近幾年來，隨著科技進步，大量資料傳輸需求增加，原本受限於空間多工技術的多重輸入多重輸出突破空間的侷限，利用多路徑增加吞吐量。球體解碼演算法雖然提供樹狀搜尋的方法得到最大概似解，但在低訊號雜訊比的複雜度仍然很高。
在本論文中，一開始 我們會先介紹球體解碼跟不同樹狀搜尋的球體解碼。之後，我們會介紹一個根據估計值選擇搜尋路徑的演算法用於多重輸入多重輸出系統，並在不同的正交振幅調變觀察複雜度與錯誤率的變化。最後，我們結合適應性的概念，在低訊號雜訊比的時候選擇較少的搜尋路徑演算，在高訊號雜訊比的時候選擇較多的搜尋路徑,權衡搜尋的路徑數量來達到損耗少部分錯誤率降低複雜度的方法。

In recent years, with the progress of science and technology, the need of a large number of data transmission is on the increasing. Originally limited by the space, the multiplexing multiple input multiple output (MIMO) system makes breakthrough the space limitation and increases the transmission throughput. Although the sphere decoding (SD) algorithm provides the optimal maximum-likelihood solution based on the tree search, the complexity of the SD algorithm at the low signal-to-noise ratio (SNR) is quite high. In this thesis, we consider the SD algorithm and the related different tree search methods. Then, we give an algorithm based on the estimated search path for the MIMO system, and observe the change in the complexity and bit-error rate (BER) for different constellations of quadrature amplitude modulation (QAM). Finally, we apply the concept of adaptation, which we choose fewer searching paths at the low signal noise ratio (SNR) and more searching paths at the high SNR. Our method provides a trade-off between the complexity and performance. We can reduce the number of searching paths to reduce the complexity with a small loss of BER.

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