超正交空時區段碼 (Super-Orthogonal Space-Time Block Codes) 是一種可以提高正交空時區段碼 (Orthogonal Space-Time Block Codes) 頻譜效益 (Spectral Efficiency) 的編碼方式，而這種編碼方式所提出來的構想，就是把正交空時區段碼利用右乘酉矩陣 (Unitary Matrix) 的運算，來增加其碼字 (Codeword) 。因為碼字的增加，碼率 (Code Rate) 也會提高，進而可以改進頻譜效益。在這篇論文當中，我們以超正交空時區段碼為基礎，找到一種更廣泛的編碼方式，稱為擴展超正交空時區段碼 (Expanded Super-Orthogonal Space-Time Block Codes) 。我們的想法是同時考慮右乘和左乘的酉矩陣，希望可以增加碼字選擇的自由度 (Degree of Freedom)。因為擴大傳送訊號的星狀圖 (Constellation) 大小，會讓效能變差，所以我們只討論兩種酉矩陣，分別是置換矩陣 (Permutation Matrix) 和旋轉矩陣 (Rotation Matrix) ，我們發現對於旋轉矩陣來說，如果同時考慮左乘和右乘，的確可以提供更多的自由度來增加碼字，但是對於置換矩陣，考慮左乘並不影響可以增加的碼字。綜合上面兩種酉矩陣，我們可以得到擴展超正交空時區段碼的相關建構參數，並用此參數去設計擴展超正交空時區段碼的編碼冊 (Codebook) 。這篇論文中，我們還提供了一個系統而且可行的方法，去建造整個擴展超正交空時區段碼的編碼冊。我們設計的編碼方式，不僅可以保持先前超正交空時區段碼的解碼複雜度 (Decoding Complexity) ，而且可以改善超正交空時區段碼的分集增益 (Diversity Gain) 。在數目比較少的接收天線，從誤碼率 (Bit Error Rate) 的曲線來看擴展超正交空時區段碼的效能，確實會比超正交空時區段碼來的好。

Space-time codes in both spatial and temporal domains have been proposed and become very
popular for use in multi-input multi output systems. This thesis introduces a more general
structure for super-orthogonal space-time codes called expanded super-orthogonal space time
codes, which can retain the property that the maximum-likelihood decoding complexity is
linear in the number of transmit antennas. Its codebook can be obtained by expanding
the original space-time block code via both sides of unitary transformations. Besides, with
a systematic parameterization, we can show a systematic procedure to obtain codebooks
with optimal diversity gain. The results demonstrate better performance compared with
super-orthogonal space-time block codes in terms of bit error rate.

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