基地台搜尋 (cell search) 是細胞式行動通訊系統中很重要的課題。在訊號能開始傳送之前，訊號前端的引導序列 (preamble sequences)會協助基地台搜尋與初步的鏈路建立。行動端藉著判斷引導序列是由哪一個基地台發送出來決定要鏈結之基地台。因此使用不同的引導序列將影響基地台搜尋的效能。

蜂巢式正交分頻多工 (cell-based orthogonal frequency division multiplexing) 系統之一的全球互通微波存取 (Worldwide Interoperability for Microwave Access) 系統，使用了114組引導序列。這些引導序列是由電腦搜尋所得，它們沒有什麼數學結構，特性是序列間相關性及序列之功率的峰均值比 ( peak-to- average power ratio )皆很小。序列間相關性小的需求是為了使我們易於判別送出序列的基地台，而峰均值比小則是為了因應正交分頻多工 ( orthogonal frequency division multiplexing) 系統會有較高的峰均值比的問題而有的需求。因此我們希望找出一系列引導序列，是除了能維持序列間相關性及序列之峰均值比小之外，還能擁有結構性的。

完全互補碼 (complete complementary codes)是由數組自互補碼 (auto-complementary codes) 構成，其中任意兩個自互補碼為互互補碼 (cross-complementary codes)。從我們的研究及文獻已知完全互補碼可從一階里德米勒碼(first-order Reed-Muller code) 的陪集產生，於是我們考慮使用完全互補碼中不同的自互補碼當引導序列。如此不僅序列的建構是有結構性的，序列傳送後之峰均值比是很小的值，並且不同組引導序列間的相關性是0，更便於我們對基地台的判定。

由於完全互補碼極好的相關性特性，導致能構成完全互補碼的自互補碼組數有限，因此能發送訊號之基地台數目也將因此受限。為了增加自互補碼之組數，這篇論文中我們從一階里德米勒碼的另一種陪集產生由多組類自互補碼 (quasi auto-complementary codes) 構成的類完全互補碼 (quasi complete complementary codes)，它在峰均值比及相關性上的特性雖不及完全互補碼般理想，但仍保持在良好的程度之上，並且擁有眾多不同的類自互補碼。因此我們使用此類完全互補碼中不同的類自互補碼當引導序列進行基地台搜尋。

模擬結果顯示，我們使用類完全互補碼當引導序列與使用全球互通微波存取系統之引導序列進行基地台搜尋，除了在衰落通道 (fading channel) 上的基地台搜尋效能有可接受程度的衰減 (degradation) ，其餘在可加性白色高斯雜訊通道 (additive white Gaussian noise channel) 上的基地台搜尋效能是差不多的。加上類完全互補碼的建構也是從里德米勒碼產生，這有豐富結構性的類完全互補碼在蜂巢式正交分頻多工系統中進行基地台搜尋時是合適的引導序列。

Establishing a radio link in cell-based mobile communication systems involves searching and
synchronizing the downlink known pattern of sequences associated with the base stations.
The searching process, often referred to as cell search, is usually completed by preamble
sequences. Therefore, the performance of cell search depends greatly on the preamble se-
quences. In this thesis, we propose a construction of quasi complete complementary codes
(QCCCs) from Reed-Muller (RM) codes. Since the constructed QCCCs have good auto-
correlation and cross-correlation properties, we employ them as preamble sequences and
propose a preamble structure based on QCCCs. Furthermore, the constructed QCCCs have
low peak-to-average power ratio (PAPR), and hence they are suitable for use in orthogonal
frequency division multiplexing (OFDM) systems. We compare the cell search performance
of using QCCCs as preambles with that of the worldwide interoperability for microwave
access (WiMAX, also referred to as IEEE standard 802.16e) preambles. Simulation results
show that there is minor or acceptable performance degradation with our QCCCs employed
as preambles, while the rich algebraic structures of QCCCs potentially permit low-complexity
encoding and decoding.

[1] R. van Nee, and R. Prasad, OFDM for Wireless Multimedia Communications. Boston:
Artech House, 2000.
[2] R. van Nee, "OFDM codes for peak-to-average power reduction and error correction," in
Proc. IEEE Global Telecommunications Conf., London, U.K., Nov. 1996, pp. 740-744.
[3] A. J. Grant and R. van Nee, "Efficient maximum likelihood decoding of peak power
limiting codes for OFDM," in Proc. IEEE Vehicular Technology Conf., Ottawa, Ontario,
Canada, May 1998, pp. 2081-2084.
[4] A. J. Grant and R. van Nee, "Efficient maximum likelihood decoding of Q-ary modulated Reed-Muller codes," IEEE Commun. Lett., vol. 2, pp. 134-136, May 1998.
[5] H.-S. Chen, "Cell search and initial link setup for WiMAX systems," M.S. thesis, Dept.
Commun. Eng., Nat. Chiao Tung Univ., Hsinchu, Taiwan, 2006.
[6] K. S. Kim, K. Chang, S. W. Kim, and Y. S. Cho, "A preamble-based cell searching
technique for OFDM cellular systems," in Proc. IEEE Vehicular Technology Conf., vol.
4, Oct. 2003, pp. 2471-2475.
[7] H. Lim, and D. S. Kwon, "Initial synchronization for WiBro," in Proc. 2005 Asia-Pacific
Conf. Communications, pp. 284-288.
[8] J.-W. Lee, and Y.-H. Lee, "Rapid cell search in OFDM-based cellular systems," in Proc.
IEEE Vehicular Technology Conf., vol. 2, June 2005, pp. 1273-1277.
[9] D. Sharma, T. Vrind, and V.C. Joseph, "Fast cell synchronization for beyond 3G
OFDMA based system ," in Proc. Wireless and Optical Communications Networks,
2006 IFPI Int. Conf., pp. 1-5.
[10] J. Kim, H. Kim, and Y. Han, "New preamble structures for synchronization and cell
searching in OFDM systems," in Proc. IEEE Vehicular Technology Conf., vol. 3, Sept.
2005, pp. 1623-1627.
[11] B. M. Popovic, "Generalized chirp-like polyphase sequences with optimum correlation
properties," IEEE Trans. Inform. Theory, vol. 38, pp. 1406-1409, July 1992.
[12] M. Tanno, K. Higuchi, H. Atarashi, and M. Sawahashi, "Experiments on three-step fast
cell search algorithm employing common pilot channel for OFCDM broadband packet
wireless access in forward link ," in Proc. IEEE Vehicular Technology Conf., vol. 2, Sept.
2004, pp. 968-973.
[13] T. Cui, and C. Tellambura, "Joint data detection and channel estimation for OFDM
systems," IEEE Trans. Commun., vol. 54, pp. 670-679, Apr. 2006.
[14] J. A. Davis and J. Jedwab, "Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes," IEEE Trans. Inform. Theory, vol. 45, pp.
2397-2417, Nov. 1999.
[15] J. A. Davis and J. Jedwab, "Peak-to-mean power control and error correction for OFDM
transmission using Golay sequences and Reed-Muller codes," Electron. Lett., vol. 33, pp.
267-268, Feb. 1997.
[16] K. G. Paterson, "Generalized Reed-Muller codes and power control in OFDM modulation ," IEEE Trans. Inform. Theory, vol. 46, pp. 104-120, Jan. 2000.
[17] N. Suehiro and M. Hatori, "N-shift cross-orthogonal sequences ," IEEE Trans. Inform.
Theory, vol. 34, pp. 143-146, Jan. 1988.
[18] H.-H. Chen, J.-F. Yeh, and N. Suehiro, "A multicarrier CDMA architecture based on
orthogonal complete complementary codes for new generations of wideband wireless
communications," IEEE Commun. Mag., vol. 39, pp. 126-134, Oct. 2001.
[19] P. Farkas and M. Turcsany, "Two-dimensional orthogonal complete complementary
codes," in Proc. Mobile Future and Symp. Trends Communications, Oct. 2003, pp.
21-24.
[20] C.-Y. Chen, C.-H. Wang, and C.-C. Chao, "Complete complementary codes, Hadamard
matrices, and generalized Reed-Muller codes," to be submitted to IEEE Trans. Inform.
Theory.
[21] C.-Y. Chen, C.-H. Wang, and C.-C. Chao, "Peak-to-average power ratio reduction in
OFDM using complementary sets and Reed-Muller Codes," to be submitted to IEEE
Trans. Inform. Theory.
[22] IEEE standard for local and metropolitan area networks - Part16: Air interface for fixed
broadband wireless access systems, IEEE Std. 802.16, 2004.
[23] "WiMAX Forum Mobile System Pro‾le Release 1.0 Approved Specification," Revision 1.2.2, Nov. 2006. Available: http://www.wimaxforum.org/technology/documents/
WiMAX Forum Mobile System Profile v1 2 2.pdf
[24] IEEE 802.16 Broadband Wireless Access Working Group,"Preambles design for
OFDMA PHY layer FFT sizes of 1024 512 and 128," IEEE C802.16e-04/125r1, Oct.
2004.
[25] IEEE 802.16 Broadband Wireless AccessWorking Group,"Channel model for fixed wireless applicaitions," IEEE 802.16.3c-01/29r4, July 2001.