Abstract
本論文提出一類適用於全盲反旋捲與頻道等化的基於高階統計量之反濾波器設計準則。這一類反濾波器設計準則僅用到反濾波器輸出信號的二個cumulants，其目的是使J_{r,m}=|Cm|^r/|Cr|^m達到最大，而得到最佳反濾波器；其中Cm(Cr) 代表反濾波器輸出信號的m階(r階) cumulant。首先，本論文理論上證明只有在 m > r ，且r 是偶數的條件下，J_{r,m}才有最大值存在；否則 J_{r,m} 為無限大(unbounded)。(r,m) 可允許的值除了包括由Tugnait、Wiggins、Shalvi和Weinstein提出的(2,3)、(2,4)和(4,6) 外，還有一些新提出的，例如(2,5)、(2,6)和(4,5) 等第。然後我們以一些模擬結果及一些語音信號反旋捲的應用結果來驗證這些反濾波 良好性能。接著，本論文提出一基於反濾波器設計準則J_{2,3}的 SGB (stochastic gradient-based) 可適性演算法則和修改過的基於反濾波 計準則J_{2,4}的SGB可適性演算法則；其次本文亦提供一些模擬結果，包括當信號為穩定(stationary)隨機信號及非穩定(nonstationary) 隨機信號兩種情形，以驗證所提出的可適性演算法則之性能。最後，我們作了一些結論。Cumulant (higher-order statistcs) based inverse filter cri-teria maximizing J_{r,m}=|Cm|^r/|Cr|^m, where m≠r and Cm (Cr)denotes the m-th order (r-th order) cumulant of the inversefil- ter output, have been reported for blind deconvolution andequa- lization with only non-Gaussian output measurements of anun-n linear time-invariant (LTI) system. First of all, thisthesis shows that the maximum of J_{r,m}, associated withtheinverse filter of the unknown LTI system exists only for rto be even and m > r; otherwise, J_{r,m} is unbounded. The ad-missible values for (r,m)=(2s,l+s) where l > s >= 1 include),(2,4) and (4,6) proposed by Tugnait, Wiggins, Shalvi andn inaddition to more new ones such as (2,5), (2,6) and gradient-based (SGB) adaptive algorithm associated with J_{2,3}amodified SGB adaptive algorithm associated with J_{2,4} areproposed, respectively. It is empirically found that theosedadaptive algorithms converge and perform well when the signalis stationary. On the other hand, when the signal is non-stationary, they also exhibit tracking capabilities of time-varying characteristics of the signal. Some simulation resultsassociated with the proposed adaptive algorithms are also pro-vided. Finally, we draw some conclusions.