Symbol-variance Feedback Equalizer for Turbo Equalization
WU Yanbo①② FANG Xiaofang②③ ZHU Min①②
①(State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China) ②(Ocean Acoustic Technology Center, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China) ③(University of Chinese Academy of Sciences, Beijing 100190, China)
A novel Symbol-Variance Feedback Equalizer (SVEF) algorithm is proposed to reduce the computational complexity of the equalizer in Turbo equalization. The derivation of the algorithm is based on the Taylor expansion of the Linear Minimum Mean Squared Error (LMMSE) estimation function. In the proposed scheme, the initial estimates are obtained from the time-invariant equalizer, then the estimates are weighted by the a priori symbol variances and finally filtered by a time-invariant filter to obtain better estimates. As the time-variant a priori symbol variances are utilized, the performance of the proposed equalizer is much closer to that of the exact MMSE linear equalizer. Simulation results show that the Signal-to-Noise Ratio (SNR) loss of the proposed scheme in Proakis C channel is reduced to 0.17 dB from 0.83 dB compared to the various time-invariant MMSE Turbo equalization, and its computational complexity can be reduced to logarithmical order by implementation based on the fast Fourier transform.
DOUILLARD C, JEZEQUEL M, BERROU C, et al. Iterative correction of intersymbol interference: Turbo- equalization[J]. European Transactions on Telecommunications and Related Technologies, 1995, 6(5): 507-511. doi: 10.1002/ett.4460060506.
[2]
TUCHLER M, KOETTER R, and SINGER A C. Turbo equalization: principles and new results[J]. IEEE Transactions on Communications, 2002, 50(5): 754-767. doi: 10.1109/TCOMM.2002.1006557.
[3]
TUCHLER M, SINGER A C, and KOETTER R. Minimum mean squared error equalization using a priori information[J]. IEEE Transactions on Signal Processing, 2002, 50(3): 673-683. doi: 10.1109/78.984761.
[4]
LOPES R R. Iterative estimation, equalization and decoding[D]. [Ph.D. dissertation], Georgia Institute of Technology, 2003.
[5]
TUCHLER M and SINGER A C. Turbo equalization: An overview[J]. IEEE Transactions on Information Theory, 2011, 57(2): 920-952. doi: 10.1109/TIT.2010.2096033.
[6]
GUO Q and HUANG D. Concise representation for the soft-in soft-out LMMSE detector[J]. IEEE Communications Letters, 2011, 15(5): 566-568. doi: 10.1109/LCOMM.2011. 032811.102073.
[7]
LAOT C, GLAVIEUX A, and LABAT J. Turbo equalization: adaptive equalization and channel decoding jointly optimized[J]. IEEE Journal on Selected Areas in Communications, 2001, 19(9): 1744-1752. doi: 10.1109/ 49.947038.
[8]
STOJANOVIC M and PREISIG J. Underwater acoustic communication channels: propagation models and statistical characterization[J]. IEEE Communications Magazine, 2009, 47(1): 84-89. doi: 10.1109/MCOM.2009.4752682.
[9]
SINGER A C, NELSON J K, and KOZAT S S. Signal processing for underwater acoustic communications[J]. IEEE Communications Magazine, 2009, 47(1): 90-96. doi: 10.1109/ MCOM.2009.4752683.
XU Hao, ZHU Min, and WU Yanbo. An algorithm of multi-array Turbo equalization of underwater acoustic communication[J]. Journal of Electronics & Information Technology, 2014, 36(6): 1465-1471. doi: 10.3724/SP.J.1146. 2013.01027.
[11]
LOU H A and XIAO C S. Soft-decision feedback Turbo equalization for multilevel modulations[J]. IEEE Transactions on Signal Processing, 2011, 59(1): 186-195. doi: 10.1109/TSP.2010.2083656.
[12]
VOGELBRUCH F and HAAR S. Low complexity Turbo equalization based on soft feedback interference cancelation [J]. IEEE Communications Letters, 2005, 9(6): 586-588. doi: 10.1109/LCOMM.2005.07016.
DOU Gaoqi, GAO Jun, TAO Wei, et al. Sequence-based block decision-aided equalizer for Turbo equalization[J]. Journal of Electronics & Information Technology, 2009, 31(9): 2152-2156.
[14]
KIM K, KALANTAROVA N, KOZAT S S, et al. Linear MMSE-optimal Turbo equalization using context trees[J]. IEEE Transactions on Signal Processing, 2013, 61(12): 3041-3055. doi: 10.1109/TSP.2013.2256899.
YANG Xiaoxia, WANG Haibin, WANG Jun, et al. Blind Turbo equalization based on channel identification for underwater acoustic communications[J]. Journal of Applied Acoustics, 2015, 34(2): 125-134.
ZHANG Dongling, YANG Yong, LI Jing, et al. Blind data recovery of single-channel mixed signals based on Turbo equalization and channel estimation[J]. Journal of Chinese Institute of Communications, 2014, 35(1): 47-61.
[17]
PROAKIS J G and MANOLAKIS D G. Digital Signal Processing: Principles, Algorithms and Applications[M]. 4th ed, New Jersey: Prentice-Hall, 2007.
[18]
PROAKIS J G and SALEHI M. Digital Communications[M]. 5th ed, New York: McGraw-Hill, 2008: 640-672.
[19]
LEE S J, SINGER A C, and SHANBHAG N R. Linear Turbo equalization analysis via BER transfer and EXIT charts[J]. IEEE Transactions on Signal Processing, 2005, 53(8): 2883-2897. doi: 10.1109/TSP.2005.850375.
[20]
MOVAHEDIAN A and MCGUIRE M. On the capacity of iteratively estimated channels using LMMSE estimators[J]. IEEE Transactions on Vehicular Technology, 2015, 64(1): 97-107. doi: 10.1109/TVT.2014.2320928.
ZHONG Kai, PENG Hua, and GE Lindong. Turbo frequency domain equalization algorithm based on Rimoldi decomposition for continuous phase modulation signals[J]. Journal of Electronics & Information Technology, 2014, 36(5): 1190-1195. doi: 10.3724/SP.J.1146.2013.00990.
