正交分頻多工系統是最近興起的高傳輸效率的無線網路技術，因其抵抗多徑衰落仿真的特性以及互相正交的高傳輸效率特性使其成為熱門的無線通訊技術。此外，在硬體的實現上可以經由快速傅利葉轉換跟反快速傅利葉轉換來實現，而可以载在方波上傳輸，也為其一大利多。在WiMAX ( 802. 16)和 寬頻區域網路 802.11(a, b, g)這兩項熱門的無線網路應用中，也都採用正交分頻多工系統。
然而，在正交分頻多工系統的傳送器和接收器的頻率不一時，會產生頻率偏移，此頻率偏移會導致嚴重的信號間互相干擾，使得正交的特性消失，接收端的錯誤率提升。因此，頻率偏移的估測與干擾消除一直以來都是正交分頻多工系統中的重要課題。傳統的方法有：在時域利用循環字首估測、在頻率域利用導航信號估測、以及利用訓練信號估測等等。
在此論文中，我們提出一種低複雜度的干擾消除矩陣，此矩陣的每一行都是循環的，因此在硬體的實現上是低複雜度的。在裡面的討論中我們可以發現，此方法可以達到跟干擾完全消除時相同的錯誤率，提供系統更好的傳輸品質。此外，在硬體的實現上，此方法可以隨著系統的要求事先建立好一些固定值的陣列，在錯誤率和硬體實現的複雜度之間有交換的自由度。另外，除了用導航信號輔助的頻率偏移估測值做為一開始的參考值之外，我們也可以用任意猜測的頻率偏移估測值來當為初始的參考值，且都會收斂到一個更為正確的估測值而不會發散。因此，在此篇論文中我們同時提出一種可以消除干擾也估測出頻率偏移值的方法。這也論證了在頻率域估測頻率偏移值時，信號間的干擾會使得估測不準，而我們的中心思想就是同時從干擾消除與頻率偏移估測著手，而在頻率偏移估測的準確度或者是錯誤率的表現上都達到很好的效果。

OFDM is a promising technique in the Universities and research laboratories all over the world. OFDM has been accepted for the Wireless Local Area Network (WLAN) from IEEE 802.11, the Digital Audio Broadcasting (DAB), etc. OFDM can resist multi-path by the cyclic prefix. However, when there is frequency mismatch between the oscillators of the transceivers, the orthogonality corrupts. With the corruption of orthogonality, the Inter Carrier Interference occurs, which increases the BER. Thus, Carrier Frequency Offset is a practical problem for OFDM.
There have been many methods proposed to combat the CFO. For example, the cyclic prefix based method in time domain, the pilot based method in frequency domain, and the training symbol based method for initial tracking, etc.
In this paper, we propose a pilot based method which is based on PTAW. The most difficult part of CFO estimation in frequency domain is the existence of ICI. Thus, by observing the regularity of each OFDM symbol block, we can find a circulant matrix with low complexity to cancel the ICI. After canceling the ICI, we will have a more accurate estimate than PTAW.

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