估測正交頻率多重傳輸系統時間偏移的最佳脈衝整型濾波器

Abstract

在正交頻率多重傳輸(Orthogonal frequency-division multiplexing)系統中，時間偏移(timing offset)及頻率偏移(frequency offset)的估測是很重要的課題。在文獻中有很多方法來估測這兩個參數,有些方法是利用訓練序列(training sequences)或領航符號(pilot symbols),有些方法則是利用週期靜態性(cyclostationary)來作估測。在利用訓練序列或領航符號的方法裡是以接收到資料的相關性(correlation)或最大概似函數(likelihood function)來估測時間及頻率偏移。本論文所討論的方法是利用最大概似函數來估測時間及頻率偏移。既有文獻的方法並沒有考慮到因取樣時間誤差所造成的非整數時間偏移。因此本論文的主要貢獻是將非整數時間偏移加入考量。我們發現使用不同的脈衝整型濾波器(pulse shaping filter)其時間及頻率偏移的估測誤差也不同。我們並推導出此二估測參數之CR邊界(Cram\'{e}r-Rao bounds)，而且設計一脈衝整型濾波器以使得估測時間偏移誤差之CR邊界為最小,之後再以模擬結果驗証其優越性。

It is important to estimate the frequency offset and timing offset in an orthogonal frequency-division multiplexing (OFDM) system. Many approaches have been developed in literature. Some approaches use training sequences or pilot symbols, others use the property of cyclostationarity for estimation. Those approaches via training sequences or pilot symbols employ the correlation or the maximum likelihood function for parameter estimation. This thesis focuses on the maximum likelihood approach. In literature, the approaches via the maximum likelihood function, as far as we know, only estimate integer timing offset but neglect the inevitable noninteger timing offset.This thesis considers this noninteger timing error. It is observed that the pulse shaping filter will influence the estimation performance. Thus we derive the Cram\'{e}r-Rao bound and use this bound as the measure to design optimal pulse shaping filter such that the Cram\'{e}r-Rao bound for the estimation error of timing offset is minimized. Simulations are then performed to verify the usefulness of this design.