為了讓無線通訊系統更能應用於實際生活，低複雜度高效能的系統是極需被開發。從之前的文獻研究得知最佳化與低複雜度難以共存，兩者只能擇其一。很幸運地，分解圖(Factor Graph)的方法看起來是有希望的。經由有效地交換含有統計特性的資訊在分解圖中，最佳化與低複雜度是可以共存的。本論文闡述如何使用分解圖的方法來解決三個無線通訊系統的問題：1)以接收信號強度為基礎的室內位置估測；2) 以信號傳遞時間為基礎的室外位置估測；3)一個無線通訊系統盲通道估測與資料偵測。
傳統以接收信號強度為基礎的室內位置估測不是因為模型不吻合而導致不準確，就是沒有考慮測量誤差的統計特性，要不然就是太複雜而無法應用。為了簡化演算法，局部線性化的技術被發展出來，它是建立在功率衰減輪廓圖(Power Decay Profile)曲面上的局部線性，而這個功率衰減輪廓圖是由訓練的指數接收信號強度測量資料所組成的，並且是從個別的無線發射台(Access Point)所蒐集到的；為了確保較好的準確性，測量誤差的統計特性與測量資料的可靠度被引用於分解圖中。實驗數據顯示：所提出演算法不僅具低複雜度，而且可達到近似的最大可能性(Maximum Likelihood)解答，而這個最大可能性解答是建構在訓練的接收信號強度測量資料之基礎上。
大部份現存以信號傳遞時間為基礎的室外位置估測演算法忽略了測量資料的可靠度，因此估測準確性受到限制。為了改善無線用戶在直視(Line-of-sight)與非直視(Nonline-of-sight)環境下的估測準確性，測量資料的可靠度觀念被引用。為了更進一步改善這個準確性，各種複雜的追蹤技術被提出。這裡為了降低追蹤技術之計算複雜度，便利用分散式的處理來實現卡門濾波器(KalmanFilter)。實驗數據顯示：結合測量資料的可靠度與分散式的處理，這演算法不僅可達到高的準確性，而且具低複雜度。
因為分解圖的方法已經被證明成功的解決複雜位置估測的問題，所以這有效的方法也可以被應用在無線通訊系統盲通道估測與資料偵測上。在盲的接收器中，簡單的差分資料偵測機制被選用。為了避免系統效率降低，複雜的通道估測技術被應用來追蹤通道的變化。所以，用分解圖為基礎的盲通道估測與資料偵測的演算法便發展出來。而電腦模擬顯示：針對快速時變的無線通道，所提出的演算法是強健的。

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