在本論文中，我們針對基於離散哈特利轉換 (discrete Hartley transform；DHT) 與雙原型濾波器之濾波器组多載波 (filter bank multicarrier；簡稱FBMC) 系統，提出一時間同步的訓練序列設計方法；我們推導出兩個頻域的訓練序列並且將之連續擺放在資料訊框中，使得對應的時域訓練序列成為一個有加入循環字首 (cyclic prefix) 和循環字尾 (cyclic postfix) 的Zadoff-Chu序列。因為Zadoff-Chu序列具有理想的自相關特性，因此粗略的時間同步 (coarse time synchronization) 可以藉由偵測接收訊號和Zadoff-Chu序列間之交相關函式 (cross-correlation function) 的高峰值而達成；然而，此高峰值不一定總是在第一條通道路徑上，因此進一步精細的時間同步 (fine time estimation) 通常是必要的。經由分析並推導出上述交相關函式的機率密度函數，我們求得一最佳判斷門檻值，以從粗略的時間估測點往回搜尋出第一條通道路徑所對應的時間點，進而完成時間同步。電腦模擬結果顯示，當通道具有較小的延遲擴展 (delay spread) 特性時，粗略時間估測值的均方誤差 (mean-squared error) 效能表現會比較好；另外，所提出之時間同步方法在ITU所規範的Indoor B、Pedestrian B與Vehicular B 通道模擬環境下，分別可達到接近99.5%、99%和97% 的時間同步正確機率。

In this thesis, we propose a training sequence design for time synchronization in a filter bank multicarrier (FBMC) system based on the discrete Hartley transform (DHT) and two prototype filters. Two frequency-domain training sequences are derived and placed successively among data frames such that the corresponding time-domain training sequence is a Zadoff-Chu sequence with appropriate cyclic prefix and postfix. Because a Zadoff-Chu sequence possesses an ideal autocorrelation property, coarse time synchronization can be easily achieved by detecting the peak of the cross-correlation function between the received signal and the Zadoff-Chu sequence. However, because the peak point is not always the first channel tap, further fine time synchronization is often necessary. By analyzing the probability density function of the cross-correlation function, we obtain the optimal threshold for searching back for the first channel tap to complete time synchronization. As demonstrated by computer simulation results, the mean-squared error performance of the coarse time estimate is better when the channel has a smaller delay spread. Moreover, the proposed approach achieves near 99.5%, 99%, and 97% of correct time synchronization under the ITU Indoor B, Pedestrian B, and Vehicular B channel models, respectively, for the DHT-based FBMC system.

[1] Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications. Amend. 4: Enhancements for Very High Throughput for Operation in Bands Below 6 GHz, IEEE Standard P802.11ac/D6.0, Jul. 2013.
[2] P. Siohan, C. Siclet, and N. Lacaille, “Analysis and design of OFDM/OQAM systems based on filterbank theory,” IEEE Trans. Signal Process., vol. 50, no. 5, pp. 1170–1183, May 2002.
[3] A. Viholaninen, M. Bellanger, and M. Huchard, “PHYDYAS-Physical layer for dynamic access and cognitive radio,” Tech. Rep. D5.1, EU FP7-ICT Future Networks, Jan. 2009. Project website: http://www.ict-phydyas.org/.
[4] B. Farhang-Boroujeny, “OFDM versus filter bank multicarrier,” IEEE Signal Process. Mag., vol. 28, no. 3, pp. 92–112, May 2011.
[5] M. G. Bellanger, “Specification and design of a prototype filter for filter bank based multicarrier transmission,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Salt Lake City, USA, May 2001, pp. 2417–2420.
[6] M. Bellanger, “Physical layer for future broadband radio systems,” in Proc. IEEE Radio Wireless Symp. (RWS), New Orleans, Louisiana, USA, Jan. 2010, pp. 436–439.
[7] R. N. Bracewell, “Discrete Hartley transform,” J. Opt. Soc. Amer., vol. 73, no. 12, pp. 1832–1835, Dec. 1983.
[8] R. N. Bracewell, “The fast Hartley transform,” Proc. IEEE, vol. 72, no. 8, pp. 1010–1018, Aug. 1984.
[9] K. Jones, The Regularized Fast Hartley Transform. Dordrecht, The Netherlands: Springer, 2010.
[10] C.-T. Tuan, “A filter bank multicarrier transmission system based on the discrete Hartley transform,” M.S. thesis, Inst. Commun. Eng., National Tsing Hua Univ., Hsinchu, Taiwan, Aug. 2016.
[11] M. Bellanger et al., “FBMC physical layer: A primer,” PHYDYAS, Tech. Rep., Jun. 2010.
[12] H.-S. Pan, “A filter bank multicarrier system based on the discrete Hartley transform and two prototype filters,” M.S. thesis, Inst. Commun. Eng., National Tsing Hua Univ., Hsinchu, Taiwan, Dec. 2017.
[13] Y. H. Yun, C. Kim, K. Kim, Z. Ho, B. Lee, and J.-Y. Seol, “A new waveform enabling enhanced QAM-FBMC systems,” in Proc. IEEE Int. Workshop Signal Process. Adv. Wireless Commun. (SPAWC), Stockholm, Sweden, Jun./Jul. 2015, pp. 116–120.
[14] H. Nam, M. Choi, S. Han, C. Kim, S. Choi, and D. Hong, “A new filter-bank multicarrier system with two prototype filters for QAM symbols transmission and reception,” IEEE Trans. Wireless Commun., vol. 15, no. 9, pp. 5998–6009, Sep. 2016.
[15] C. Kim, Y. H. Yun, K. Kim, and J. Y. Seol, “Introduction to QAM-FBMC: From waveform optimization to system design,” IEEE Commun. Mag., vol. 54, no. 11, pp. 66–73, Nov. 2016.
[16] Q. Bai and J. Nossek, “On the effects of carrier frequency offset on cyclic prefix based OFDM and filter-bank based multicarrier systems,” in Proc. IEEE Int. Workshop Signal Process. Adv. Wireless Commun. (SPAWC), Marrakech, Morocco, Jun. 2010, pp. 1–5.
[17] T. Fusco, A. Petrella, and M. Tanda, “Sensitivity of multi-user filter-bank multicarrier systems to synchronization errors,” in Proc. IEEE Int. Symp. on Commun., Control and Signal Process. (ISCCSP), St. Julian’s, Malta, Mar. 2008, pp. 393–398.
[18] W. Chung et al., “Synchronization error in QAM-based FBMC system,” in Proc. IEEE Military Commun. Conf. (MILCOM), Baltimore, Maryland, USA, Oct. 2014, pp. 699–705.
[19] T. Fusco and M. Tanda, “Blind frequency-offset estimation for OFDM/OQAM systems,” IEEE Trans. Signal Process., vol. 55, no. 5, pp. 1828–1838, May 2007.
[20] T. Fusco, A. Petrella, and M. Tanda, “Data-aided symbol timing and CFO synchronization for filter bank multicarrier systems,” IEEE Trans. Wireless Commun., vol. 8, no. 5, pp. 2705–2715, May 2009.
[21] W. Chung, C. Kim, S. Choi, and D. Hong, “Synchronization sequence design for FBMC/OQAM systems,” IEEE Trans. Wireless Commun., vol. 15, no. 10, pp. 7199–7211, Oct. 2016.
[22] M. Hua, M. Wang, K. Yang, and K. Zou, “Analysis of the frequency offset effect on Zadoff-Chu sequence timing performance,” IEEE Trans. Commun., vol. 62, no. 11, pp. 4024–4039, Nov. 2014.
[23] C.-L. Wang and H.-C. Wang, “On joint fine time adjustment and channel estimation for OFDM systems,” IEEE Trans. Wireless Commun., vol. 8, no. 10, pp. 4940–4944, Oct. 2009.
[24] Guidelines for Evaluations of Radio Transmission Technologies for IMT-2000, ITU-R M.1225, 1997.