在這篇論文中，我們分析了在雙向式中繼網路(Tow-Way Relay Networks, TWRNs)下加入通道估測(Channel Estimation)不完美而產生的誤差對整體效能的影響，我們還討論當中繼點假設為不同時，如何使用檢測式網路(Censoring Network)來進行雙向式中繼點網路之中繼點挑選(Relay Selection)。
在放大傳送(Amplified-and-forward)雙向式的中繼點網路中，各自的來源端所收到的訊號往往需要減去自我干擾(Self-Interference)的部分，而通道增益往往是所謂的串聯通道增益(Cascade Channel)，該通道之通道估測必須完美的得到雙方的通道資訊(Channel State Information, CSI)，各個訊號源端才能將接收訊號減去自己傳送的訊息來獲得對方來源端之傳送訊息，在該部分中我們假設完美的通道估測不存在，並運用最小邊界值(Cramér-Rao Bound, CRLB)的概念，求解出通道估測在最理想的時候所產生的估測誤差，由於自我干擾本身也需要通道估測，除了原本傳送訊號的通道誤差外，我們還加上由自我干擾所產生的估測誤差，在不忽略這些誤差的情況下，分析整體網路的中斷率(Outage Probability)，並證明此時的整體效能可保有完美的通道多樣性(Diversity)。
當系統假設為頻分雙工（Frequency-Division Duplexing, FDD），並使用解碼傳送(Decode-and-forward)之中繼點時，前面所提到的機會式中繼點選擇法(Opportunistic relaying)會因為通道變成對等(Non-reciprocal)通道，單靠後段通道做選擇，導致雙向式中繼點網路產生錯誤漫延降低通道多樣性，我們想到將原本的終端式網路(Terminal Network)改為檢測式網路，讓每個中繼點自己判斷是否進行傳輸，該做法有別於終端式網路，可以避免掉通道資訊不足對多樣性所造成的影響，使雙向式中繼點網路也可以在該環境中運作。

The impact of channel estimation errors is investigated in two-way relay networks (TWRNs) with two different channel state information (CSI) estimation schemes, namely, cascaded and separate. In the cascaded scheme, the relay node is selected on the basis of the CSI of the individual channels between the source nodes and the relay node. In the separate scheme, relay node selection is based on the CSI of the cascaded channel between the two source nodes. For both estimation schemes, the effect of the CSI estimation error on the outage probability is examined by Cramer-Rao lower bound. Contrary to previous reports, the source nodes in the TWRN are assumed to yield different estimation errors. Numerical results confirm the validity of the derived expression and indicate that the presence of different estimation errors at the two source nodes can significantly influence the performance of the TWRN.
However, we extend the relay selection problem to non-reciprocal TWRNs. We propose a selection scheme based on the concept of censoring rule, in which each relay node can decide whether the received signal should be forwarded. This method can save a level of transmission power and maintain the diversity gain without gathering all of the CSI between the source nodes and relay nodes at a central node. The effectiveness of the proposed scheme is evident in the simulation results.

論文審定書 i
誌謝 ii
中文摘要 iii
Abstract iv
目錄 iv
圖次 vii
第一章 導論 1
1.1 研究動機 2
1.2 論文架構 3
第二章 雙向式中繼點網路 4
2.1 合作式通訊 4
2.2 雙向式中繼點網路架構 5
2.2-1 放大傳送 6
2.2-2 解碼傳送 7
第三章 基於TWRN下中繼點選取與其中斷率 9
3.1 Opportunistic Relay Selection 9
3.2 中斷率分析 10
3.3 系統多樣性推導 13
第四章 考慮估測誤差之接收端系統模型與效能分析 16
4.1 通道估測誤差 16
4.2 通道估測誤差之CRLB 17
4.3 考慮估測誤差之效能分析 19
4.3-1各別通道之估測 19
4.3-2聯合通道之估測 28
第五章 運用檢測式中繼點在非互惠通道下之中繼點挑選 33
5.1檢測式中繼點與DF傳輸架構 33
5.2檢測式中繼點其門檻設定 36
5.3檢測式中繼點之中繼點選擇 38
第六章模擬分析與討論 42
6.1考慮估測誤差之中斷率模擬結果 42
6.2考慮感知網路選取中繼點之模擬結果 46
第七章結論 49
參考文獻 50
中英對照表 55
縮寫對照表 58

[1] P. K. Upadhyay and S. Prakriya, “Performance of two-way opportunistic relaying with analog network coding over nakagami-m fading,” IEEE Trans. Veh. Technol., vol. 60, no. 4, pp. 1965–1971, May 2011.
[2] Z. Ding and K. K. Leung, “Impact of imperfect channel state information on bi-directional communications with relay selection,” IEEE Trans. Signal Process., vol. 59, no. 11, pp. 5657–5662, Nov. 2011.
[3] 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. Veh. Technol., vol. 61, no. 3, pp. 1197–1207, Mar. 2012.
[4] H. Guo and J. Ge, “Outage probability of two-way opportunistic amplify-and-forward relaying,” Electron. Lett., vol. 46, no. 13, June 2010.
[5] K.-S. Hwang, M. Ju, and M.-S. Alouini, “Outage performance of opportunistic two-way amplify-and-forward relaying with outdated channel state information,” IEEE Trans. Commun., vol. 61, no. 9, pp. 3635–3643, Sep. 2013.
[6] W.-W. Hu, C.-P. Li, and J.-C. Chen, “Peak power reduction for pilot-aided OFDM systems with semi-blind detection,” IEEE Commun. Lett., vol. 16, no. 7, pp. 1056–1059, July 2012.
[7] M. Zeng, R. Zhang, and S. Cui, “On design of collaborative beamforming for two-way relay networks,” IEEE Trans. Signal Process., vol. 59, no. 5, pp. 2284–2295, May 2011.
[8] Q. Zhao, Z. Zhou, and B. Vucetic, “Low complexity semi-blind channel estimation algorithm in two-way relay networks,” in Proc. IEEE PIMRC, vol. 1, Toronto, Canada, Sep. 2011.
[9] K. Zhong, X. Lei, S. Hu, and S. Li, “On channel estimation and detection for amplify-and-forward orthogonal frequency division multiplexing based two-way relay systems under unknown non-reciprocal doubly selective fading channels,” IET Commun., vol. 8, no. 3, pp. 378–389, 2014.
[10] 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. Wireless Commun., vol. 9, no. 3, pp. 1159–1167, Mar. 2010.
[11] Y. Li, Q. Yin, W. Xu, and H. M. Wang, “On the design of relay selection strategies in regenerative cooperative networks with outdated CSI,” IEEE Trans. Wireless Commun., vol. 10, no. 9, pp. 3086–3097, Sep. 2011.
[12] M. Chen, Ted C.-K. Liu, and X Dong, “Opportunistic multiple relay selection with outdated channel state information,” IEEE Trans. Veh. Technol., vol. 61, no. 3, pp. 1333–1345, Mar. 2012.
[13] H. Cui, R. Zhang, L. Song, and B. Jiao, “Relay selection for bidirectional AF relay network with outdated CSI,” IEEE Trans. Veh. Technol., vol. 62, no. 9, pp. 4357–4365, Nov. 2013.
[14] L. Fan, X. Lei, R. Q. Hu, and W. Seah, “Outdated relay selection in two-way relay network,” IEEE Trans. Veh. Technol., vol. 62, no. 8, pp. 4051–4057, Oct. 2013.
[15] S.-H. Wang and C.-P. Li, “A low-complexity PAPR reduction scheme for SFBC MIMO-OFDM systems,” IEEE Signal Process. Lett., vol. 16, no. 11, pp. 941–944, Nov. 2009.
[16] M. Biguesh and A. B. Gershman, “Training based MIMO channel estimation: a study of estimator tradeoffs and optimal training signals,” IEEE Trans. Signal Process., vol. 54, no. 3, pp. 884–893, Mar. 2006.
[17] Y. Jing and X. Yu, “ML-based channel estimations for non-regenerative relay retworks with multiple transmit and receive antennas,” IEEE J. Sel. Areas Commun., vol. 30, no. 8, pp. 1428–1439 Sep. 2012.
[18] F. Roemer and M. Haardt, “Tensor-based channel estimation and iterative refinements for two-way relaying with multiple antennas and spatial reuse,” IEEE Trans Signal Process., vol. 58, no. 11, pp. 5720–5735, Nov. 2010.
[19] C. W. R. Chiong, Y. Rong, and Y. Xiang, “Channel estimation for two-way MIMO relay systems in frequency-selective fading environments,” IEEE Trans. Wireless Commun., vol. 14, no. 1, pp. 399–409, Jan. 2015.
[20] S. Abdallah and I. N. Psaromiligkos, “Blind channel estimation for amplify-and-forward two-way relay networks employing M-PSK modulation,” IEEE Trans. Signal Process., vol. 60, no. 7, pp. 3604–3615, July 2012.
[21] C.-P. Li and W.-C. Huang, “A constructive representation for the fourier dual of the Zadoff-Chu sequences,” IEEE Trans. Inf. Theory, vol. 53, no. 11, pp. 4221–4224, Nov. 2007.
[22] G. Farhadi and N. C. Beaulieu, “Power-optimized amplify-and-forward multi-hop relaying systems,” IEEE Trans. Wireless commun., vol. 8, no. 9, pp. 4634–4643, Sep. 2009.
[23] F. S. Tabataba, P. Sadeghi, and M. R. Pakravan, “Outage probability and power allocation of amplify and forward relaying with channel estimation errors,” IEEE Trans. Wireless Commun., vol. 10, no. 1, pp. 124–134, Jan. 2011.
[24] 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. Veh. Technol., vol. 58, no. 4, pp. 1731–1740, May 2009.
[25] S. Bharadwaj and N. B. Mehta, “Accurate performance analysis of single and opportunistic AF relay cooperation with imperfect cascaded channel estimates,” IEEE Trans. Commun., vol. 61, no. 5, pp. 1764–1775, May 2013.
[26] H. Cui, R. Zhang, L. Song, and B. Jiao, “Capacity analysis of bidirectional AF relay selection with imperfect channel state information,” IEEE Wireless Commun. Lett., vol. 2, no. 3, pp. 255–258, June 2013.
[27] C.-P. Li and W.-W. Hu, “Super-imposed training scheme for timing and frequency synchronization in OFDM systems,” IEEE Trans. Broadcast., vol. 53, issue 2, pp. 574–583, Jun. 2007.
[28] F. Gao, R. Zhang, and Y.-C. Liang, “Optimal channel estimation and training design for two-way relay networks,” IEEE Trans. Commun., vol. 57, no. 10, pp. 3024–3033, Oct. 2009.
[29] S. Zhang, F. Gao, and C.-X. Pei, “Optimal training design for individual channel estimation in two-way relay networks,” IEEE Trans. Signal Process., vol. 60, no. 9, pp. 4987–4991, Sep. 2012.
[30] W.-W. Hu, S.-H. Wang, and C.-P. Li, “Gaussian integer sequences with ideal periodic autocorrelation functions,” IEEE Trans. Signal Process., vol. 60, no. 11, pp. 6074–6079, Nov. 2012.
[31] A. Jeffrey and D. Zwillinger, Table of integrals, series, and products. Academic Press, 2007.
[32] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover: New York, 1972.
[33] W.-C. Huang, C.-P. Li, and H.-J. Li, “A computationally efficient DFT scheme for applications with a subset of non-zero inputs,” IEEE Signal Process. Lett., vol. 15, pp. 206–208, 2008.
[34] T. Y. Wang and J. Y. Wu, “Cooperative communications using reliability-forwarding relays,” IEEE Trans. Commun., vol. 61, no. 5, pp. 1776–1785, May 2013.
[35] C.-P. Li, S.-H. Wang, and C.-L. Wang, “Novel low-complexity SLM schemes for PAPR reduction in OFDM systems,” IEEE Trans. Signal Process., vol. 58, no. 5, pp. 2916–2921, May 2010.
[36] H. L. V. Trees, Detection, Estimation, and Modulation Theory, Part I. John Wiley & Sons, Inc., 2001.
[37] S. S. Ikki and M. H. Ahmed, “On the performance of cooperative diversity networks with the n-th best-relay selection scheme,” IEEE Trans. Commun., vol. 58, no. 11, pp. 3062–3069, Nov. 2007.
[38] J.-C. Chen and C.-P. Li, “Tone reservation using near-optimal peak reduction tone set selection algorithm for PAPR reduction in OFDM systems,” IEEE Signal Process. Lett., vol. 17, no. 11, pp. 933–936, Nov. 2010.
[39] A. Bletsas, A. Khisti, D. P. Reed, and A. Lippman, “A simple cooperative diversity method based on network path selection,” IEEE J. Sel. Areas Commun., vol. 24, no. 3, pp. 659–672, Mar. 2006.