在此論文裡，我們考慮作用於單傳送和單輸出瑞利區塊衰減通道 (single-input-single-output Rayleigh block fading channel)的非同調通訊系統 (noncoherent communication system)，而使用的編碼方式是差分調變。首先，我們比較以查表法為基礎的差分調變 (look-up table based differential modulation)和以規則為基礎的差分調變 (Rule based differential modulation)去找出在此通道環境下可以精準衡量具有不同傳送能量的訊號向量的距離法則 (distance measure)。在找出適用於此通道環境下的距離法則後，我們使用以查表法為基礎的差分調變來建造一個多維度差分調變，而且我們採用線性離散碼 (linear dispersion codes)去建造新穎的多維度差分調變訊號集合，基因演算法 (Genetic Algorithm)則是我們用來搜尋可以改善錯誤效能的多維度差分調變集合的方法。在此演算法中，我們提出一個搜尋標準去找出一個最佳化的線性離散碼。除此之外，對已建立的表格分配資料位元 (data bit assignment)的步驟， 我們採用二位元交換演算法 (binary-switch algorithm )並把成對錯誤率 (pairwise error probability)和距離準則的關係應用於演算法。

In this thesis, a noncoherent communication system over single-input-single-output (SISO) Rayleigh block fading channel is considered. A look-up table based differential modulation is used to construct multi-dimensional differential modulation. Furthermore, linear dispersion codes are adopted to construct novel multi-dimensional differential signal sets, where the Genetic Algorithm is used to help us search for signal sets which can improve the error performance.

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