OFDM信道估计算法研究
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摘要
正交频分复用(OFDM, Orthogonal frequency division multiplexing)具有高的频谱利用率和良好的抗多径干扰能力,是未来无线通信的核心技术之一。
信道估计是OFDM的研究热点之一。依据归一化帧频偏(NFDS, Normalized FrameDoppler),其定义为帧长度与信道相关时间之比,本文将信道划分为三类：慢时变(NFDS≤0.1),中等时变(0.11)。主要工作如下：
(一)在慢时变典型城市信道,重点研究了线性内插、Sinc内插、高斯内插和线性最小均方误差(LMMSE, Linear minimum mean square error)算法。针对LMMSE存在统计适配的问题,提出基于门限的自适应LMMSE算法,通过仿真发现：当插入导频较密时,Sinc内插和高斯内插的性能逼近LMMSE,考虑它们的复杂度非常低,因此非常具有吸引力；当统计相关函数同实际信道存在适配时,自适应LMMSE算法的均方误差相对于LMMSE有4dB的信噪比提升。
(二)在三种典型时变城市信道,重点研究了二维LMMSE、单维LMMSE、Sinc函数内插和基于多项式函数基展开算法。为了降低复杂度,我们提出加权二次样条函数信道估计算法。仿真表明：在所有三种信道条件下,因为充分挖掘了信道的统计特性,二维LMMSE始终是性能最优的信道估计器,同时也是复杂度最高的估计器；基于多项式函数基展开和二次样条函数基展开具有复杂度低和性能优的特点,因此也具有较大吸引力；特别指出的是,当0.3≤NFDS≤0.8时,二次样条函数基展开算法实现了复杂度和性能的较好折衷。
Orthogonal frequency division multiplexing (OFDM) has the following advantages: high spectrum efficiency and a good ability to combat muti-path interference. Thus, it is considered as one of the key techniques of future wireless communications.
Channel estimation is one of the hot research topics of OFDM. According to normalized frame Doppler spread (NFDS=frame time length/coherent time), wireless channels are divided into three categories: slow time-varying channel(NFDS≤0.1), medium time-varying channel(0.11). The main works are as follows:
a) In slow time-varying typical Urban (TU) channel, we focus mainly on investigating linear interpolation (LI), Sinc interpolation (SI), Gaussian interpolation (GI) and linear minimum mean square error (LMMSE). The problem of the LMMSE algorithm is statistics mismatch, in order to solve it, an adaptive LMMSE algorithm based on threshold is proposed. Simulation shows: in the case of a dense pilot grid, the performance of SI and GI is close to that of LMMSE, considering their low complexity, they are very attractive; this adaptive algorithm achieves a 4dB signal-to-noise ratio (SNR) gain on mean square error (MSE) performance over the original LMMSE when there is mismatch between statistical correlation and exact correlation.
b) In three time-varying TU channels, we focus mainly on the study of two-dimensional LMMSE (2D LMMSE), one-dimensional time-frequency LMMSE (1D LMMSE), sinc interpolation (SI), and polynomial basis expansion based model algorithm. To reduce complexity of channel estimation, a weighted second-order spline (WSOS) basis algorithm is proposed. Simulation results show: due to its exploiting the statistical property of time-varying channels, the 2D LMMSE perform best in three time-varying channels, however, its computational amount is very high compared with polynomial, WSOS and 1D LMMSE; due to low complexity and good performance, polynomial and WSOS are attractive for time-varying channel estimation; particularly, the proposed WSOS can strike a good balance between complexity and performance for 0.3≤NFDS≤0.8.
信道估计是OFDM的研究热点之一。依据归一化帧频偏(NFDS, Normalized FrameDoppler),其定义为帧长度与信道相关时间之比,本文将信道划分为三类：慢时变(NFDS≤0.1),中等时变(0.1
(一)在慢时变典型城市信道,重点研究了线性内插、Sinc内插、高斯内插和线性最小均方误差(LMMSE, Linear minimum mean square error)算法。针对LMMSE存在统计适配的问题,提出基于门限的自适应LMMSE算法,通过仿真发现：当插入导频较密时,Sinc内插和高斯内插的性能逼近LMMSE,考虑它们的复杂度非常低,因此非常具有吸引力；当统计相关函数同实际信道存在适配时,自适应LMMSE算法的均方误差相对于LMMSE有4dB的信噪比提升。
(二)在三种典型时变城市信道,重点研究了二维LMMSE、单维LMMSE、Sinc函数内插和基于多项式函数基展开算法。为了降低复杂度,我们提出加权二次样条函数信道估计算法。仿真表明：在所有三种信道条件下,因为充分挖掘了信道的统计特性,二维LMMSE始终是性能最优的信道估计器,同时也是复杂度最高的估计器；基于多项式函数基展开和二次样条函数基展开具有复杂度低和性能优的特点,因此也具有较大吸引力；特别指出的是,当0.3≤NFDS≤0.8时,二次样条函数基展开算法实现了复杂度和性能的较好折衷。
Orthogonal frequency division multiplexing (OFDM) has the following advantages: high spectrum efficiency and a good ability to combat muti-path interference. Thus, it is considered as one of the key techniques of future wireless communications.
Channel estimation is one of the hot research topics of OFDM. According to normalized frame Doppler spread (NFDS=frame time length/coherent time), wireless channels are divided into three categories: slow time-varying channel(NFDS≤0.1), medium time-varying channel(0.1
a) In slow time-varying typical Urban (TU) channel, we focus mainly on investigating linear interpolation (LI), Sinc interpolation (SI), Gaussian interpolation (GI) and linear minimum mean square error (LMMSE). The problem of the LMMSE algorithm is statistics mismatch, in order to solve it, an adaptive LMMSE algorithm based on threshold is proposed. Simulation shows: in the case of a dense pilot grid, the performance of SI and GI is close to that of LMMSE, considering their low complexity, they are very attractive; this adaptive algorithm achieves a 4dB signal-to-noise ratio (SNR) gain on mean square error (MSE) performance over the original LMMSE when there is mismatch between statistical correlation and exact correlation.
b) In three time-varying TU channels, we focus mainly on the study of two-dimensional LMMSE (2D LMMSE), one-dimensional time-frequency LMMSE (1D LMMSE), sinc interpolation (SI), and polynomial basis expansion based model algorithm. To reduce complexity of channel estimation, a weighted second-order spline (WSOS) basis algorithm is proposed. Simulation results show: due to its exploiting the statistical property of time-varying channels, the 2D LMMSE perform best in three time-varying channels, however, its computational amount is very high compared with polynomial, WSOS and 1D LMMSE; due to low complexity and good performance, polynomial and WSOS are attractive for time-varying channel estimation; particularly, the proposed WSOS can strike a good balance between complexity and performance for 0.3≤NFDS≤0.8.
引文
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[46]S G Kang, Y M Ha, E K Joo. A Comparative Investigation on Channel Estimation Algorithms for OFDM in Mobile Communications. IEEE Trans on Broadcasting, vol.49, no. 2, June.2003, pp.142-144
[47]S Coleri, M Ergen, A Puri, A Bahai. A Study of Channel Estimation in OFDM Systems. IEEE 56th Vehicular Technology Conference, vol.2, Dec.2002, pp.894-898
[48]N Wang, P Deng. Interpolation in OFDM channel estimation based on pilot arrangement. Journal of ChengDu University of Information Technology, vol.23, no.2, Apr. 2008, pp.141-146
[49]Y Zhao. A Huang. A novel channel estimation method for OFDM Mobile Communications Systems based on pilot signals and transform domain processing, in Proc. IEEE 47th Vehicular Technology Conference, Phoenix, USA, May.1997, pp.2089-2093
[50]J J Beek, M Sandell, P O B"orjesson. ML Estimation of Time and Frequency Offset in OFDM Systems. IEEE Trans on Signal Processing, vol.45, no.7, July.1997, pp.1801-1802
[51]F Shu, Y b Han, Y f Bi, S.x.Cheng. Threshold-based ML Channel Estimation for OFDM System in Sparse Wireless Channel. IEEE International Symposium on Microwave, Antenna, Propagation, and EMC Technologies For Wireless Communications,2007, pp. 1208-1214
[52]M Morelli, U Mengali. A Comparison of Pilot-Aided Channel Estimation Methods for OFDM Systems. IEEE Trans on Signal Processing, vol.49, no.12, Dec.2001, pp.3067-3073
[53]Y Li. Pilot-symbol-aided channel estimation for OFDM in wireless system. IEEE 49th Vehicular Technology Conference, vol.2, July.1999, pp.1131-1135
[54]Nilsson R, Edfors O, Sandell M, Borjesson P O. Two-Dimensional Pilot-Symbol Assisted Modulation for OFDM. In Proceedings of IEEE International Conference on Personal Wireless Communications (ICPWC 97), Bombay, India, Dec.1997, pp.71-74
[55]Yang B, Letaief K B, Cheng R S, Cao Z. Channel Estimation for OFDM Transmission in Multipath Fading channels Based on Parametric Channel Modeling. IEEE Transactions on Communications, vol.49, Mar.2001, pp.467-479
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[2]王文博,郑侃.宽带无线通信OFDM技术.北京：人民邮电出版社,2003,11
[3]佟学俭,罗涛.OFDM移动通信技术原理与应用.北京：人民邮电出版社,2003,6
[4]S B Weistein, P M Ebert. Data transmission by frequency-division multiplexing using the discrete fourier transform. IEEE Trans. Commun, vol.19, no.5, Oct.1971, pp.628-634
[5]ESTI. Radio broadcasting systems:Digital Audio Broadcasting(DAB) to mobile, portable and fixed receivers. Technical Report, ETS 300 401, ETSI, May.1997
[6]M Alard, R Lassalle. Principles of modulation and channel coding for digital broadcasting for mobile receivers. EBUReview, no.224, Aug.1987, pp.3-25
[7]ESTI. Digital Video Broadcasting(DVB):framing structure, channel coding and modulation for digital terrestrial television. ETS 300 744, ETSI, Aug.1997
[8]IEEE 802.11. IEEE standard for wireless LAN medium accss control and physical layer specifications.1997
[9]ETSI ETS 300 652/A2. Radio Equipment and Systems(RES), High Performance Radio Local Area Network(HIPERLAN) Type 1. Functional specification,1998
[10]Y Su Kim. New Rayleigh Fading Channel Estimator Based on PS AM Channel Sounding Technique. IEEE international conference on communications, vol.3, Jun.1997, pp. 1518-1520
[11]3GPP2 C.S0084-001 v2.0, Ultra Mobile Broadband Air Interface Specification. Sep. 2007
[12]Wang M M, Dong M. Channelization in ultra mobile broadband communication systems:the forward link. Int. Wirel, Commun, Mobile Comput,2008, pp.614-620
[13]Wang M M, Dong M. Channelization in ultra mobile broadband communication systems:the reverse link. Int. Wirel. Commun, Mobile Comput, Aug.2008, pp.367-372
[14]IEEE Standard for Local and metropolitan area networks Part 20:Air interface for mobile broadband wireless access systems supporting vehicular mobility physical and media access control layer specification. Aug.2008
[15]Greespan A, Klerer M, Tomcik J, Canchi R, Wilson J. IEEE 802.20:mobile broadband wireless access for the twentyfirst century. IEEE Commun. Mag,2008,46, pp.56-63
[16]3GPP TS36.201:LTE physical layer-general description. Aug.2007
[17]Khan F. LTE for 4G mobile broadband:air interface technologies and performance. Cambridge University Press,2009
[18]Astely D, Dahlaman E, Furuskar A, Jading Y, Lindstrom M, Parkwall S. LTE:the evolution of mobile broadband. IEEE Commun. Mag,2009,47, pp.44-51
[19]POOLE I. Elements turorial-what exactly is LTE, IET Commun. Eng,2007,5, pp.46-47
[20]IEEE P802.16e/D12:Air interface for fixed and mobile broadband wireless access systems. Oct.2006
[21]Conti J. The long road to WiMAX [wireless MAN standard]. IEEE Rev,2005,51, pp. 38-42
[22]IEEE P802.16, WiMAX Specification, Draft 8, May.2005
[23]M M Wang, T Ji. Dynamic resource allocation for interference management in orthogonal frequency division multiple access cellular communications. IET Communications, 22nd. Oct.2009
[24]R Negi, J Cioffi. Pilot tone selection for channel estimation in a mobile OFDM system. IEEE Trans on Consumer Electronics, vol.44, no.3, Aug.1998, pp.1122-1127
[25]J J Beek, O Edfors, M Sandell, S K.Wilson, P O Borjesson. On Channel Estimation in OFDM Systems. IEEE 4th Vehicular Technology Conference, vol.2,1995, pp.815-819
[26]Edfors, M Sandell, J J Beek, S K Wilson, P O B¨orjesson. OFDM Channel Estimation by Singular Value Decomposition. IEEE Trans Commun, vol.46, no.7, July.1998, pp. 931-938
[27]F Shu, J Lee, L N Wu, G L Zhao. Time-frequency channel estimation for digital amplitude modulation broadcasting systems based on OFDM. IEEE Proc. Commun, vol.150, no.4,Aug.2003,pp.259-163
[28]L Xiao, X d Dong, Anthony, C K Soong. On the Design of Sinc Interpolator for Pilot Symbol Assisted Modulation Systems. IEEE Trans on Wireless Commun, vol.5, no.9, Sep, 2006, pp.2578-2579
[29]H Hijazi, L Ros. Polynomial Estimation of Time-Varying Multipath Gains With Intercarrier Interference Mitigation in OFDM Systems. IEEE Transactions on Vehicular Technology, vol.58, no.1, Jan.2009, pp.144-150
[30]X w Wang, K J Ray Liu, Channel Estimation for Multicarrier Modulation Systems Using a Time-Frequency Polynomial Mode. IEEE Trans Commun, vol.50, no.7, July.2002, pp.1045-1048
[31]M X Chang, Y T Su. Model-Based Channel Estimation for OFDM Singals in Ray-leigh Fading. IEEE Trans Commun, vol.50, no.4, April.2002, pp.540-543
[32]Leonard J. Cimini JR. Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing. IEEE Trans. Commun, vol.33, no.7, July.1985, pp.665-675
[33]徐以涛,程云鹏.数字信号处理.西安：西安电子科技大学出版社,2009
[34]Hoeher S, Kaiser P, Robertson. Two-dimensional pilot-symbol-aided channel estimation by Wiener filtering. IEEE International Conference, vol.3,1997, pp.1845-1848
[35]Hou X, Li S, Liu D, Yin C, Yue G.. On Two-dimensional Adaptive Channel Estimation in OFDM Systems.60th IEEE Vehicular Technology Conference, Los Angeles, Ca, vol.1, Sep.2004, pp.498-502
[36]S Coleri, M Ergen, A Puri, A Bahai. Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems. IEEE Transactions on Broadcasting, vol.48, no.3, Sep. 2002, pp.223-229
[37]M Han, Hsieh, C H Wei. Channel Estimation for OFDM systems Based on Comb-Type Pilot Arrangement in Frequency selective Fading Channel. IEEE Transactions on Consumer Electronics, vol.44, no.1, Feb.1998, pp.217-222
[38]张继东,郑宝玉.基于导频的OFDM信道估计及其研究进展.通信学报,vol.23,no.11.Nov.2003
[39]Y Shen, E Martinez. Channel Estimation in OFDM Systems, Freescale Semiconductor, 2006, pp.3-8
[40]T S Rappaport. Wireless Communication principles and practice.2nd Edition.电子工业出版社,2006,7
[41]杨大成.移动传播环境：理论基础、分析方法和建模技术.北京：机械工业出版社,2003,8
[42]S Haykin, M Moher. Modern Wireless Communications.北京：电子工业出版社,2006,5
[43]H H Chen, M Guizani. Next Generation Wireless Systems and Networks.北京：机械工业出版社,2008,1
[44]ETSI, Universal Mobile Telecommunications System (UMTS). ETSI TR 125 943 V5. 1.0.2002.6
[45]O Simeone, Y Bar-Ness, U Spagnolini. Pilot-Based Channel Estimation for OFDM Systems by Tracking the Delay-Subspace. IEEE Trans on Wireless Commun, vol.3, no.1, Jan. 2004, pp.315-325
[46]S G Kang, Y M Ha, E K Joo. A Comparative Investigation on Channel Estimation Algorithms for OFDM in Mobile Communications. IEEE Trans on Broadcasting, vol.49, no. 2, June.2003, pp.142-144
[47]S Coleri, M Ergen, A Puri, A Bahai. A Study of Channel Estimation in OFDM Systems. IEEE 56th Vehicular Technology Conference, vol.2, Dec.2002, pp.894-898
[48]N Wang, P Deng. Interpolation in OFDM channel estimation based on pilot arrangement. Journal of ChengDu University of Information Technology, vol.23, no.2, Apr. 2008, pp.141-146
[49]Y Zhao. A Huang. A novel channel estimation method for OFDM Mobile Communications Systems based on pilot signals and transform domain processing, in Proc. IEEE 47th Vehicular Technology Conference, Phoenix, USA, May.1997, pp.2089-2093
[50]J J Beek, M Sandell, P O B"orjesson. ML Estimation of Time and Frequency Offset in OFDM Systems. IEEE Trans on Signal Processing, vol.45, no.7, July.1997, pp.1801-1802
[51]F Shu, Y b Han, Y f Bi, S.x.Cheng. Threshold-based ML Channel Estimation for OFDM System in Sparse Wireless Channel. IEEE International Symposium on Microwave, Antenna, Propagation, and EMC Technologies For Wireless Communications,2007, pp. 1208-1214
[52]M Morelli, U Mengali. A Comparison of Pilot-Aided Channel Estimation Methods for OFDM Systems. IEEE Trans on Signal Processing, vol.49, no.12, Dec.2001, pp.3067-3073
[53]Y Li. Pilot-symbol-aided channel estimation for OFDM in wireless system. IEEE 49th Vehicular Technology Conference, vol.2, July.1999, pp.1131-1135
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