在本文中，我們將探討無線網路之正交分頻多工系統，透過最小平均平方誤差演算法與卡爾曼濾波器進行通道頻率響應的計算與估測。我們將分別介紹最小平均平方誤差與卡爾曼濾波器的演算法，並使用幾種通道模型來加以分析與模擬。我們將傳輸通道設定為頻率慢速衰減通道，這些通道雜訊為白色高斯模型以及通道衰減為雷利衰減模型。我們將最小平均平方誤差演算法與卡爾曼濾波器結合，以最小平均平方誤差演算法在時間與頻率之間估測與計算出初始之通道頻率響應值，再以卡爾曼濾波器預測、量測、與估算後續之通道頻率響應值，並模擬一個正交分頻多工傳輸系統。最後在通道估測中應用符號錯誤率與信號對雜訊比量測估測之效能。

In this report, the channel frequency response of the wireless Orthogonal Frequency-Division Multiplexing system has been estimated and modeled by utilizing the minimum mean-square-error (MSE) algorithm and kalman filtering algorithm. Two channel models have been developed for the system considered, namely, an additive white Gaussian noise only channel and a Rayleigh slow-fading channel with white Gaussian noise added channel. With the models developed several examples have been simulated to study the resulting system symbol error rates vs. signal to noise ratios and fading factors to study the effectiveness of the developed algorithm.

目錄
第一章：序論...................................................................................................1
1.1　研究動機與目的	....................................................................1
1.2　無線區域網路之發展................................................................3
1.3　OFDM系統	...........................................................................5
1.4　系統架構....................................................................................8
1.5　各章節提要................................................................................9
第二章：無線區域網路之規格.....................................................................10
2.1  頻帶分配特性..........................................................................10
2.2  框架格式..................................................................................13
2.3  802.11a時間參數....................................................................15
2.4  802.11a傳輸速率參數............................................................16
2.5  802.11a調變格式....................................................................18
第三章：MMSE演算法技術……..……......................................................22
3.1　OFDM系統接收端................................................................22
3.2　二維通道估計法.....................................................................23
3.3　MMSE演算法........................................................................25
3.4　MMSE演算法例子................................................................28
第四章:卡爾曼濾波器....................................................................................33
4.1　卡爾曼濾波器簡介.................................................................33
4.2  卡爾曼濾波器演算法.............................................................34
4.3  卡爾曼濾波器運算之數學推導.............................................38
第五章　通道估計.........................................................................................42
5.1  系統架構.................................................................................42
5.2　運用MMSE演算法與卡爾曼濾波器... ............. .................43
5.3  雷利(Rayleigh)模型...............................................................46
5.4  模擬結果.................................................................................48
第六章 結論與未來展望...............................................................................58
Appendix A  Least-square Algorithm………………...………………….59
Appendix B  Linear Minimum-Mean-square Error Algorithm……......60
參考目錄.........................................................................................................63
表目錄
表格 1.1 無線區域網路標準...............................................................4
表格 2.1 802.11a 時間參數表............................................................15
表格 2.2 802.11a 傳輸速率參數表....................................................16
表格 2.3 RATE field 的定義內容......................................................17
表格 2.4 MOD K 在各調變格式的參數...................................................18
表格 2.5 BPSK 編碼表......................................................................19
表格 2.6 QPSK 編碼表......................................................................19
表格 2.7 16-QAM 編碼表.................................................................20
表格 2.8 64-QAM 編碼表.................................................................21
表格 3.1 參考通道值...........................................................................28
表格 3.2 pp R 值.....................................................................................29
表格 3.3 p h R ˆ 值....................................................................................30
表格 3.4 1
ˆ ) 1 ( − + I
SNR
R R pp p h 值.............................................................31
表格 3.5 估計通道值...........................................................................32
圖目錄
圖表 1.1 FDM 與OFDM 表示圖.........................................................6
圖表 1.2 整數週期弦波.........................................................................7
圖表 1.3 正交分頻多工系統之通訊示意圖.........................................8
圖表 2.1 802.11a 和HiperLAN 頻帶分配圖.....................................11
圖表 2.2 IEEE 802.11a 頻道分配圖...................................................12
圖表 2.3 IEEE 802.11a 之OFDM 訓練序列及框架結構.................14
圖表 2.4 Signal field 的位元分配圖...................................................14
圖表 2.5 BPSK 星座圖........................................................................19
圖表 2.6 QPSK 星座圖........................................................................19
圖表 2.7 16-QAM 星座圖....................................................................20
圖表 2.8 64-QAM 星座圖....................................................................21
圖表 3.1 OFDM 接收端模型..............................................................22
圖表 3.2 導引信號位置圖...................................................................23
圖表 3.2 實際通道值與估計值差異圖...............................................32
圖表 4.1 卡爾曼濾波器系統狀態與量測流程圖...............................34
圖表 4.2 卡爾曼濾波器整體流程圖...................................................36
圖表 4.3 卡爾曼濾波器之下一步預估狀態線性系統流程圖...........39
圖表 5.1 正交分頻多工系統之通訊示意圖.......................................42
圖表 5.2 通訊系統加入雷利(Rayleigh)模型通道示意圖.................47
圖表 5.3 雷利(Rayleigh)模型組成示意圖 .......................................47
圖表 5.4 BPSK 使用卡爾曼濾波器進行最佳通道估計與收斂圖....50
圖表 5.5 QPSK 使用卡爾曼濾波器進行最佳通道估計與收斂圖....51
圖表 5.6 16QAM 使用卡爾曼濾波器進行最佳通道估計與收斂圖52
圖表 5.7 64QAM 使用卡爾曼濾波器進行最佳通道估計與收斂圖.53
圖表 5.8 OFDM 中16-QAM 調變模擬與估計錯誤率比較圖.........54
圖表 5.9 OFDM 中64-QAM 調變模擬與估計錯誤率比較圖.........55
圖表 5.10 在Rayleigh 通道中理論與模擬以及估計錯誤率比較圖.56
圖表 5.11 在Rayleigh 通道中模擬資料多寡之錯誤率範圍.... .. .....57

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