前置編碼技術在空間多工多輸入多輸出系統中已有相當多的研究，主要用於克服通道衰減效應避免效能損失。假設傳送端可以完整知道通道狀態資訊，則可以根據使用在接收機的檢測器類型來最佳化前置編碼器。在接收機使用最大相似性估測，並且在通道雜訊為高斯分佈時，前置編碼器的設計可以等效於最大化接收端訊號點倆倆之間的最小距離，此距離亦稱為自由距離。但此問題求解複雜度相當高且困難，目前常見的方法為用X架構前置編碼器來解決這個問題。藉由對通道做奇異值分解得出獨立的子通道，再將子通道配對成數個2×2的子系統，如此便可有效降低設計複雜度。然而，最大化自由距離主要是針對符元向量錯誤而設計而非位元錯誤率。換句話說，接收端訊號星狀圖有可能不符合格雷碼的法則，進而降低位元錯誤率表現。本研究將探討如何將格雷碼納入傳送端的設計，並評估其是否可以進一步改善位元錯誤率。模擬結果顯示在缺秩的前置編碼器情況中，納入格雷碼設計的確可以改善系統效能。

The precoding technique has been widely considered a promising way to combat the channel fading in spatial-multiplexing multiple-input multiple-output (MIMO) systems. With the channel state information at the transmitter, the precoder can be designed according to the receiver type. For the maximum-likelihood (ML) receiver, the precoder design criterion for high signal-to-noise ratio (SNR) can be equivalent to the maximization of the minimum distance between the received constellation. This minimum distance is also referred to as free distance. However, the ML precoder design problem is very difficult and complicated. X-structured precoding is known an effective method to overcome the difficulty. The main idea is to first decompose the MIMO channel into parallel subchannels. By pairing the subchannels, we have independent 2x2 subsystems. Then, the precoder can be separately optimized in each subsystem, significantly reducing the design complexity. However, the free distance maximization criterion is based on the symbol-vector error rate (SVER), rather than bit error rate (BER). In other words, the BER performance improvement is not guaranteed as the Gray coding is not considered in the conventional design. In this work, we will investigate how to include the Gray coding in the X-structured precoding. Simulations show that our scheme indeed provides the further improvement in BER.

摘要 i
Abstract ii
誌謝 iv
目錄 v
表目錄 vii
圖目錄 viii
第一章 緒論 1
第二章 系統和訊號模型 3
2.1 空間多工MIMO系統模型 3
2.2 MIMO系統估測的方法 3
2.2.1 強制歸零估測 4
2.2.2 最小均方誤差估測 4
2.2.3 最大相似性估測 5
2.3 具有前置編碼器的空間多工MIMO系統模型 6
第三章 最小距離最大化的前置編碼器設計 7
3.1 自由距離的定義 7
3.2 具有前置編碼器的最大相似性估測 7
3.3 X架構前置編碼器 8
3.4 前置編碼器的參數化形式 10
3.5 對於QPSK調變的前置編碼器 11
3.5.1 前置編碼器F1 12
3.5.2 前置編碼器F2 14
3.5.3 通道臨界值γ0 18
3.5.4 前置編碼器F3 18
3.5.5 前置編碼器F4 21
3.5.6 通道臨界值γ1 22
3.6 對於16-QAM調變的前置編碼器 23
3.6.1 前置編碼器F5 23
3.6.2 前置編碼器F6 25
3.6.3 通道臨界值γ2 28
第四章 使用格雷碼傳送訊號設計 29
4.1 格雷碼 29
4.2 QPSK調變下使用格雷碼的接收端星狀圖 30
4.2.1使用格雷碼的接收端星狀圖前置編碼器F1 30
4.2.2使用格雷碼的接收端星狀圖前置編碼器F2 32
4.3 16-QAM下使用格雷碼的接收端星狀圖 33
4.3.1使用格雷碼的接收端星狀圖前置編碼器F4 34
4.3.2使用格雷碼的接收端星狀圖前置編碼器F5 35
4.3.3使用格雷碼的接收端星狀圖前置編碼器F3和F6 36
4.4使用格雷碼的接收端星狀圖X架構前置編碼器 36
第五章 模擬結果 37
5.1 參數設定 37
5.2 有無使用格雷碼的接收端星狀圖2 × 2前置編碼器性能比較 37
5.3 有無使用格雷碼的接收端星狀圖4 × 4前置編碼器性能比較 45
5.4 有無使用格雷碼的接收端星狀圖6 × 6前置編碼器性能比較 47
第六章 結論 49
參考文獻 50

[1] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Pers. Commun., vol. 6, no. 3, pp. 311-335, Mar. 1998.
[2] A. Paulraj, D. Gore, R. Nabar and H. Bolcskei, “An overview of mimo communications – a key to gigabit wireless,” Proc. IEEE, vol. 92, no. 2, pp. 198-218, 2004.
[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. Inf. Theory, vol. 44, no. 2, pp. 744-765, Mar. 1998.
[4] G. J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas,” Bell Labs Tech. J., vol. 1, no. 2, pp. 41-59, 1996.
[5] S. M. Alamouti, “A simple diversity technique for wireless communications,” IEEE J. Select. Areas Commun., vol. 16, pp. 1451-1458, Oct. 1998.
[6] G. D. Golden, G. J. Foschini, P. W. Wolnianski and R. A. Valenzuela, “VBLAST: A high capacity space-time architecture for the rich scattering wireless channel,” in Proc. Int. Symp. Advanced Radio Techol., Boulder, CO, Sep. 9-11, 1998.
[7] P. Stoica and G. A. Ganesan, “Maximum-SNR spatial-temporal formatting designs for MIMO channels,” IEEE Trans. Signal Process., vol. 50, pp. 3036-3042, Dec. 2002.
[8] H. Sampath, P. Stoica and A. J. Paulraj, “Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion,” IEEE Trans. Commun., vol. 49, pp. 2198-2206, Dec. 2001.
[9] J.-K. Zhang, A. Kavcic and K. M. Wong, “Equal-diagonal QR decomposition and its application to precoder design for successive-cancellation detection,” IEEE Trans. Inf. Theory, vol. 51, no. 1, pp. 154-172, Jan. 2005.
[10] B. Vrigneau, J. Letessier, P. Rostaing, L. Collin, and G. Burel, “Extension of the MIMO precoder based on the minimum Euclidean distance: A cross-form matrix,” IEEE J. Sel. Topics Signal Process., vol. 2, no. 2, pp. 135-146, Apr. 2008.
[11] K. P. Srinath and B. S. Rajan, “A low ML-decoding complexity, full-diversity, full-rate MIMO precoder,” IEEE Trans. Signal Process., vol. 59, no. 11, pp. 5485-5498, Nov. 2011.
[12] S. K. Mohammed, E. Viterbo, Y. Hong, and A. Chockalingam, “MIMO precoding with X- and Y-codes,” IEEE Trans. Inf. Theory, vol. 57, no. 6, pp. 3542-3566, Jun. 2011.
[13] L. Collin, O. Berder, P. Rostaing, and G. Burel, “Optimal minimum distance-based precoder for MIMO spatial multiplexing systems,” IEEE Trans. Signal Process., vol. 52, no. 3, pp. 617-627, Mar. 2004.
[14] Q.-T Ngo, O. Berder, and P. Scalart, “Minimum Euclidean distance based precoders for MIMO systems using rectangular QAM modulations,” IEEE Trans. Signal Process., vol. 60, no. 3, pp. 1527-1533, Mar. 2012.
[15] Y. Jiang, J. Li, and W. W. Hager, “Joint transceiver design for MIMO communications using geometric mean decomposition,” IEEE Trans. Signal Process., vol. 53, no. 10, pp. 3791-3803, Oct. 2005.
[16] C.-T. Lin and W.-R. Wu, “X-structured precoder design for spatial multiplexing MIMO systems,” in Proc. IEEE. Global Telecommun. Conf., Anaheim, CA, pp. 3880-3885, Dec. 2012.
[17] Q. T. Ngo and O. Berder, “Minimum Euclidean distance-based precoding for three-dimensional multiple input multiple output spatial multiplexing systems,” IEEE Trans. Wireless Commun., vol. 11, no. 7, pp. 2486-2495, Jul. 2012.
[18] C.-T. Lin and W.-R. Wu, “QRD-based precoder selection for maximum-likelihood MIMO detection,” in Proc. IEEE Int. Symp. Pers. Indoor Mobile Radio Commun., Istanbul, Turkey, pp. 455-460, Sep. 2010.
[19] Q.-T. Ngo, O. Berder, B. Vrigneau and O. Sentieys, “Minimum distance based precoder for MIMO-OFDM systems using 16-QAM modulation,” IEEE Int. Conf. Commun. (ICC), Jun. 2009.
[20] R. Van Nee, A. Van Zelst and G. Awater, “Maximum likelihood decoding in a space division multiplexing system,” IEEE Fall Veh. Technol. Conf., pp. 6-10, Sep. 2000.
[21] Y. Jiang, W. Hager and J. Li, “The geometric mean decomposition,” Linear Algebra Its Applications, vol. 396, pp. 373-384, Feb. 2005.
[22] Y.-T. Hwang, W.-D. Chen and C.-R. Hong, “A low complexity geometric mean decomposition computing scheme and Its high throughput VLSI implementation,” Circuits and Systems I: Regular Papers IEEE Transacrion on, vol. 61, no. 3, pp. 1170-1182, Apr. 2014.
[23] Y. Li, J. Wang and A. Cichocki, “Blind source extraction from convolutive mixtures in ill-conditioned multi-input multi-output channels,” IEEE Trans. Circuits Syst. I Reg. Papers, vol. 51, no. 9, pp. 1814-1822, 2004.
[24] Rakshith Saligram and Rakshith T R, “Contemplation of synchronous gray code counter and its variants using reversible logic gates,” IEEE Intl. Conf. on Info. & Comm. Tech., Apr. 2013.
[25] S. M. Kay, “Fundamentals of Statistical Signal Processing: Estimation Theory,” Englewood Cliffs: NJ:Prentice-Hall, pp. 344-348, 1993.