在現代社會中，行動通訊及多媒體設備已成為人們不可或缺的一部分。高速且穩定的無線網路對我們而言相當重要，滿足此需求的關鍵在於增加無線通訊傳輸通道之容量 (Channel Capacity)。其中，最直接的方式為增加傳輸頻寬，亦即使用寬頻無線通訊。然而，在實際應用中，可供使用之頻寬卻是有限的。另一種在無線通訊中有效獲得高速傳輸的方法，是使用多輸入多輸出無線通訊系統 (MIMO)，即是擁有多根傳輸天線和多根接收天線之系統。此系統之優勢在於：傳輸通道之容量會與傳輸天線及接收天線數量呈線性增加。而在多重存取通道 (Multiple Access Channel) 中，多使用者多輸入多輸出系統 (MU-MIMO, Multi-User MIMO) 可進一步提升頻寬之使用效率。時間空間碼 (Space-Time Code) 為一種多輸入多輸出系統之應用方式，此技術能夠提高頻譜效率和降低錯誤率。可除性代數 (Division Algebra) 為設計時間空間碼時，一個相當實用且常見之數學工具。分集與多工增益之權衡 (Diversity-Multiplexing Tradeoff) 是評估時間空間碼效能高低的公平比較準則。在本篇論文中，我們推導出在多重存取頻率非選擇性衰退通道 (Multiple Access Frequency-Nonselective Fading Channels) 下，線性調變的時間空間碼設計準則。此文使用了最佳的迴旋邊碼器 (Convolutional Encoder)，並且設計一個簡單且基於可除性代數之最佳空間編碼器。接著，推導出此文中時間空間碼在單一使用者和多使用者情形下之分集與多工增益之權衡。和傳統最佳時間空間碼之分集與多工增益權衡比較後可以得到：在低多工增益 (Multiplexing Gain) 的情況下，本文系統不論單一使用者或多使用者，其分集增益 (Diversity Gain) 皆比傳統最佳時間空間碼之分集增益大上許多。然而，在此系統中，多工增益無法達到傳統最佳時間空間碼之最大多工增益可能值。

In this thesis, we derived the rank design criterion of a space-time coding scheme for
linear modulation over multiple access frequency-nonselective fast fading channels
and gave a simple code construction for multiple access channels.
We also evaluated the diversity and multiplexing tradeoffs under both single and
multiple users cases. We observed that the diversity gain of our space-time coding
scheme is greater than that of the uncoded optimal one in low multiplexing gain, but
is smaller in high multiplexing gain.

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