在多用戶的上傳系統中，用戶間的時間同步是個長久以來被討論的議題，在傳統PON上傳系統中，多個ONUs傳輸至OLT以分時多重存取(TDMA)的方式讓不同用戶在不同時間槽傳輸，然而此種方式需要精準的時間同步與時間分配，才能避免用戶間彼此干擾。而由於OFDM技術的發展進步，人們希望藉由此更高的頻譜效益的技術進行傳輸，然而，在多用戶的OFDM系統中，不同用戶之間的時間同步比起其他傳統上傳系統更為重要，若用戶訊息到達基地台的時間不一致，將無法使OFDM訊號正確的解調回來，而在實際生活中，大多數情況使用者皆在不同時間地點上傳訊號到基地台。
此篇論文中，我們將把傳統用於CDMA系統中的非同步碼，金氏碼，運用在OFDM系統中，經過時域展頻後，使使用者彼此間時間不同步的情況下，依然可以因為其高的自相關與不論任何時間延遲的低互相關將使用者訊號獨立解調出來。這裡，我們將以兩路使用者分別傳輸不同的光纖長度後，接收端將會在不同時間接收訊號，而使用金氏碼編碼後的OFDM訊號依然可以解回兩路不同使用者的訊號，並且BER表現皆在FEC threshold下。

In multiuser uplink system, the timing synchronization for users has been discussed for a long time. In traditional PON uplink system, TDMA is a way for users transmitting signals from multiple ONUs to OLT in different time slot. However, in order to avoid interference among different users, timing synchronization and arrangement are employed. With OFDM technology getting improved, its target is to transmit signal with high spectral efficiency. However, in multi-user OFDM system, the synchronization among different users is more important than other traditional uplink systems. If the information of users arrive at the baseband at different time, the OFDM signal may not be demodulated correctly. In our real life, users transmit information to the central office at different time and place in most cases.
In this work, we employed one of asynchronous code which is used in traditional CDMA system, Gold code, to OFDM system. After time spreading, users’ signals can be individually demodulated based on their high auto-correlation and low cross-correlations in time asynchronous scenario. Here, we make two users transmit signals via different lengths of fiber. Even the receiver may receive the signal at different time, the OFDM signals coded by Gold sequence from different users can still be demodulated, and their bit-error-rate (BER) are all below FEC threshold.

[1] The Cisco. (2017, Feb.). Global Mobile Data Traffic Forecast Update, 2016–2021 White Paper. [Online]. Available: https://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/mobile-white-paper-c11-520862.html
[2] K. C. Kao and G.A. Hockham, “Dielectric-fibre surface waveguides for optical frequencies,” Proceedings of the Institution of Electrical Engineers, vol. 113, pp. 1151-1158, 1966.
[3] N. Cvigetic, “OFDM for next-generation optical access networks [Invited],” Journal of Lightwave Technology, vol. 30, pp. 384-398, 2012.
[4] K. Qiu, X. Yi, J. Zhang, H. Zhang, M. Deng, and C. Zhang, “OFDM-PON optical fiber access technologies [Invited],” 2011 Asia Communications and Photonics Conference and Exhibition, paper 830921.
[5] Y. Zhang. (2010, May). EPON Main Slide. [Online]. Available: https://www.slideshare.net/RockyS11/epon-main-slide
[6] J-J. van de Beek, P. O. Borjesson, M-L. Boucheret, D. Landstrom, J. M. Arenas, P. Odling, C. Ostberg, M. Wahlqvist, and S. K. Wilson, “A time and frequency synchronization scheme for multiuser OFDM,” IEEE Journal on Selected Areas in Communications, vol. 17, pp. 1900-1914, 1999.
[7] M. Morelli, “Timing and frequency synchronization for the uplink of an OFDMA system,” IEEE Transactions on Communications, vol. 52, pp. 296-306, 2004.
[8] R. Gold, “Maximal recursive sequences with 3-valued recursive cross-correlation functions,” IEEE Transactions on Information Theory, vol. 14, pp. 154-156, 1968.
[9] J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Mathematics of Computation, vol. 19, pp. 297-301, 1965.
[10] K. S. Gilhousen, I. M. Jacobs, R. Padovani, A. J. Viterbi, L. A. Weaver, and C. E. Wheatley III, “On the capacity of a cellular CDMA system,” IEEE Transactions on Vehicular Technology, vol. 40, pp. 303-312, 1991.
[11] R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, “Theory of spread-spectrum communications--a tutorial,” IEEE Transactions on Communications, vol. 30, pp. 855-884, 1982.
[12] R. A. Scholtz, “The origins of spread-spectrum communications,” IEEE Transactions on Communications, vol. 30, pp. 822-854, 1982.
[13] X. D. Lin and K. H. Chang, “Optimal PN Sequence Design for Quasisynchronous CDMA Communication Systems,” IEEE Transactions on Communications, vol. 45, pp. 221-226, 1997.
[14] E. H. Dinan and B. Jabbari, “Spreading codes for direct sequence CDMA and wideband CDMA cellular networks,” IEEE Communications Magazine, vol. 36, pp. 48-54, 1998.
[15] W. K. Pratt, J. Kane, and H. C. Andrews, “Hadamard Transform Image Coding,” Proceedings of the IEEE, vol. 57, pp. 58-68, 1969.
[16] P. Chawla and B. Singh, “Role of Walsh Codes and pseudorandom noise sequences in CDMA,” 2014 IEEE International Conference on Industrial Engineering and Engineering Management, pp. 1076-1080.
[17] F. J. Macwilliams and N. J. A. Sloane, “Pseudo-random sequences and arrays,” Proceedings of the IEEE, vol. 64, pp. 1715-1729, 1976.
[18] Gaussianwaves. (2015, Jun.). Hardware Implementation of Gold code generator. [Online]. Available: https://www.gaussianwaves.com/2015/06/hardware-implementation-of-gold-codes/
[19] JPL’s Wireless Communication Reference Website. (2018, Nov.).Gold Sequences. [Online].Available:http://www.wirelesscommunication.nl/reference/chaptr05/cdma/codes/gold.htm
[20] M. B. Mollah and M. R. Islam, “Comparative analysis of Gold Codes with PN codes using correlation property in CDMA technology,” 2012 International Conference on Computer Communication and Informatics, pp. 1-6.
[21] S. Hara and R. Prasad, “Overview of multicarrier CDMA,” IEEE Communications Magazine, vol. 35, pp. 126-133, 1997.
[22] S. Hara and R. Prasad, “Design and performance of multicarrier CDMA system in frequency-selective Rayleigh fading channels,” IEEE Transactions on Vehicular Technology, vol. 48, pp. 1584-1595, 1999.
[23] H. H. Chen, J. F. Yeh, and N. Suehiro, “A multicarrier CDMA architecture based on orthogonal complementary codes for new generations of wideband wireless communications,” IEEE Communications Magazine, vol. 39, pp. 126-135, 2001.
[24] R. A. Shafik, M. S. Rahman, and A. R. Islam, “On the Extended Relationships Among EVM, BER and SNR as Performance Metrics,” 2006 International Conference on Electrical and Computer Engineering, pp. 408-411.