可靠的高速網絡傳輸、可攜式多媒體應用和通訊設備已經成為我們生活中不可或缺的一部分。為了滿足人類的需求，實現這一目標的關鍵是增加通道容量。最直觀的方法是放大傳輸頻寬。 但是，可用頻譜資源有限。另一種有效方式是使用MIMO系統，即多個傳輸天線和多個接收天線。MIMO系統的優點是通道容量會隨著發射天線數量及接收天線數量而呈現線性增長。
近年來，時間空間碼已被證明是一種強大的技術可以提高頻譜效率和降低錯誤率。 從1998年起，Alamouti、Tarokh、Stephen…等人提出各種時間空間碼的設計，並不斷加以改進。隨著高資料傳輸率的要求越來越高，傳統上假設通道是頻率非選擇性衰退也就不太適用。當資料在頻率選擇性衰退通道下傳輸時，由於不同路徑的獨立性，我們希望能獲得相對於頻率非選擇性衰退通道更大的分集增益。
在本論文中，我們推導出了在頻率選擇性衰落通道下線性調變使用超取樣技術的時間空間碼秩設計準則。 使用最佳的迴旋編碼器和最佳的空間編碼器，最後利用簡單的矩陣運算計算出整體的增益大小。在解碼端我們設計了一個用於維特比解碼器的有限狀態機器，以此得到最佳錯誤率解碼。在本系統下，可以得到的分集增益為迴旋碼的有效長度 (ECL) 與傳送天線個數、接收天線個數、超取樣率的乘積再加上多重路徑個數與超取樣率的差。最後放上模擬圖，模擬結果顯示了使用超取樣技術是非常有效的，也驗證了理論推導的正確性。

In this thesis, we derived the rank design criterion of a space-time code scheme for linear modulation over frequency-selective fast fading channels with oversampling technique. With an optimal convolutional temporal encoder and an optimal spatial encoder achieving the full transmit spatial diversity, the overall diversity gain is at least Lr(L*ECL*L) if L<=l and Lr(Lt*ECL*l+L-l) if L >l, where Lr is the number of receive antennas, Lt the number of transmit antennas, ECL the effective code length of the convolutional encoder, l the oversampling factor and L the number of taps in the equivalent tapped-delay-line channel model.
We have devised an finite-state machine for a Viterbi decoder which implements the maximum likelihood sequential detection of the received signal.Simulation results have confirmed that this coding scheme is very effective.

1 Introduction 4
2 Frequency-Selective Fading Channel Model 6
2.1 Tapped-Delay-Line Channel Model................. 6
2.2 WSS-US Two-path Channel..................... 10
2.3 A Separable WSS-US Multipath Fading Channel with One-sided
Gaussian Power Prole........................ 12
3 A Scheme for Space-Time Coding with Linear Modulation 15
3.1 A Space-Time Coding Scheme.................... 15
3.2 Space-Time Code Design Criteria for Linear Modulation..... 18
4 Space-Time Encoder Design 26
4.1 Convolutional Encoder........................ 26
4.2 Spatial Encoder (Full Rank Matrix Design)............. 27
4.2.1 Division Rings......................... 27
4.2.2 Embedding Field Extension into Mn*n(F) ......... 28
4.2.3 Design of Matrices Whose Differences Have Full Rank... 29
4.2.4 Linear Modulation Code Design with Cyclotomic Field Ex-
tension ............................. 31
4.3 Transmit Diversity Advantage of the Space-Time Code...... 32
5 MLSD Viterbi Decoder and Simulation Results 38
5.1 An Overview............................. 38
5.2 The Finite-State Machine for the Viterbi Decoder......... 39
5.3 Simulation Results.......................... 41
5.3.1 Parameter Setting...................... 41
5.3.2 Performance Comparison over Fast Fading Channels... 44
6 Conclusion 47

[1] G. J. Foschini and M. J. Gans, "On limits of wireless communications in a fading environment when using multiple antennas," Wireless Personal Commun., vol.6,pp.311-335,Mar.1998.
[2] I. E. Teletar, "Capacity of multi-antenna Gaussian channels," Europ. Trans. Telecom-mun., vol.10,pp.585-595,Nov./Dec.1999.
[3] V. Tarokh, N. Seshadri, and A. R. Calderbank, "Space-time codes for high data rate wireless communication: performance criterion and code construction," IEEE Trans.Inform.Theory, vol.44,no.2,pp.744-765,Mar.1998.
[4] M. R.Bell,J.-C. Guey, M. P. Fitz, and W. Kou, "Signal design for transmitter diversity wireless communication systems over Rayleigh fading channels, "IEEE Trans. Commun., vol.47, Apr 1999.
[5] S. M. Alamouti, "A simple transmit diversity technique for wireless communications, " IEEE J. Select. Areas Commun., vol.16,pp.1451-1458,Oct. 1998. IEEE Trans. Commun., vol.47, Apr 1999.
[6] B. A. Sethuraman, B. S. Rajan, and V. Shashidhar, "Full-diversity,high-rate space-time block codes from division algebras," IEEE Trans.Inform. Theory, vol.49,no.10,pp.2596-2616,Oct.2003.
[7] C.-C. Cheng and C.-C.Lu,"Space-time code design for CPFSK modulation over frequency-nonselective fading channels," IEEE Trans. Commun., vol.53, no. 9,pp.1477-1489,Sep.2005.
[8] S.-C.Chou, "A space-time code design for CPFSK modulation over
frequency- selective fading channels, "Master's thesis, National Tsing Hua University, Tai-wan,2006.
[9] M.-C. Shih, "Space-time code design for QPSK modulation over frequency-nonselective fading channels, "Master's thesis, National Tsing Hua University, Tai-wan,2007.
[10] H.-Y. Cheng, "Space-time code design over frequency-nonselective fading channels by division algebras, "Master's thesis, National Tsing Hua University, Tai-wan,2008.
[11] Y.-H. Lin, "A receiver with oversampling for multipath fading channels, "Master's thesis, National Tsing Hua University, Tai-wan,1994.
[12] C.-C .Lu and J.-P.Chen, An optimal test of Zq-convolutional coded CPFSK for communications over Rayleigh fading channels, "to be submitted for publication.
[13] I. N. Herstein, Abstract Algebra, 3rd edn. January 30, 1996.
[14] R. J. McEliece, Finite Fields for Computer Scientists and Engineers. Kluwer, 1989.
[15] J. G. Proakis, Digital Communications,4th edn. McGraw Hill,2001.