摘要:针对高速运动环境下多普勒效应导致的载波频偏,建立了正交频分复用(OFDM)动态状态空间模型,提出了基于改进的强跟踪无迹卡尔曼滤波(STUKF)的频偏跟踪和估计算法。该算法将强跟踪滤波思想跟UKF相结合,通过在计算量测预测协方差和互协方差时引入渐消因子,在调整前一时刻频偏估计误差协方差的同时又控制过程噪声协方差,实时调整增益矩阵,增强了对时变频偏的跟踪能力,提高了估计精度。最后分别在非时变和时变频偏模型下对所提算法进行了仿真验证。仿真结果表明,与UKF频偏估计算法相比,所提算法在时变频偏中具有更好的跟踪和估计性能,在相同误码率(BER)下信噪比(SNR)大约有1dB的提升。
关键词:移动通信;正交频分复用;强跟踪无迹卡尔曼滤波;多普勒效应;频偏估计
中图分类号: TN911.7
文献标志码:A
Abstract: Towards the large frequency offset caused by Doppler effect in high speed moving environment, a dynamic state space model of Orthogonal Frequency Division Multiplexing (OFDM) was built, and a kind of frequency offset tracking and estimation algorithm in OFDM based on improved Strong Tracking Unscented Kalman Filter (STUKF) was proposed. By combining strong tracking filter theory and UKF together, the fading factor was introduced during the process of calculating the measurement predictive covariance and cross covariancethe fading factor was introduced during the process of the covariance and cross covariance forecast in calculating measurements
对于“计算量测预测”的翻译,是否正确?请明确。
The frequency offset estimation error covariance was adjusted; meanwhile, the process noise covariance was also controlled, and the gain matrix was adjusted in realtime. So the tracking ability to timevarying frequency offset was enhanced and the estimated accuracy was raised. The simulation test was carried out in timeinvariant and timevarying frequency offset models. The simulation results show that the proposed algorithm has better tracking and estimation performance than the UKF frequency offset estimation algorithm, the SignaltoNoise Ratio (SNR) raises about 1dB under the same Bit Error Rate (BER).
Key words: mobile communication; Orthogonal Frequency Division Multiplexing (OFDM); Strong Tracking Unscented Kalman Filter (STUKF); Doppler effect; frequency offset estimation
0引言
正交频分复用(Orthogonal Frequency Division Multiplexing, OFDM)系统凭借其具有抗多径效应、高频谱利用率、低实现复杂度等优点,迅速成为研究研究热点并被作为核心技术广泛应用于多个无线标准,例如IEEE802.11a/g,802.16、数字视频广播(Digital Video Broadcasting, DVB)、LTE(Long Term Evolution)、B3G(Beyond Third Generation)等[1]。虽然OFDM在理论研究和工程应用上都已经比较成熟,但是依然存在对载波频移(Carrier Frequency Offset, CFO)、相位噪声敏感,峰均比高等问题。在高速移动环境下难以满足系统的要求,如航空机载通信、陆上高铁通信、低轨卫星通信等终端高速运动环境中[2],终端的高速运动引起的多普勒效应产生大的载波频偏,从而导致OFDM子载波间的正交性遭到破坏引起载波间干扰(InterCarrierInterference, ICI),造成系统性能极大恶化。
近年来,国内外学者已经提出了多种ICI消除算法。Zhao等[3]提出的自消除(SelfCancellation, SC)算法,以及随后提出的基于SC算法的改进算法,如共轭、加权共轭、相位旋转共轭SC算法等[4-6]都是基于相邻ICI系数差别较小的原理。此类算法在二进制相移键控(Binary Phase Shift Keying, BPSK)调制时性能较好,但在大频偏、高阶调制下性能变差,并且频带利用率只有50%。文献[7]提出的最大似然估计(Maximum Likelihood Estimation, MLE)法通过在频域插入两个连续的导频符号,接收端根据相邻符号的相位差估计频偏。MLE算法具备较高的估计精度,与SC算法一样,在大频偏、高阶调制时性能较差。基于滤波原理,文献[8]提出采用扩展卡尔曼滤波(Extended Kalman Filter, EKF)来跟踪和估计频偏,在大频偏下取得较好效果,且具有较高频带利用率。文献[9]针对EKF存在因泰勒展开,舍弃高阶分量带来的截断误差和用EKF频偏估计算法计算Jacobian矩阵运算量大、估值波动大、收敛慢等缺陷,提出了基于无迹卡尔曼滤波(Unscented Kalman Filter, UKF)的频偏估计算法。该算法在大频偏下取得了较好的效果,在收敛性、估值精度、稳定度方面优于EKF算法;然而该算法对时变频偏跟踪能力较弱,在模型误差、干扰、噪声等不确定因素影响比较大时滤波精度和鲁棒性会降低。
本文在对ICI进行数学分析的基础上,针对非时变和时变频偏分别建立了动态状态空间模型,为了提高对时变频偏的跟踪性能,将强跟踪滤波的思想跟UKF结合,在计算量测预测协方差和互协方差时引入渐消因子,实现实时调整增益矩阵,提出了基于改进的强跟踪无迹卡尔曼滤波(Strong Tracking Unscented Kalman Filter, STUKF)的OFDM频偏迭代估计算法。仿真分析表明,与UKF频偏估计算法相比,该算法在跟踪和估计时变频偏方面性能较好,且具备较强的鲁棒性。
3仿真分析
为了验证本文所提的STUKF频偏估计算法的性能,分别在非时变和时变模型下对其频偏跟踪和估计性能进行仿真验证。仿真参数为:子载波数N=64;训练序列采用PN序列,长度为64;归一化载波频偏为ε=0.25;AR1模型初始频偏ε0=0.25;采用16正交幅度调制(16 Quadrature Amplitude Modulation, 16QAM)高阶调制,加性高斯白噪声信道;STUKF的参数选择为κ=0,α=1, β=2频偏估计的初值设置为0.01,系统噪声和量测噪声的均值;系统噪声方差都取0,量测噪声方差取0.04。
图3(a)为定频偏ε=0.25时的误码率(Bit Error Rate, BER)曲线。通过比较可以发现,SC算法、MLE算法在大频偏高阶调制下传输性能下降,存在地板效应,而UKF和本文所提出的STUKF在大频偏下依然具有较好的传输性能。图3(b)为时变频偏下误码率曲线。此种情况下,本文算法比UKF算法性能好,说明了本文算法对时变频偏具有更好的跟踪能力。UKF和STUKF频偏估计算法性能接近,这是因为两种算法的频偏估值是经过多次迭代后的结果,都达到收敛状态时,已经接近频偏真值。故在每个信噪比(SignaltoNoise Ratio, SNR)下通过蒙特卡罗仿真求平均后的误码率非常接近。为了比较两者的收敛特性,本文分别在固定频偏和时变频偏下进行了仿真分析。
图4为SNR=15dB、固定频偏ε=0.25时的收敛曲线。通过分析可以看出,在迭代开始时由于频偏未知,频偏估值不准确,误差较大,但是随着迭代的进行大约在30步实现了对频偏的精确跟踪和估计。本文提出的STUKF比UKF收敛速度稍快,精度略高。这是因为固定频偏下强跟踪滤波的跟踪性能体现得不明显。图5中CFOAR1代表初始频偏为0.25时AR1模型的时变频偏的变化曲线,为了体现本文算法的对噪声的鲁棒性,系统噪声和量测噪声方差都取值为0.04。可以明显地看到迭代进行到大约30步时本文所提出的强跟踪UKF算法已经实现对时变频偏的有效跟踪和精确估计,相比文献[9]中的基于UKF频偏估计算法在对时变频偏的跟踪能力和估计精度上都有明显提高。
4结语
通过对多普勒效应导致的OFDM载波间干扰问题的数学分析,建立了频偏的动态状态空间模型,采用改进的强跟踪UKF频偏估计算法进行了仿真分析。实验结果表明,该算法在大频偏、高阶调制下传输性能较好,对时变频偏具有较强的跟踪和估计性能,能够有效纠正频偏引起的星座图旋转,提升系统的传输性能。
参考文献:
[1]LI D, ZHANG H. Review of key technology of 3G and TDLTE mobile communication systems for highspeed railway [J]. Application Research of Computers, 2013, 30(5): 1297-1301.(李丹,庄宏成.高速铁路3G及TDLTE移动通信关键问题研究综述[J].计算机应用研究,2013,30(5):1297-1301.)
[2]CHEN Q, YANG X, OUYANG C, et al. Estimation of carrier frequency offset in aeronautical mobile communication OFDM system based on TDNLMS algorithm [J]. Journal of Air Force Engineering University: Natural Science Edition, 2013, 14(1): 71-74.(陈强,杨霄鹏,欧阳超,等.基于TDNLMS的航空移动通信OFDM系统载波频率偏移消除[J].空军工程大学学报:自然科学版,2013,14(1):71-74.)
[3]ZHAO Y, HAGGMAN S. Intercarrier interference selfcancellation scheme for OFDM mobile communication systems [J]. IEEE Transactions on Communications, 2001, 49(7): 1185-1191.
[4]PENG YH, KUO YC, LEE GR, et al. Performance analysis of a new ICI selfcancellation scheme in OFDM systems [J]. IEEE Transactions on Consumer Electronics, 2007, 53(4): 1333-1338.
[5]WANG C, HUANG Y. Intercarrier interference cancellation using general phase rotated conjugate transmission for OFDM systems [J]. IEEE Transactions on Communications, 2010, 58(3): 812-819.
[6]TSENG SM, HUANG YS. A novel ICI selfcancellation scheme for OFDM systems [J]. International Journal of Communication Systems, 2011, 24(11): 1496-1505.
[7]YU J, SU Y. Pilotassisted maximumlikelihood frequencyoffset estimation for OFDM systems [J]. IEEE Transactions on Communications, 2004, 52(11): 1997-2008.
[8]ZHAO P, KUANG L, LU J. Carrier frequency offset estimation using extended Kalman filter in uplink OFDMA systems [C]// Proceedings of the 2006 IEEE International Conference on Communications. Washington, DC: IEEE Computer Society, 2006: 2870-2874.
[9]ZHANG X, YE F, YANG B, et al. Application of SigmaPoint Kalman filter to carrier frequency offset estimation of OFDM system [J]. Journal of Tianjin University: Science and Technology, 2013, 46(5): 458-462.(张鑫明,叶锋,杨波,等.SigmaPoint卡尔曼滤波用于OFDM载波频偏估计[J].天津大学学报:自然科学与工程技术版,2013,46(5):458-462.)
[10]ZHANG X M, YANG B, LI S. An unscented Kalman filter for ICI cancellation in highmobility OFDM system [C]// Proceedings of the IEEE 73th Vehicular Technology Conference. Washington, DC: IEEE Computer Society, 2011: 1-5.
[11]JULIER S, UHLMANN J, DURRANTWHYTE H F. A new method for the nonlinear transformation of means and covariance in filters and estimators [J]. IEEE Transactions on Automatic Control, 2000, 45(3): 477-482.
[12]GUO Z, MIAO L, ZHAO H. An improved strong tracking UKF and the application in initial alignment under large azimuth misalignment angles[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(1): 203-214.(郭泽,缪玲娟,赵洪松.一种改进的强跟踪UKF算法及其在SINS大方位失准角初始对准中的应用[J].航空学报,2014,35(1):203-214.)
[13]WANG X, ZHAO L, XIA Q, et al. Strong tracking filter based on unscented transformation [J]. Control and Decision, 2010, 25(7): 1063-1068.(王小旭,赵琳,夏全喜,等.基于Unscented变换的强跟踪滤波器[J].控制与决策,2010,25(7):1063-1068.)
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