在多重輸入多重輸出(MIMO) 正交分頻多工(OFDM) 系統中， 由於多天線與大量的次載波
(Subcarrier)數目，使得基於QR分解的多重輸入輸出偵測器面臨了高運算複雜度的QR分解問題。因此， 基於內插(Interpolation)運算的QR分解被提出以降低複雜度。此篇論文中， 我們提出了一個適用於群組排序(Grouped-ordering)內插結構之具可擴展性的內插式QR分解演算法， 此演算法去除了傳統Gram-Schmidt方法中的開根號及除法運算， 因此擁有運算穩定性。此外， 它的可擴展性對於未來行動通訊系統中低秩(Lower-rank)的多重輸入多重輸出結構，提供了一個節省功率的架構，我們同時也開發其硬體架構以達到硬體複雜度與運算時間的平衡。最後，分析結果顯示所提出之演算法在4x4多重輸入多重輸出正交分頻多工系統中， 可降低複雜度為傳統方法之25.4%~61.3%。

In the MIMO-OFDM system, QR-based MIMO detection suffers from high computational complexity of the QR decomposition due to the large numbers of antennas and subcarriers. Thus, interpolation-based QR decomposition was proposed to reduce the complexity. In this paper, we present a scalable interpolation-based QR decomposition algorithm for the grouped-ordering interpolation scheme. The proposed algorithm possesses
computational stability because it eliminates the square root and division operations in the traditional Gram-Schmidt-based scheme.Besides, its scalability offers a power-saving structure for the lower-rank MIMO scheme in the future mobile communication systems. A hardware architecture is also developed to balance the hardware complexity and computation time. Finally, analysis result shows that the proposed algorithm reduces the complexity to 25.4% ~ 61.3% of the traditional algorithm in the 4x4 MIMO-OFDM system.