盲蔽式量子濾波器等化技術在頻率選擇性通道下之演算法與效能分析

Abstract

近年來，有關於量子濾波器 (Particle Filter) 在系統通道等化器之應用問題已經在很多論文當中引起廣泛的討論。如同參考資料[3]中所提到，當通道有一個很微弱的直線傳輸路徑(light of sight, LOS)時，連續關鍵取樣(Sequential Importance Sampling, SIS)等化器的系統效能會被嚴重的影響而衰退。在參考資料[3]中同時也提出了一種延遲連續關鍵取樣演算法(Delayed SIS Algorithm)來試圖解決這個問題。然而這種演算法需要大量的運算複雜度來提升系統的效能，因此在本篇論文中我們提出一種新的盲蔽式(blind)連續關鍵取樣演算法，該演算法不會受通道直線傳輸路徑的強弱影響而衰退。 在論文中，我們首先簡單的介紹量子濾波器的理論，並建立起量子濾波等化器的系統架構。接著透過錯誤率(bit error rate, BER)的數學分析，我們可以了解到一個擁有微弱的直線傳輸路徑的通道是如何的影響連續關鍵取樣等化器的效能。為了克服這個問題，我們利用最小相位濾波器(minimum phase filter)的概念來轉化原來的通道，使轉化後的等效通道的直線傳輸路徑增強。這種方式稱做連續關鍵取樣決策回授等化器(SIS decision feedback equalizer, SIS DFE)。在通道已知的情況下，最小相位濾波器可以用回授等化器來實現，其中濾波器的係數可以根據(zero-forcing, ZF)或最小平方平均誤差(minimum mean square error, MMSE)準則來求出。而在通道係數未知以及時變通道的系統中，我們提出適應性盲蔽式連續關鍵取樣等化器，利用適應性濾波器演算法如最小平均平方(least mean-square, LMS)或遞迴最小平方(recursive least squares, RLS)來調出最小相位濾波器的係數。針對上述兩種情況，我們都提出電腦模擬結果來驗證這種連續關鍵取樣決策回授等化器可以改善系統的效能。另外我們也比較連續關鍵取樣決策回授等化器與延遲連續關鍵取樣演算法的效能，並證明我們提出的方法不論在錯誤率或系統複雜度方面都有更好的表現。 此外，為了更進一步簡化這種適應性連續關鍵取樣等化器的複雜度，我們提出最大比重適應性盲蔽式連續關鍵取樣決策回授等化器(Max-Weight blind SIS DFE)。透過電腦模擬結果，我們證明這種節省系統資源的演算法可以大幅減少系統的複雜度，卻可以提供幾乎不遜於原本的適應性盲蔽式連續關鍵取樣決策回授等化器的效能。

The use of particle filter on the channel equalization problem has been studied by many researches for years. As mentioned in [3], the weak light-of-sight (LOS) channel is one of the problems limiting the performance of the sequential importance-sampling (SIS) based equalization. In [3], the delayed-SIS (D-SIS) algorithm was proposed to solve this problem at the expense of high computation complexity. In this thesis we introduce a new class of blind SIS equalization algorithms for the frequency selective channels no matter how the first impulse of CIR (Channel Impulse Response) is. We begin with a brief review of the particle filtering theory and establish the model of the particle filter equalizer. After the mathematical analysis of the BER in the particle filter based channel equalization systems, we can know how the performance of the SIS equalization algorithm is affected by the channel with an attenuated LOS. To overcome this problem and improve the performance, we use the idea of minimum-phase pre-filtering to maximize the LOS of the equivalent channel and propose the SIS decision feedback equalization algorithms. In the case when the channel state information (CSI) is known, this minimum- phase pre-filtering can be implemented with the decision feedback equalizers (DFE), whose coefficients are computed based on either the zero-forcing (ZF) or minimum mean square error (MMSE) criteria. In the case of unknown CSI and time-varying channel, the proposed adaptive blind SIS equalization algorithm pre-filters the receiver input by using the adaptive filters such as the least mean-square (LMS) or the recursive least squares (RLS). In both cases, we conduct the computer simulations to illustrate how the proposed SIS DFE algorithms improve the performance. We compare the performance of the D-SIS equalization and the proposed SIS decision feedback equalization and find that our approach outperforms the D-SIS on both the BER performance and the computation complexity. Moreover, to save the computation of the adaptive SIS equalization algorithms, we propose a simplified scheme of the adaptive blind SIS DFE, named the Max-Weight blind SIS DFE algorithm We show that the proposed cost-effective algorithm can provide the performance almost the same as the original adaptive SIS DFE algorithm from the computer simulation results.