高相關係數簡化法在正交頻率多工系統的應用

Abstract

本論文首先介紹正交頻率多工系統的結構。同時，介紹了許多同步與等化的方法。我們提出線性最小平均估計法在時間與頻率領域等效的証明以及以平均錯誤為標準的效能理論分析。最小平均估計法與最小平方法類似，都與接收機的訊雜比成反比且在對數座標下是一條直線。 以乘法器數目為考量，最小平均估計法的複雜度過高，因此我們要尋找低複雜度的方法，同時利用特殊的多路徑時域關係。新提出的演算法是一種高相關係數的簡化法。理論及模擬的結果相當接近。與最佳的最小平均估計法比較，在可忽略的訊雜比損失的情況下，這種方法節省了一半的複雜度。

In this thesis, we first introduce the structure of OFDM systems. Many techniques for synchronization and equalization are reported. The equivalence of LMMSE estimators for the OFDM channel estimation are derived analytically both in time and frequency domains. So are their theoretical performances in the mean square sense. With some approximation, the LMMSE performance, like the LS method, is inversely proportional to the receiver SNR and is a straight line in log scale. Considering the numbers of the multiplier, the optimal LMMSE is so complex and we seek for low complexity method due to the special relation between multipaths in transform domain. A new low complexity algorithm is proposed with high correlation truncation method. The numerical and randomized simulation results are close. Compared with the optimal LMMSE, this method achieves negligible SNR loss with half complexity.