針對接收天線數等於甚至多於空間多工訊號傳送量之多重輸入輸出天線系統，許多低複雜度之偵測演算法相繼被提出以克服傳統 ML 解碼搜尋上的高複雜度問題。然而，目前仍鮮少有理想的偵測方法去探討當接收天線數少於傳送訊號數（過載多重輸入輸出）時的複雜度問題。
在本篇論文中，首先我們將介紹幾種低運算複雜度的偵測定理，包含 ZF 和MMSE；同時為了改上述方法在天線數增加時可能的高錯誤率，我們將結合連續干擾消除 (SIC) 的方法來改善偵測錯誤的機率。另一方面，球體解碼為目前簡化多輸入輸出系統之運算搜尋的理想演算法，同時也能達到最佳的 ML 偵測效能。在分支分界的法則之下，進一步使用較小之搜尋半徑並結合 MMSE-SIC 解碼重新排列的系統架構，我們可以更有效縮小樹狀搜尋的範圍。
最後，本論文將著重於解決過載訊號使用球體解碼時所遇到的偵測瓶頸。平板解碼藉由“接近”的概念將可能的解碼結果限制在一個平板中，避免過多搜尋而造成運算上的浪費。同時我們也利用 MMSE-SIC 的運算，使得系統模式可以更容易運用於球體解碼上。

For multiple-input multiple-output (MIMO) antenna systems where the number of receive antennas is at least the number of signals multiplexed in spatial domain, ML detection can be implemented efficiently using sphere decoding or other suboptimal detectors, with reasonable performance and low complexity. Nonetheless, it is much less understood on obtaining good detection at affordable complexity if there are less number of receive antennas than transmitted signals (overloaded MIMO).
In this thesis, we give a brief introduction to suboptimal MIMO detection including zero-forcing (ZF) and minimum mean-square error (MMSE) to reduce the high complexity of ML detection. And then, successive interference cancellation (SIC) technique is applied to improve the bit error rate performance. To achieve the ML detection, we propose sphere decoding combined with re-arranged search order, such that the tree-search complexity can be further reduced.
Finally, we focus on the symbol detection of overloaded MIMO systems based on the aforementioned sphere decoding algorithms. From the closeness points by slab decoding, we can discard the unnecessary candidate sequences to efficiently obtain the exact ML performance. We also apply MMSE optimal SIC (OSIC) for overloaded MIMO systems to further reduce the detection complexity.

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