Low-Complexity Joint Channel Estimation and Symbol Detection for OFDMA Systems
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摘要
In this paper, we propose a joint channel estimation and symbol detection(JCESD) algorithm relying on message-passing algorithms(MPA) for orthogonal frequency division multiple access(OFDMA) systems. The channel estimation and symbol detection leverage the framework of expectation propagation(EP) and belief propagation(BP) with the aid of Gaussian approximation, respectively. Furthermore, to reduce the computation complexity involved in channel estimation, the matrix inversion is transformed into a series of diagonal matrix inversions through the Sherman-Morrison formula. Simulation experiments show that the proposed algorithm can reduce the pilot overhead by about 50%, compared with the traditional linear minimum mean square error(LMMSE) algorithm, and can approach to the bit error rate(BER) performance bound of perfectly known channel state information within 0.1 dB.
In this paper, we propose a joint channel estimation and symbol detection(JCESD) algorithm relying on message-passing algorithms(MPA) for orthogonal frequency division multiple access(OFDMA) systems. The channel estimation and symbol detection leverage the framework of expectation propagation(EP) and belief propagation(BP) with the aid of Gaussian approximation, respectively. Furthermore, to reduce the computation complexity involved in channel estimation, the matrix inversion is transformed into a series of diagonal matrix inversions through the Sherman-Morrison formula. Simulation experiments show that the proposed algorithm can reduce the pilot overhead by about 50%, compared with the traditional linear minimum mean square error(LMMSE) algorithm, and can approach to the bit error rate(BER) performance bound of perfectly known channel state information within 0.1 dB.
In this paper, we propose a joint channel estimation and symbol detection(JCESD) algorithm relying on message-passing algorithms(MPA) for orthogonal frequency division multiple access(OFDMA) systems. The channel estimation and symbol detection leverage the framework of expectation propagation(EP) and belief propagation(BP) with the aid of Gaussian approximation, respectively. Furthermore, to reduce the computation complexity involved in channel estimation, the matrix inversion is transformed into a series of diagonal matrix inversions through the Sherman-Morrison formula. Simulation experiments show that the proposed algorithm can reduce the pilot overhead by about 50%, compared with the traditional linear minimum mean square error(LMMSE) algorithm, and can approach to the bit error rate(BER) performance bound of perfectly known channel state information within 0.1 dB.
引文
[1]L.Dai,B.Wang,Y.Yuan,S.Han,C.I,and Z.Wang,“Non-orthogonal multiple access for 5G:solutions,challenges,opportunities,and future research trends,”IEEE Commun.Mag.,vol.53,no.9,Sep.2015,pp.74-81.
[2]W.Feng,Y.Wang,D.Lin,N.Ge,J.Lu,and S.Li,“When mmWave communications meet network densification:a scalable interference coordination perspective,”IEEE J.Sel.Areas Commun.,vol.35,no.7,Jul.2017,pp.1459-1471.
[3]R.Zhang,M.Wang,L.X.Cai,Z.Zheng,X.Shen,and L.Xie,“LTEunlicensed:the future of spectrum aggregation for cellular networks,”IEEEWireless Commun.,vol.22,no.3,June.2015,pp.150-159.
[4]F.Zheng,W.Li,L.Meng,P.Yu,and L.Peng,“Distributed energy saving mechanism based on CoMP in LTE-A system,”China Communications,vol.13,no.7,Jul.2016,pp.39-47.
[5]P.Guan,D.Wu,T.Tian,J.Zhou,X.Zhang,L.Gu,A.Benjebbour,M.Iwabuchi,and Y.Kishiyama,“5G field trials:OFDM-based waveforms and mixed numerologies,”IEEE J.Sel.Areas Commun.,vol.35,no.6,Jun.2017,pp.1234-1243.
[6]V.Vahidi and E.Saberinia,“OFDM high speed train communication systems in 5G cellular networks,”in 2018 15th IEEE Annual Consumer Communications Networking Conference(CCNC),Jan.2018,pp.1-6.
[7]H.Tan,Y.Liu,Z.Feng,and Q.Zhang,“Coexistence analysis between 5G system and fixed-satellite service in 3400a3600 mhz,”China Communications,vol.15,no.11,Nov.2018,pp.25-32.
[8]Y.Ma and R.Tafazolli,“Channel estimation for OFDMA uplink:a hybrid of linear and BEMinterpolation approach,”IEEE Trans.Signal Process.,vol.55,no.4,Apr.2007,pp.1568-1573.
[9]B.Yang,Z.Cao,and K.B.Letaief,“Analysis of low-complexity windowed DFT-based MMSEchannel estimator for OFDM systems,”IEEETrans.Commun.,vol.49,no.11,Nov.2001,pp.1977-1987.
[10]M.R.Raghavendra,E.Lior,S.Bhashyam,and K.Giridhar,“Parametric channel estimation for pseudo-random tile-allocation in uplink OFD-MA,”IEEE Trans.Signal Process.,vol.55,no.11,Nov.2007,pp.5370-5381.
[11]M.O.Pun,S.-H.Tsai,and C..J.Kuo,“An EM-based joint maximum likelihood estimation of carrier frequency offset and channel for uplink OFDMA systems,”in IEEE 60th Vehicular Technology Conference,2004.VTC2004-Fall.2004,vol.1,Sep.2004,pp.598-602 Vol.1.
[12]M.O.Pun,M.Morelli,and C..J.Kuo,“Maximum-likelihood synchronizationand channel estimation for OFDMA uplink transmissions,”IEEE Trans.Commun.,vol.54,no.4,Apr.2006,pp.726-736.
[13]S.Sezginer and P.Bianchi,“Joint frequency offset and channel estimation in the OFDMA uplink:Cramer-Rao bounds and training sequence design,”in IEEE 6th Workshop on Signal Processing Advances in Wireless Communications,2005.,Jun.2005,pp.585-589.
[14]S.Omar,A.Ancora,and D.T.M.Slock,“Performance analysis of general pilot-aided linear channel estimation in LTE OFDMA systems with application to simplified MMSE schemes,”in 2008 IEEE 19th International Symposium on Personal,Indoor and Mobile Radio Communications,Sep.2008,pp.1-6.
[15]O.Edfors,M.Sandell,J..van de Beek,S.K.Wilson,and P.O.Borjesson,“OFDM channel estimation by singular value decomposition,”in Proceedings of Vehicular Technology ConferenceVTC,vol.2,Apr.1996,pp.923-927 vol.2.
[16]H.Zhang,X.Dai,D.Li,and S.Ye,“Linearly time-varying channel estimation and symbol detection for OFDMA uplink using superimposed training,”EURASIP Journal on Wireless Communications and Networking,vol.2009,no.1,Mar.2009,pp.307-375.[Online].Available:https://doi.org/10.1155/2009/307375
[17]B.Yang,K.B.Letaief,R.S.Cheng,and Z.Cao,“Channel estimation for OFDM transmission in multipath fading channels based on parametric channel modeling,”IEEE Trans.Commun.,vol.49,no.3,Mar.2001,pp.467-479.
[18]Y.Liu,Z.Tan,H.Hu,L.J.Cimini,and G.Y.Li,“Channel estimation for OFDM,”IEEE Communications Surveys Tutorials,vol.16,no.4,Fourthquarter.2014,pp.1891-1908.
[19]J.-X.Pan and K.-T.Fang,“Maximum likelihood estimation,”in Growth curve models and statistical diagnostics.Springer,2002,pp.77-158.
[20]W.Dai and O.Milenkovic,“Subspace pursuit for compressive sensing signal reconstruction,”IEEETrans.Inf.Theory,vol.55,no.5,May.2009,pp.2230-2249.
[21]T.K.Moon,“The expectation-maximization algorithm,”IEEE Signal Process.Mag.,vol.13,no.6,Nov.1996,pp.47-60.
[22]F.R.Kschischang,B.J.Frey,and H.A.Loeliger,“Factor graphs and the sum-product algorithm,”IEEE Trans.Inf.Theory,vol.47,no.2,2002,pp.498-519.
[23]C.Zhang,Z.Yuan,Z.Wang,and Q.Guo,“Low complexity sparse Bayesian learning using combined belief propagation and mean field with a stretched factor graph,”Signal Process.,vol.131,Aug.2017,pp.344-349.
[24]J.P.Vila and P.Schniter,“Expectation-maximization gaussian-mixture approximate message passing,”IEEE Trans.Signal Process.,vol.61,no.19,Oct.2013,pp.4658-4672.
[25]M.F.Sabahi and N.Ghasemi,“Joint blind equalization and decoding in OFDM systems using particle filtering,”Wireless Personal Communications,vol.97,no.3,pp.3875-3889,Dec.2017.
[26]M.Taherzadeh,H.Nikopour,A.Bayesteh,and H.Baligh,“SCMA codebook design,”in 2014 IEEE80th Vehicular Technology Conferenc(VTC2014-Fall),Sep.2014,pp.1-5.
[27]S.Wu,L.Kuang,Z.Ni,D.Huang,Q.Guo,and J.Lu,“Messagepassing receiver for joint channel estimation and decoding in 3D massive MI-MO-OFDM systems,”IEEE Trans.Wireless Commun.,vol.15,no.12,Dec.2016,pp.8122-8138.
[28]C.Wang,H.Li,and D.Zhao,“Preconditioning toeplitz-plus-diagonal linear systems using the Sherman-Morrison-Woodbury formula,”J.Comput.Appl.Math.,vol.309,no.C,Jan.2017,pp.312-319.
[29]S.Wu,L.Kuang,Z.Ni,D.Huang,Q.Guo,and J.Lu,“Expectation propagation approach to joint channel estimation and decoding for OFDMsystems,”in Proc.IEEE Int.Conf.on Acoust.,Speech and Signal Process.(ICASSP),Florence,Italy,May.2014,pp.1941-1945.
[30]X.Meng,S.Wu,L.Kuang,and J.Lu,“An expectation propagation perspective on approximate message passing,”IEEE Signal Process.Lett.,vol.22,no.8,Aug.2015,pp.1194-1197.
[31]D.Zhang,L.L.Mendes,M.Matthé,I.S.Gaspar,N.Michailow,and G.P.Fettweis,“Expectation propagation for near-optimum detection of MI-MO-GFDM signals,”IEEE Trans.Wireless Commun.,vol.15,no.2,Feb.2016,pp.1045-1062.
[32]C.Novak,G.Matz,and F.Hlawatsch,“IDMA for the multiuser MIMO-OFDM uplink:A factor graph framework for joint data detection and channel estimation,”IEEE Trans.Signal Process.,vol.61,no.16,Aug.2013,pp.4051-4066.
[33]H.Wymeersch,Iterative Receiver Design.Cambridge,U.K.:Cambridge Univ.Press,2007.
[34]Y.Liu,L.Brunel,and J.J.Boutros,“Joint channel estimation and decoding using gaussian approximation in a factor graph over multipath channel,”in 2009 IEEE 20th International Symposium on Personal,Indoor and Mobile Radio Communications,Sep.2009,pp.3164-3168.
[35]M.Series,“Guidelines for evaluation of radio interface technologies for IMT-Advanced,”Report ITU,vol.638,2009.
[36]M.Speth,S.Fechtel,G.Fock,and H.Meyr,“Optimum receiver design for OFDM-based broadband transmission.ii.a case study,”IEEETrans.on Commun.,vol.49,no.4,Apr.2001,pp.571-578.
[37]Q.Guo and D.Huang,“EM-based joint channel estimation and detection for frequency selective channels using gaussian message passing,”IEEE Trans.Signal Process.,vol.59,no.8,Aug.2011,pp.4030-4035.
[38]S.Wu,L.Kuang,Z.Ni,J.Lu,D.D.Huang,and Q.Guo,“Lowcomplexity iterative detection for large-scale multiuser MIMO-OFDM systems using approximate message passing,”IEEE J.Sel.Topics in Signal Process.,vol.8,no.5,Oct.2014,pp.902-915.
[39]S.Coleri,M.Ergen,A.Puri,and A.Bahai,“Channel estimation techniques based on pilot arrangement in OFDM systems,”IEEE Trans Broadcasting,vol.48,no.3,Sep.2002,pp.223-229.
[40]K.Hayashi and H.Sakai,“Uplink channel estimation for OFDMA system,”in Acoustics,Speech and Signal Processing,2007.ICASSP 2007.IEEEInternational Conference on,vol.3.IEEE,Apr.2007,pp.III-285.
[41]T.T.Nguyen,B.Berscheid,H.H.Nguyen,and J.E.Salt,“A novel iterative OFDMA channel estimation technique for DOCSIS 3.1 uplink channels,”IEEE Trans.Broadcast.,vol.63,no.2,Jun.2017,pp.361-375.
[42]Y.Abbes,S.Najeh,and H.Besbes,“The impact of the superposition coding concept on admission control strategy in OFDMA-based network,”China Communications,vol.15,no.6,Jun.2018,pp.68-83.
[43]S.Wu,Z.Ni,X.Meng,and L.Kuang,“Block expectation propagation for downlink channel estimation in massive MIMO systems,”IEEECommun.Lett.,vol.20,no.11,Nov.2016,pp.2225-2228.
[44]S.Wu,L.Kuang,Z.Ni,J.Lu,D.Huang,and Q.Guo,“Low-complexity iterative detection for large-scale multiuser MIMO-OFDM systems using approximate message passing,”IEEE J.Sel.Topics Signal Process.,vol.8,no.5,Oct.2014,pp.902-915.
[45]C.Liu,W.Feng,and T.Wei,“Fairness-oriented hybrid precoding for massive MIMO maritime downlink systems with large-scale CSIT,”China Communications,vol.15,no.1,Jan.2018,pp.52-61.
[2]W.Feng,Y.Wang,D.Lin,N.Ge,J.Lu,and S.Li,“When mmWave communications meet network densification:a scalable interference coordination perspective,”IEEE J.Sel.Areas Commun.,vol.35,no.7,Jul.2017,pp.1459-1471.
[3]R.Zhang,M.Wang,L.X.Cai,Z.Zheng,X.Shen,and L.Xie,“LTEunlicensed:the future of spectrum aggregation for cellular networks,”IEEEWireless Commun.,vol.22,no.3,June.2015,pp.150-159.
[4]F.Zheng,W.Li,L.Meng,P.Yu,and L.Peng,“Distributed energy saving mechanism based on CoMP in LTE-A system,”China Communications,vol.13,no.7,Jul.2016,pp.39-47.
[5]P.Guan,D.Wu,T.Tian,J.Zhou,X.Zhang,L.Gu,A.Benjebbour,M.Iwabuchi,and Y.Kishiyama,“5G field trials:OFDM-based waveforms and mixed numerologies,”IEEE J.Sel.Areas Commun.,vol.35,no.6,Jun.2017,pp.1234-1243.
[6]V.Vahidi and E.Saberinia,“OFDM high speed train communication systems in 5G cellular networks,”in 2018 15th IEEE Annual Consumer Communications Networking Conference(CCNC),Jan.2018,pp.1-6.
[7]H.Tan,Y.Liu,Z.Feng,and Q.Zhang,“Coexistence analysis between 5G system and fixed-satellite service in 3400a3600 mhz,”China Communications,vol.15,no.11,Nov.2018,pp.25-32.
[8]Y.Ma and R.Tafazolli,“Channel estimation for OFDMA uplink:a hybrid of linear and BEMinterpolation approach,”IEEE Trans.Signal Process.,vol.55,no.4,Apr.2007,pp.1568-1573.
[9]B.Yang,Z.Cao,and K.B.Letaief,“Analysis of low-complexity windowed DFT-based MMSEchannel estimator for OFDM systems,”IEEETrans.Commun.,vol.49,no.11,Nov.2001,pp.1977-1987.
[10]M.R.Raghavendra,E.Lior,S.Bhashyam,and K.Giridhar,“Parametric channel estimation for pseudo-random tile-allocation in uplink OFD-MA,”IEEE Trans.Signal Process.,vol.55,no.11,Nov.2007,pp.5370-5381.
[11]M.O.Pun,S.-H.Tsai,and C..J.Kuo,“An EM-based joint maximum likelihood estimation of carrier frequency offset and channel for uplink OFDMA systems,”in IEEE 60th Vehicular Technology Conference,2004.VTC2004-Fall.2004,vol.1,Sep.2004,pp.598-602 Vol.1.
[12]M.O.Pun,M.Morelli,and C..J.Kuo,“Maximum-likelihood synchronizationand channel estimation for OFDMA uplink transmissions,”IEEE Trans.Commun.,vol.54,no.4,Apr.2006,pp.726-736.
[13]S.Sezginer and P.Bianchi,“Joint frequency offset and channel estimation in the OFDMA uplink:Cramer-Rao bounds and training sequence design,”in IEEE 6th Workshop on Signal Processing Advances in Wireless Communications,2005.,Jun.2005,pp.585-589.
[14]S.Omar,A.Ancora,and D.T.M.Slock,“Performance analysis of general pilot-aided linear channel estimation in LTE OFDMA systems with application to simplified MMSE schemes,”in 2008 IEEE 19th International Symposium on Personal,Indoor and Mobile Radio Communications,Sep.2008,pp.1-6.
[15]O.Edfors,M.Sandell,J..van de Beek,S.K.Wilson,and P.O.Borjesson,“OFDM channel estimation by singular value decomposition,”in Proceedings of Vehicular Technology ConferenceVTC,vol.2,Apr.1996,pp.923-927 vol.2.
[16]H.Zhang,X.Dai,D.Li,and S.Ye,“Linearly time-varying channel estimation and symbol detection for OFDMA uplink using superimposed training,”EURASIP Journal on Wireless Communications and Networking,vol.2009,no.1,Mar.2009,pp.307-375.[Online].Available:https://doi.org/10.1155/2009/307375
[17]B.Yang,K.B.Letaief,R.S.Cheng,and Z.Cao,“Channel estimation for OFDM transmission in multipath fading channels based on parametric channel modeling,”IEEE Trans.Commun.,vol.49,no.3,Mar.2001,pp.467-479.
[18]Y.Liu,Z.Tan,H.Hu,L.J.Cimini,and G.Y.Li,“Channel estimation for OFDM,”IEEE Communications Surveys Tutorials,vol.16,no.4,Fourthquarter.2014,pp.1891-1908.
[19]J.-X.Pan and K.-T.Fang,“Maximum likelihood estimation,”in Growth curve models and statistical diagnostics.Springer,2002,pp.77-158.
[20]W.Dai and O.Milenkovic,“Subspace pursuit for compressive sensing signal reconstruction,”IEEETrans.Inf.Theory,vol.55,no.5,May.2009,pp.2230-2249.
[21]T.K.Moon,“The expectation-maximization algorithm,”IEEE Signal Process.Mag.,vol.13,no.6,Nov.1996,pp.47-60.
[22]F.R.Kschischang,B.J.Frey,and H.A.Loeliger,“Factor graphs and the sum-product algorithm,”IEEE Trans.Inf.Theory,vol.47,no.2,2002,pp.498-519.
[23]C.Zhang,Z.Yuan,Z.Wang,and Q.Guo,“Low complexity sparse Bayesian learning using combined belief propagation and mean field with a stretched factor graph,”Signal Process.,vol.131,Aug.2017,pp.344-349.
[24]J.P.Vila and P.Schniter,“Expectation-maximization gaussian-mixture approximate message passing,”IEEE Trans.Signal Process.,vol.61,no.19,Oct.2013,pp.4658-4672.
[25]M.F.Sabahi and N.Ghasemi,“Joint blind equalization and decoding in OFDM systems using particle filtering,”Wireless Personal Communications,vol.97,no.3,pp.3875-3889,Dec.2017.
[26]M.Taherzadeh,H.Nikopour,A.Bayesteh,and H.Baligh,“SCMA codebook design,”in 2014 IEEE80th Vehicular Technology Conferenc(VTC2014-Fall),Sep.2014,pp.1-5.
[27]S.Wu,L.Kuang,Z.Ni,D.Huang,Q.Guo,and J.Lu,“Messagepassing receiver for joint channel estimation and decoding in 3D massive MI-MO-OFDM systems,”IEEE Trans.Wireless Commun.,vol.15,no.12,Dec.2016,pp.8122-8138.
[28]C.Wang,H.Li,and D.Zhao,“Preconditioning toeplitz-plus-diagonal linear systems using the Sherman-Morrison-Woodbury formula,”J.Comput.Appl.Math.,vol.309,no.C,Jan.2017,pp.312-319.
[29]S.Wu,L.Kuang,Z.Ni,D.Huang,Q.Guo,and J.Lu,“Expectation propagation approach to joint channel estimation and decoding for OFDMsystems,”in Proc.IEEE Int.Conf.on Acoust.,Speech and Signal Process.(ICASSP),Florence,Italy,May.2014,pp.1941-1945.
[30]X.Meng,S.Wu,L.Kuang,and J.Lu,“An expectation propagation perspective on approximate message passing,”IEEE Signal Process.Lett.,vol.22,no.8,Aug.2015,pp.1194-1197.
[31]D.Zhang,L.L.Mendes,M.Matthé,I.S.Gaspar,N.Michailow,and G.P.Fettweis,“Expectation propagation for near-optimum detection of MI-MO-GFDM signals,”IEEE Trans.Wireless Commun.,vol.15,no.2,Feb.2016,pp.1045-1062.
[32]C.Novak,G.Matz,and F.Hlawatsch,“IDMA for the multiuser MIMO-OFDM uplink:A factor graph framework for joint data detection and channel estimation,”IEEE Trans.Signal Process.,vol.61,no.16,Aug.2013,pp.4051-4066.
[33]H.Wymeersch,Iterative Receiver Design.Cambridge,U.K.:Cambridge Univ.Press,2007.
[34]Y.Liu,L.Brunel,and J.J.Boutros,“Joint channel estimation and decoding using gaussian approximation in a factor graph over multipath channel,”in 2009 IEEE 20th International Symposium on Personal,Indoor and Mobile Radio Communications,Sep.2009,pp.3164-3168.
[35]M.Series,“Guidelines for evaluation of radio interface technologies for IMT-Advanced,”Report ITU,vol.638,2009.
[36]M.Speth,S.Fechtel,G.Fock,and H.Meyr,“Optimum receiver design for OFDM-based broadband transmission.ii.a case study,”IEEETrans.on Commun.,vol.49,no.4,Apr.2001,pp.571-578.
[37]Q.Guo and D.Huang,“EM-based joint channel estimation and detection for frequency selective channels using gaussian message passing,”IEEE Trans.Signal Process.,vol.59,no.8,Aug.2011,pp.4030-4035.
[38]S.Wu,L.Kuang,Z.Ni,J.Lu,D.D.Huang,and Q.Guo,“Lowcomplexity iterative detection for large-scale multiuser MIMO-OFDM systems using approximate message passing,”IEEE J.Sel.Topics in Signal Process.,vol.8,no.5,Oct.2014,pp.902-915.
[39]S.Coleri,M.Ergen,A.Puri,and A.Bahai,“Channel estimation techniques based on pilot arrangement in OFDM systems,”IEEE Trans Broadcasting,vol.48,no.3,Sep.2002,pp.223-229.
[40]K.Hayashi and H.Sakai,“Uplink channel estimation for OFDMA system,”in Acoustics,Speech and Signal Processing,2007.ICASSP 2007.IEEEInternational Conference on,vol.3.IEEE,Apr.2007,pp.III-285.
[41]T.T.Nguyen,B.Berscheid,H.H.Nguyen,and J.E.Salt,“A novel iterative OFDMA channel estimation technique for DOCSIS 3.1 uplink channels,”IEEE Trans.Broadcast.,vol.63,no.2,Jun.2017,pp.361-375.
[42]Y.Abbes,S.Najeh,and H.Besbes,“The impact of the superposition coding concept on admission control strategy in OFDMA-based network,”China Communications,vol.15,no.6,Jun.2018,pp.68-83.
[43]S.Wu,Z.Ni,X.Meng,and L.Kuang,“Block expectation propagation for downlink channel estimation in massive MIMO systems,”IEEECommun.Lett.,vol.20,no.11,Nov.2016,pp.2225-2228.
[44]S.Wu,L.Kuang,Z.Ni,J.Lu,D.Huang,and Q.Guo,“Low-complexity iterative detection for large-scale multiuser MIMO-OFDM systems using approximate message passing,”IEEE J.Sel.Topics Signal Process.,vol.8,no.5,Oct.2014,pp.902-915.
[45]C.Liu,W.Feng,and T.Wei,“Fairness-oriented hybrid precoding for massive MIMO maritime downlink systems with large-scale CSIT,”China Communications,vol.15,no.1,Jan.2018,pp.52-61.