以子空間方法設計離線及適應性盲目等化器

Abstract

本論文的目的是針對單一輸入多重輸出(single input multiple output, SIMO)的情況下，以子空間方法設計盲目等化器。由於在高速數位通訊傳輸下，傳輸訊號經過多路徑無線通道，會造成傳輸訊號有嚴重地符號間干擾(intersymbol interference, ISI)，除此外， 接收機對於無線通道與傳輸訊號一般而言是一無所知的，所以傳統中的無線通訊系統是使用訓練序列(training sequences)讓接收機了解無線通道之特性，不過使用訓練序列是相當浪費頻寬，因此需要使用盲目等化器來改善頻寬的使用與降低符號間干擾。

本論文將提出兩種新型離線式盲目等化器之方法並改良其一方法使其為適應性盲目等化器。第一種離線式方法，吾人利用過度取樣(Oversampling)生成特殊之Toeplitz架構的通道矩陣，且將此通道矩陣之特性與接收訊號的二階統計(second order statistics, SOS)的子空間運用，在與MRE(mutually referenced filters)方法搭配即是吾人提出的第一種盲目等化器方法。第二種離線式方法，利用MRE擁有地特性並與最小平方法(Least Square Method)和二階統計的子空間相互結合，得到了疊代式的最小平方法亦即是吾人提出的第二種盲目等化器方法。最後，應用了子空間追蹤(subspace tracking)與二次疊代(Bi-iteration)的奇異值分解(singular value decomposition, SVD)將所提出的第一種離線式方法改進為可以 不斷更新等化器參數的適應性盲目等化器。

在論文最後，使用電腦的數值模擬與其他文獻提出之方法比較。所使用的比較標準分別為符號間干擾(ISI)與訊號雜波比(signal-to-interference-noise ratio, SINR)，經由數值模擬的驗證，判斷方法的優越性。

In wireless communication systems, equalization is often required in order to suppress the intersymbol interference (ISI) caused by multipath channels. Conventional approaches use training sequences for equalizer design which wastes the bandwidth. The blind equalizer can perform equalization in no need of the training sequences and thus achieves more efficient channel bandwidth usage. In this thesis, we present new methods based on the subspace approach for computing fractionally spaced blind equalizers in single input multiple output (SIMO) systems.

We first present a new offline method using the properties of the channel matrix structure and the idea of mutually referenced filters. This method is later used to develop an adaptive blind equalizer by employing the OPAST algorithm and the bi-iteration singular value decomposition. We also use the idea of mutually reference filters to develop a new blind equalizer design using the iterative least squares method.

Finally, simulations are performed to demonstrate the better performance of the proposed algorithms compared to existing approaches.