本論文提出一應用於雙向合作式網路之低複雜度預編碼技術與半盲式通道估測法，可應用於多個中繼站之雙向合作式網路，以及頻率選擇性衰減通道。本論文提出之預編碼技術係利用旋轉矩陣為基礎，應用其相關特性達到低複雜度的編(解)碼程序；透過接收訊號之二階統計特性，進行綜合的通道脈衝響應(composite channel impulse response)估測，同時結合少量的訓練符號，進而消除直接鏈路(direct link)所衍生的估測不明確性(estimation ambiguity)；本論文同時分析該半盲式通道估測器於兩個漸進式情況(asymptotic case)之估測效能，兩漸進式情況分別假設無限多個資料符號，以及非常高的訊雜比(signal-to-noise ratio)，兩漸進式分析將分別得到此半盲式通道估測器，於非完美直接鏈路通道估測下，或具有統計誤差下之效能分析，此分析結果亦透過電腦模擬獲得驗證；模擬結果顯示估測效能與訊雜比及資料長度成反比，訊雜比越高或資料長度越長，將得到越好的估測效能。

Consider amplify-and-forward two-way relay networks with multiple relays and frequency selective fading channels, a low-complexity precoding scheme and semi-blind channel estimation method are proposed in this dissertation. Precoding is performed using a rotation-based matrix and decoding is low-complexity and easily scalable to the number of relays and/or the channel length since the decoding process requires only a circulant shifting of the received blocks. The composite channel impulse response of each source-relay-destination link is estimated based on the second-order statistics of the received signals. The ambiguity in the proposed channel estimates caused by the channel information of the direct link is eliminated using a small number of training blocks. The accuracy of the proposed semi-blind channel estimates is examined by deriving the mean square error of the channel estimates for two asymptotic cases, namely an infinite number of data blocks and a high signal-to-noise ratio (SNR) regime. The two cases thus provide a useful insight into the effects on the estimation performance of imperfect direct link information and statistical errors of the ensemble correlations, respectively. The asymptotic analyses are confirmed by the simulation results, which show that the normalized mean square error of the channel estimates varies inversely with the SNR and the number of data blocks.

致謝 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
中文摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2 System Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Chapter 3 Precoding Design at Relays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Chapter 4 Semi-Blind Channel Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1 LS Channel Estimation of Direct Links. . . . . . . . . . . . . . . . . . . . 23
4.2 Semi-Blind Channel Estimation of Source-Relay-Destination Links. . 24
Chapter 5 Asymptotic Analysis of Semi-Blind Channel Estimates . . . . . . . 27
5.1 Asymptotic analysis as Nd . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.2 Asymptotic analysis at high SNR . . . . . . . . . . . . . . . . . . . . . . . . 31
Chapter 6 Computer Simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Chapter 7 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
A Proof of Property 4 of Lemma 1 . . . . . . . . . . . . . . . . . . . . . . . . . 50
B Proof of Property 5 of Lemma 1 . . . . . . . . . . . . . . . . . . . . . . . . . 52
C Proof of Property 6 of Lemma 1 . . . . . . . . . . . . . . . . . . . . . . . . . 53
Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

[1] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity – part I: system
description,” IEEE Trans. Commun., vol. 51, no. 11, pp. 1927–1938, Nov. 2003.
[2] A. Sendonaris, E. Erkip, and B. Aazhang, “User Cooperation DiversityXPart II:
Implementation Aspects and Performance Analysis,” IEEE Trans. Commun., vol.
51, no. 11, pp. 1939–1948, Nov. 2003.
[3] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless
networks: efficient protocols and outage behavior,” IEEE Trans. Inform. Theory, vol.
50, no. 12, pp. 3062–3080, Dec. 2004.
[4] Y.-W. Hong, W.-J. Huang, F.-H. Chiu, and C.-C. J. Kuo, “Cooperative communications
in resource-constrained wireless networks,” IEEE Signal Processing Mag.,
vol. 24, no. 3, pp. 47–57, May 2007.
[5] K.-C. Lee, C.-P. Li, T.-Y. Wang, and H.-J. Li, “Performance analysis of dual-hop
amplify-and-forward systems with multiple antennas and co-channel interference,”
IEEE Trans. on Wireless Commun., vol. 13, no. 6, pp. 3070–3087, June 2014.
[6] T.-Y. Wang, J.-W. Pu, and C.-P. Li, “Joint detection and estimation for cooperative
communications in cluster-based networks,” Wireless Communications and Mobile
Computing, Published online: DOI: 10.1002/wcm.1199, Oct. 2011.
[7] W.-C. Huang, K.-C. Lee, C.-P. Li, H.-J. Li, “Subcarrier power allocation in OFDMbased
dual-hop systems with AF relaying,” IEICE Trans. on Communications, vol.
93-B, no. 11, pp.3184–3188, Nov. 2010.
[8] 3GPP TS 36.213, Evolved universal terrestrial radio access (E-UTRA): physical
layer procedures, Tech. Spec. Group Radio Access Network Rel. 12, 2014.
[9] S.W. Peters and R.W. Heath, “The future of WiMAX: Multihop relaying with IEEE
802.16j,” IEEE Communications Magazine, vol. 47, pp. 104–111, Jan. 2009.
[10] Y.-S. Yang, W.-C. Huang, C.-P. Li, H.-J. Li, and G. Stuber, “A low-complexity
transceiver structure for OFDM-based coordinated multi-point systems,” IEEE
Trans. on Comm., vol. 63, no. 7, pp. 2658–2670, July 2015.
[11] K.-C. Lee, S.-H. Wang, C.-P. Li, H.-H. Chang, and H.-J. Li, “Adaptive resource
allocation algorithm based on cross-entropy method for OFDMA systems,” IEEE
Trans. on Broadcasting, vol. 60, no. 3, pp. 524–531, Sept. 2014.
[12] W.-C. Huang, C.-P. Li, and H.-J. Li, “On the power allocation and system capacity
of OFDM systems using superimposed training schemes,” IEEE Trans. on Vehicular
Tech., vol. 58, no. 4, pp. 1731–1740, May 2009.
[13] C.-P. Li and W.-W. Hu, “Super-imposed training scheme for timing and frequency
synchronization in OFDM systems,” IEEE Trans. on Broadcasting, vol. 53, issue 2,
pp. 574–583, June 2007.
[14] S.-H. Wang, C.-P. Li, and C.-C. Wang, “An interference cancellation scheme for
carrier frequency offsets compensation in the uplink of OFDMA systems,” International
Journal of Electrical Engineering (IJEE), vol. 14, no. 5, pp. 339–347, Oct.
2007.
[15] Y. Liang and R. Schober, “Cooperative amplify-and-forward beamforming for
OFDM systems with multiple relays,” Proc. of IEEE International Conference on
Communications (ICC), pp. 1–6, 2009.
[16] Y. Li, W. Zhang and X.-G. Xia, “Distributive high-rate space-frequency codes
achieving full cooperative and multipath diversities for asynchronous cooperative
communications,” IEEE Trans. on Vehicular Tech., vol.58, no.1, pp.207–217, Jan.
2009.
[17] S.-H. Wang and C.-P. Li, “A low-complexity PAPR reduction scheme for SFBC
MIMO-OFDM systems,” IEEE Signal Processing Letters, vol. 16, no. 11, pp. 941–
944, Nov. 2009.
[18] S.-H.Wang, J.-C. Xie, C.-P. Li, and Y.-F. Chen, “A low-complexity PAPR reduction
scheme for OFDMA uplink systems,” IEEE Trans. on Wireless Commun., vol. 10,
no. 4, pp. 1242–1251, Apr. 2011.
[19] S.-H. Wang, C.-P. Li, K.-C. Lee, and H.-J. Su, “A novel low-complexity precoded
OFDM system with reduced PAPR,” IEEE Trans. on Signal Processing, vol. 63, no.
6, pp. 1366–1376, Mar. 2015.
[20] S.-H. Wang, K.-C. Lee, and C.-P. Li, “A low-complexity architecture for PAPR reduction
in OFDM systems with near-optimal performance,” IEEE Trans. on Vehicular
Tech., vol. 65, no. 1, pp. 169–179, Jan. 2016.
[21] B. Gedik and M. Uysal, “Two channel estimation methods for amplify-and-forward
relay networks,” Proc. IEEE Electrical and Computer Engineering (CCECE), pp.
615–618, May 2008.
[22] C. S. Patel and G. L. Stuber, “Channel estimation for amplify and forward relay
based cooperation diversity systems,” IEEE Trans. on Wireless Commun., vol.6,
no.6, pp. 2348–2356, Jun. 2007.
[23] F. Gao, T. Cui, and A. Nallanathan, “On channel estimation and optimal training
design for amplify and forward relay networks,” IEEE Trans. on Wireless Commun.,
vol. 7, No. 5, pp. 1907–1916, May 2008.
[24] W.-C. Huang, C.-P. Li, and H.-J. Li, “An investigation into the noise variance and
the SNR estimators in imperfectly-synchronized OFDM systems,” IEEE Trans. on
Wireless Commun., vol. 9, no. 3, pp. 1159–1167, Mar. 2010.
[25] W.-C. Huang, C.-H. Pan, C.-P. Li, and H.-J. Li, “Subspace-based semi-blind channel
estimation in uplink OFDMA systems,” IEEE Trans. on Broadcasting, vol. 56, no.
1, pp. 58–65, Mar. 2010.
[26] W.-C. Huang, C.-P. Li, and H.-J. Li, “Optimal pilot sequence design for channel
estimation in CDD-OFDM systems,” IEEE Trans. on Wireless Commun., vol. 11,
no. 11, pp. 4006–4016, Nov. 2012.
[27] W.-C. Huang, Y.-S. Yang, C.-P. Li, and H.-J. Li, “A new pilot architecture for subband
uplink OFDMA systems,” IEEE Trans. on Broadcasting, vol. 59, no. 3, pp.
461–470, June 2013.
[28] K. Kim, H. Kim, and H. Park, “OFDM channel estimation for the amply-andforward
cooperative channel,” Proc. IEEE Veh. Technol. Conf. (VTC-Spring), pp.
1642–1646, Apr. 2007.
[29] S. G. S. Katti and D. Katabi, “Embracing wireless interference: analog network coding,”
in Computer Science and Artificial Intelligence Laboratory Technical Report,
Feb. 2007.
[30] M. P. Wilson, K. Narayanan, H. D. Pfister, and A. Sprintson, “Joint physical layer
coding and network coding for bidirectional Relaying,” IEEE Trans. on Inform. Theory,
vol.56, no.11, pp.5641–5654, Nov. 2010.
[31] R. Zhang, Y.-C. Liang, C.-C. Chai, and S. Cui, “Optimal beamforming for two-way
multi-antenna relay channel with analogue network coding,” IEEE Journal on Sel.
Areas in Commun., vol. 27, no.5, pp.699–712, June 2009.
[32] S. Talwar, Y. Jing, and S. S. Panahi, “Joint relay selection and power allocation for
two-way relay networks,” IEEE Signal Processing Letters, vol.18, no. 2, pp.91–94,
Feb. 2011.
[33] T. Cui, F. Gao, T. Ho, and A. Nallanathan, “Distributed space-time coding for twoway
wireless relay networks,” in Proc. of IEEE International Conference on Communications
(ICC), Beijing, China, May 2008, pp. 3888–3892.
[34] F. Gao, R. Zhang, and Y.-C. Liang, “Channel estimation for OFDM modulated twoway
relay networks,” IEEE Trans. on Signal Processing, vol. 57, no. 11, pp. 4443–
4455, Nov. 2009.
[35] S. Abdallah, and I.N. Psaromiligkos, “Semi-blind channel estimation for amplifyand-
forward two-way relay networks employing constant-modulus constellations,”
44th Annual Conference on Information Sciences and Systems (CISS), March 2010.
[36] J.-W. Pu, T.-Y.Wang, S.-H. Li, C.-P. Li, and H.-J. Li, “Performance analysis of relay
selection in two-way relay networks with channel estimation errors,” IEEE Trans.
on Broadcasting, vol. 61, no. 3, pp. 482–493, Sept. 2015.
[37] C. Wang, T. C.-K. Liu, and X. Dong, “Impact of channel estimation error on the
performance of amplify-and-forward two-way relaying,” IEEE Trans. on Vehicular
Tech., vol. 61, no. 3, pp. 1197–1207, Mar. 2012.
[38] B. Jiang, F. Gao, X. Gao, and A. Nallanathang, “Channel estimation and training
design for two-way relay networks with power allocation,” IEEE Trans. on Wireless
Comm., Vol. 9, No. 6, pp. 2022–2032, June 2010.
[39] X. Xie, M. Peng, Y. Li, W. Wang, and H. V. Poor, “Channel estimation for two-way
relay networks in the presence of synchronization errors,” IEEE Trans. on Signal
Processing, vol. 62, no. 23, pp. 6235–6248, Dec. 2014.
[40] G. Wang, F. Gao, W. Chen, and C. Tellambura, “Channel estimation and training
design for two-way relay networks in time-selective fading environments,” IEEE
Trans. on Wireless Comm., Vol. 10, No. 8, pp. 2681–2691, Aug. 2011.
[41] F. Gao, R. Zhang, and Y.-C. Liang, “Optimal channel estimation and training design
for two-way relay networks,” IEEE Trans. on Comm., vol. 57, no. 10, pp. 3024–
3033, Oct. 2009.
[42] G. Wang, F. Gao, Y.-C. Wu, and C. Tellambura, “Joint CFO and channel estimation
for OFDM-based two-way relay networks,” IEEE Trans. on Wireless Comm., vol.
2, no. 2, pp. 456–465, Feb. 2011.
[43] X. Xu, J. Wu, S. Ren, X. Luan, and H. Xiang, “Superimposed training and channel
estimation for two-way relay networks,” IEEE International Conference on Advanced
Communication Technology (ICACT), pp. 1050–1054, Feb. 2014.
[44] N. Wang, Y. Su, J. Shi, Y. Zhou, and G. Gui, “Sparse channel estimation for OFDM
based two-way relay networks,” IEEE International Conference on Comm. (ICC),
pp. 4524–4529, Apr. 2014.
[45] S. Abdallah and I. N. Psaromiligkos, “EM-based semi-blind channel estimation in
amplify-and-forward two-way relay networks,” IEEE Trans. on Comm., vol. 2, no.
5, pp. 527–530, Oct. 2013.
[46] S. Abdallah and I. N. Psaromiligkos, “Blind channel estimation for amplify-andforward
two-way relay networks employing M-PSK modulation,” IEEE Trans. on
Signal Processing, vol. 60, no. 7, pp. 3604–3615, July 2012.
[47] Q. Zhao, Z. Zhou, J. Li, and B. Vucetic, “Joint semi-blind channel estimation and
synchronization in two-way relay networks,” IEEE Trans. on Vehicular Tech., vol.
63, no. 7, pp. 3276–3293, Sep. 2014.
[48] X. Liao, L. Fan, and F. Gao, “Blind channel estimation for OFDM modulated twoway
relay network,” IEEE Wireless Communications and Networking Conference
(WCNC), Apr. 2010.
[49] S. Zhang, F. Gao, and C.-X. Pei, “Optimal Training Design for Individual Channel
Estimation in Two-Way Relay Networks,” IEEE Trans. on Signal Processing, Vol.
60, No. 9, pp. 4987–4991, Sep. 2012.
[50] X. Xu, J. Wu, S. Ren, L. Song, and H. Xiang, “Superimposed training design based
on Bayesian optimisation for channel estimation in two-way relay networks,” Communications,
IET Journals & Magazines , Vol. 6, Iss. 18, pp. 3131–3139, 2012.
[51] C.W. R. Chiong, Y. Rong, and Y. Xiang, “Channel Estimation for Two-Way MIMO
Relay Systems in Frequency-Selective Fading Environments,” IEEE Trans. on Wireless
Comm., Vol. 14, No. 1, pp. 399–409, Jan. 2015.
[52] R. Wang, M. Tao, H. Mehrpouyan, and Y. Hua, “Channel Estimation and Optimal
Training Design for Correlated MIMO Two-Way Relay Systems in Colored Environment,”
IEEE Trans. on Wireless Comm., Vol. 14, No. 5, pp. 2684–2699, May.
2015.
[53] J. Zhang, K. Naskovska, and M. Haardt, “Tensor-based channel estimation for nonregenerative
two-way relaying networks with multiple relays,” 2014 48th Asilomar
Conference Conference on Signals, Systems and Computers, pp.591–595, Nov.
2014.
[54] I. V. Cavalcante, A.L.F. de Almeida, and M. and Haardt, “Tensor-based approach to
channel estimation in amplify-and-forward MIMO relaying systems,” IEEE Conference
on Sensor Array and Multichannel Signal Processing Workshop (SAM),
pp.445–448, June 2014.
[55] Y. Lu, F. Gao, P. Sadasivan, and A. Nallanathan, “Semi-Blind Channel Estimation
for Space-Time Coded Amplify-and-Forward Relay Networks,” IEEE Global
Telecomm. Conference, (GLOBECOM), Nov. 2009.
[56] T.-T.-T. Thuy, T.-V. Dung, and N.-L. Hung, “Time-selective channel estimation in
two-way multi-relay MIMO-OFDM transmissions,” IEEE Conference on Advanced
Technologies for Communications (ATC), pp.28–32, 2013.
[57] B. O’Hara and A. Petrick, The IEEE 802.11 Handbook: A Designer’s Companion,
Standards Information Network IEEE Press, Dec. 1999.
[58] M.-L. Wang, C.-P. Li, and W.-J. Huang, “Semiblind channel estimation and precoding
scheme in two-way multirelay networks,” IEEE Trans. on Signal Processing,
vol. 65, no. 10, pp. 2576–2587, May 2017.
[59] M.-L. Wang, C.-P. Li, W.-J. Huang, Yen-Cheng Chen, and Li-Chung Lo, “Semiblind
multipath channel estimation and precoding design in AF two-way relay networks,”
Proc. IEEE Vehicular Technology Conference (VTC Fall), pp. 1–5, Sept.
2013.
[60] M.-L.Wang, C.-P. Li, andW.-J. Huang, “Pilot-based channel estimation in amplifyand-
forward multipath cooperative networks,” Proc. 8th IEEE Asia Pacific Wireless
Communication Symposium (IEEE APWCS), Aug. 2011.