023 [3] SUN H, WU K T, ROBERTS K. Real-time measurements of a 40Gb/s coherent system[J]. Optics Express, 2008, 16(2):873-879. doi: 10.1364/OE.16.000873 [4] CHUNG H S, SUN H C, KIM K, et al. Effects of carrier phase estimation on front-end IQ mismatch compensation in DP-QPSK coherent receiver[C]//Optoelectronics and Communications Conference Held Jointly with 2013 International Conference on Photonics in Switching. New York, USA: IEEE, 2013: TuPR_2. [5] SAVORY S J. Digital coherent optical receivers: algorithms and subsystems[J]. IEEE Journal of Selected Topics in Quantum Electronics, 2010, 16(5):1164-1179. doi: 10.1109/JSTQE.2010.2044751 [6] WANG X J, LEIBLE B, WANG W H, et al. Joint IQ imbalance compensation and channel estimation in coherent optical OFDM systems[C]//2016 10th International Conference on Signal Processing and Communication Systems. New York, USA: IEEE, 2016: 16653749. [7] FATADIN I, SAVORY S J, IVES D. Compensation of quadrature imbalance in an optical QPSK coherent receiver[J]. IEEE Photonics Technology Letters, 2008, 20(20):1733-1735. doi: 10.1109/LPT.2008.2004630 [8] SUN H C, CHUNG H S, KIM K. Impact of quadrature imbalance in optical coherent QPSK receiver[J]. IEEE Photonics Technology Lett-ers, 2009, 21(11):709-711. doi: 10.1109/LPT.2009.2016759 [9] PETROU C S, VGENIS A, ROUDAS I, et al. Quadrature imbalance compensation for PDM QPSK coherent optical systems[J]. IEEE Photonics Technology Letters, 2009, 21(24):1876-1878. doi: 10.1109/LPT.2009.2034750 [10] FARUK M S, KIKUCHI K. Compensation for in-phase/quadrature imbalance in coherent-receiver front end for optical quadrature am-plitude modulation[J]. IEEE Photonics Journal, 2013, 5(2):7800110. doi: 10.1109/JPHOT.2013.2251872 [11] NGUYEN T H, GOMEZ-AGIS F, GAY M, et al. IQ imbalance compensation based on maximum SNR estimation in coherent QPSK systems[C]//2014 16th International Conference on Transparent Optical Networks. New York, USA: IEEE, 2014: 14526430. [12] FARUK M S, SAVORY S J. Digital signal processing for coherent transceivers employing multilevel formats[J]. Journal of Lightwave Technology, 2017, 35(5):2-13. doi: 10.1109/JLT.2017.2683160 [13] MAGARINI M, BARLETTA L, SPALVIERI A, et al. Pilot-symbols-aided carrier-phase recovery for 100G PM-QPSK digital cohe-rent receivers[J]. IEEE Photonics Technology Letters, 2012, 24(9):739-741. doi: 10.1109/LPT.2012.2187439 [14] FLUDGER C R S, BOSCO G, BILAL S M, et al. Multistage carrier phase estimation algorithms for phase noise mitigation in 64-quadrature amplitude modulation optical systems[J]. Journal of Lightwave Technology, 2014, 32(17):2973-2980. doi: 10.1109/JLT.2014.2325064 [15] PAJOVIC M, MILLAR D, KOIKEAKINO T, et al. Multi-pilot aided carrier phase estimation for single carrier coherent systems[C]//Signal Processing in Photonic Communications. Washington DC, USA: The Optical Society of America, 2015: 3-4. [16] HOSSAIN M J, FARUK M S. An efficient scheme for receiver-side quadrature imbalance compensation in coherent optical receivers[C]// 2012 International Conference on Fiber Optics and Photonics. New York, USA: IEEE, 2012: 13597286. [17] FANG Y, GU Q. Angle statistical blind compensation method for IQ imbalance of QPSK signal [J]. System Simulation Technology, 2012, 8(2):87-92(in Chinese). [18] CHANG Q, BI C K, ZHANG Q Sh. The principle and implementation of Costas ring in DSSSK system[J]. Microcomputer Information, 2006, 22(35):241-242(in Chinese). [19] ZHANG X. Digital baseband signal processing algorithm for spread spectrum communication and its VLSI implementation [M]. Beijing: Science Press, 2004:113-115(in Chinese). [20] DU Y. MATLAB and FPGA implementation of digital communication synchronization technology[M]. Beijing: Publishing House of Electronics Industry, 2015:96-218(in Chinese).