在傳統的單一天線通訊中，儘管很多方法被提出為了增加效能, 但是始終沒有善加利用在空間維度上的通信能力，使得通訊品質一直受限於Shannon的上界；反之，MIMO系統則可像增加管線一般提升通訊效益。不過相對於多天線傳送與多天線的接收，解調的方法也變得比以往複雜，所以也有更多值得研究的地方。
在本篇論文中，一開始會先大略介紹一下簡單的解調方式(ZF、MMSE、ML),為了改善ML的高複雜度與ZF、MMSE的效能，許多改進的解調方式相繼被提出，其中發展最早也具代表性的是美國朗訊科技(Lucent Tech.)貝爾實驗室所提出的BLAST(Bell-labs Layered Space Time)，不過隨著天線數目的增加，BLAST和ML之間的差距也越來越大。因此球狀解碼用來達成ML解調方式的簡化模式。
在本篇論文中，
我們也利用分支分界法(branch and bound)在MIMO系統中，達到和球狀解碼相同的錯誤率。而在第四章節，我們將探討通道對於各個解調方式的影響，並且針對通道的不完美，利用晶格簡化(Lattice reduction)的方式，調整通道去做解調，達到更佳的效果。

Although many techniques were proposed to get better performance in traditional SISO (single input single output) systems, they always don’t use the diversity of space well. As a result, they were limited by the low bound of Shannon. On the contrary, the MIMO system can improve the channel capacity as well as increase the number of pipe lines. The methods of decoding would become more complex as the number of antenna increases; we can observe many interesting effects happened in the MIMO.
In this thesis, we would give a brief introduction to general MIMO decoding algorithms including zero forcing (ZF), Minimize the mean squared error (MMSE), Maximum likelihood (ML). In order to reduce the high complexity of ML algorithm and to increase the performance of ZF and MMSE algorithms, many new schemes have been proposed. BLAST (Bell-labs Layered Space Time) was an significant technique and was investigated at the earliest by Lucent Tech. of BELL LAB, but the gap between the ML and BLAST would become large as the number of antennas increase. Sphere decoding algorithm was proposed to reduce the complexity of ML.
We also use branch and bound in MIMO system to get the same performance as sphere decoding algorithm. In the chapter 4, we discuss the effect of channel condition and use lattice reduction-aid detector to change the ill channel matrix to a better one. We make hard decision after the changed matrix to get better performance.

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