在無線通訊系統中，無線通道的正交性轉換最近在多天線解碼器中是一個重要方法。正交性轉換成不同基底去解碼會達到不一樣效果。這樣的技術在錯誤率上的表現可以取得多樣性而且很接近最大可能性解碼器的表現。正交性的轉換利用幾個參考來代表轉換過後基底的正交程度，正交缺陷指數是在正交性轉換中的一個參考。這個指數是所有基底的長度連乘積跟所有基底圍乘的體積的比例。在這篇提出一個演算法想找出轉換過後有最小正交缺陷指數的基底。這個方法利用一個指數，命名為正交補數。這個是從Schur complement的公式演化而來。正交缺陷跟正交補數一樣代表正交性，而正交補數可說是是表現一個向量對現有的晶格的依賴性。另外一方面，在現存的如LLL跟Seysen的轉換方法中都未曾使用排序，他們提供了不一樣晶格減縮的想法。LLL利用兩兩交換來確認任兩個基底的最大減縮，而Seysen提供晶格和補晶格的雙重減縮，雙重減縮結果上可以達到比較低的錯誤率。在這篇文章利用雙重減縮的想法跟正交補數排序。正交補數針對一個基底做排序，找出可以減縮的基底因此也降低了複雜度。全部的比較上來說提出的演算法在錯誤率或正交性都是最好的轉換，在基底更新次數統計上，相對來說也比較少。從後面的模擬圖中可以證實了這個方法的有效性跟較低的複雜度。

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