近幾年來正交分頻多工系統的發展頗受矚目，正交分頻多工系統可以應用在許多不同的方面上，如數位音訊廣播、高畫質電視地面廣播、非對稱數位用戶迴路…等等，採用正交分頻多工系統的理由有幾個，第一，正交分頻多工系統可以有效地對抗多重路徑效應，在給定相同程度的延遲擴散下，正交分頻多工系統的實現會比單一載波系統來的簡單，因為正交分頻多工系統可以簡單地利用保護時間而不需要太複雜的等化器，就可以對抗延遲擴散所造成的各種效應；第二，正交分頻多工系統利用多個子載波來平行地傳送資料，可以達到整體高資料速率的目的；第三，正交分頻多工系統可以有效地對抗窄頻帶的干擾。但是另一方面，正交分頻多工系統同時也存在有兩個缺點，一個是對頻率偏移太敏感，另一個則是正交分頻多工符號具有太高的峰均值。
本篇論文的重點是放在解決正交分頻多工符號的高峰均值問題上。脈波整形法是一個可以有效地降低正交分頻多工符號峰均值的方法，而且可以適用於任意子載波數的正交分頻多工系統，因此在使用上是非常具有彈性的。而脈波整形法如果和選擇對映法或是部分傳輸序列法相比，脈波整形法並不需要額外的反快速傅立葉轉換處理器，因此系統的實現複雜度會比較小，而如果跟峰值剪截法相比，脈波整形法的位元錯誤率效能表現會比較好，因為脈波整形法不對正交分頻多工符號造成任何失真。根據脈波整形法，本論文找到一個不錯的波形，這個波形具有讓正交分頻多工符號峰均值不超過2左右的能力。

In recent years, the development of OFDM system has received a lot of attention. Some examples of existing systems where OFDM system is used are digital audio broadcasting, high-definition television terrestrial broadcasting, asymmetric digital subcarrier lines and so on. There are several reasons for using OFDM systems. First, OFDM system is an efficient way to deal with multipath effect. Under a fixed amount of delay spread, the implementation complexity of OFDM system is much less than that of single-carrier system. The reason is that OFDM system can simply use guard time to process delay spread without a complex equalizer. Second, OFDM system can achieve high data rate to transmit by using large number of subcarriers. Third, OFDM system can also efficiently combat with narrow band interference. On the other hand, OFDM system also has two main drawbacks. One is more sensitive to frequency offset, the other is higher PAPR.
This thesis focuses on the PAPR problem. Pulse shaping method is an effective way to solve this problem. It can be used for any number of subcarriers of OFDM systems, so it is very flexible. It doesn’t have any additional IFFTs in comparison to the selected mapping or partial transmit sequence method. Its implementation is simpler. And because it also doesn’t distort the OFDM symbols, its bit error performance should be better than the clipping method. According to the pulse shaping method, we get a better waveform that can make the PAPR of OFDM symbols do not exceed about 2.

中文摘要 i
Abstract ii
本文目錄 iii
圖目錄 v
表目錄 ix
第一章 前言 1
1.1 研究背景 1
1.2 各章提要 2
第二章 正交分頻多工系統概觀 4
2.1 正交分頻多工系統的基本特性 4
2.2 正交分頻多工系統的基本架構 5
2.2.1 連續時間型式的正交分頻多工系統架構 5
2.2.2 離散時間型式的正交分頻多工系統架構 9
2.2.3 保護時間、循環延展和窗型化 10
2.3 峰均值 12
2.3.1 正交分頻多工符號的峰均值 13
2.3.2 離散時間型式正交分頻多工符號峰均值的機率分佈 16
2.3.3 連續時間型式正交分頻多工符號峰均值的機率分佈 19
2.4 降低正交分頻多工符號峰均值的方法 20
2.4.1 信號失真 20
2.4.2 相位旋轉 24
2.4.3 編碼 27
第三章 脈波整形法 28
3.1 脈波外形對正交分頻多工符號的影響 28
3.2 現有利用脈波整形法降低正交分頻多工符號峰均值的方法 31
3.2.1 時域循環位移 31
3.2.2 母時域波形的限制條件 34
第四章 母時域波形的選擇 39
4.1 正交分頻多工符號的最大峰均值與子載波數之間的關係 39
4.1.1 數學分析討論 39
4.1.2 程式模擬結果 46
4.2 較佳的母時域波形 59
4.2.1 較佳母時域波形所具有的特性 59
4.2.2 母時域波形的數學通式 68
4.2.3 較佳母時域波形的實例 75
第五章 結論 79
附錄1 80
附錄2 81
參考文獻 83

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