基於最小平方通道估測演算法之效能極限和其延伸應用於正交頻分多工系統中之都卜勒位移估測

Abstract

在同調偵測的系統中，接收端必須利用通道狀態資訊來恢復所傳送之訊息信號。有關通道參數估計的問題，例如：相對時間延遲(relative delay)，衰減值(attenuation)以及相位(phase)估測之研究已經在諸多文獻中被討論。在實際的通道狀態裡，重疊多路徑通道(即路徑間隔為一個符元區間之內)可能在很多通訊環境裡發生。在這篇論文內，我們對於如何在緊密間隔多路徑(closely-spaced multipath)通道的環境中解析重疊路徑成分(overlapped multipath components)的問題感到興趣，因為這是通道估測過程中最具挑戰的情況之一。 許多基於最小平方準則(Least-square criterion)或近似最小平方法之通道參數估測技術已經在文獻中被提出。在此研究的第一部分，我們將描述如何利用已知收發機濾波器之資訊，來實現最小平方通道估測演算法。並且解釋欲估測之複合通道事實上是位於由收發機濾波器之脈衝響應所構成的子空間(subspace)中。因此，我們將研究在接收端不知道正確路徑延遲的前提下，所假設的子空間(hypothesis subspace)對最小平方通道估測法的衝擊。此外，我們推導出在基於最小平方準則下，通道參數之估計均方誤差(MSE)的上下界理論值。此上下界理論值可用來說明路徑延遲間隔假定(delay hypothesis spacing)和過取樣比(oversampling ratio)是如何影響通道估測器的性能。 論文的第二部分將討論正交頻分多工(OFDM)傳輸中，由都卜勒擴散通道(Doppler spread channel)所產生的載波間干擾(ICI)效應。在移動通道中，都卜勒擴展會破壞子載波之間的正交性，將而導致載波間干擾。其結果可能嚴重地降低系統性能的表現。由於都卜勒偏移(Doppler shift)可以視為在頻域上的“時間延遲”，因此前述的最小平方估測法可以直接延伸應用於估計正交頻分多工系統中所遭受的都卜勒偏移。最後，基於最小平方準則之通道估測演算法，我們會提供有關參數設計上的導引和建議，如路徑延遲間隔假定、過取樣比和相關器之相關視窗大小(the width of the correlation window)等參數之取決。

In the coherent detection systems, the knowledge of the channel states is necessary to recover the transmitted information signal. The problem of estimating channel parameters such as relative delay, attenuation and phase has been addressed in the literature. In the realistic channel condition the overlapped multipath components (at most one symbol apart) may happen in many communication environments. In this thesis, we are interested in the problem of solving overlapped multipath components in the closely-spaced multipath scenario because this is one of the most challenging situation in the channel estimation process. Many channel estimation techniques have been proposed based on least-square criterion or to give the approximate least-square estimates. In the first part of this research, we describe a least-square algorithm to incorporate a prior knowledge of the transmit and receive filters into the channel estimation procedure. It is shown that the composite channel lies on the subspace formed by the impulse responses of the transceiver filters. We will investigate the impact of not modelling the time delays exactly when constructing this hypothesis subspace. Moreover, a lower and an upper bound of mean-square-error (MSE) for least-square based algorithms are derived, which show how the performance depends on the delay hypothesis spacing and oversampling ratio. The second part of the thesis discusses the problem of inter-carrier interference (ICI) due to Doppler spread channel in orthogonal frequency division multiplexing (OFDM) transmission. The Doppler spread in mobile radio channel distort the orthogonality among subcarriers resulting in ICI, which seriously degrades the performance of systems. It is observed that the Doppler shifts looks like the 'delay' in the frequency domain. The least-square technique can be directly extended to estimate Doppler shifts for OFDM systems. We will give a guidance in selecting some implementation parameters such as path hypothesis spacing, oversampling factor and the width of the correlation window for the least-square based channel estimation algorithms.