利用二階統計特性作分數取樣頻道估測及等化之研究

Abstract

使用傳統高階統計方法做頻道估測及等化會造成收斂速度十分緩慢。而近年來所提出的二階方法像是外積分解法(OPDA)和多步預測法(MSPA)則被認為是非常吸引人的解決之道。然而從此篇論文的討論中可以發現，當副頻道間的零點聚集時，外積分解法和多步預測法都對有限估測所產生之誤差相當敏感。我們發現當頻道有聚集零點時，使用外積分解法和多步預測法均可能造成頻道估測及等化的失敗，尤其是當聚集零點不在單位圓內時。我們針對零點的聚集行為分析，發現聚集零點的大小距離及數量的改變，均會對頻道估測及等化造成不同程度的影響。因此我們針對了原有的演算法提出了截斷修正方法來改善當頻道有聚集零點時所產生的問題。我們也使用了實際的微波頻道來比較各種方法的表現。由電腦模擬中我們可以發現，當頻道有聚集零點時，截斷修正方法對於原來的演算法而言有極大的改進。而其結果也較傳統的高階方法為佳。

The channel identification and equalization has a slow convergence rate when the high-order statistics methods are used. The second-order statistics methods, such as OPDA and MSPA proposed recently, however, are considered to be an attractive solution. From the discussion in this thesis, we can find that OPDA and MSPA are sensitive to the estimation error due to limited observed data when the subchannels have clustered zeros. We also discover that the channel identification and equalization using OPDA and MSPA may fail when the channel has clustered zeros. Then we analyze the effects of the clustered zeros and we find that the effects of the clustered zeros are dependent on their magnitudes, distances, and numbers. Thus we proposed the truncated OPDA and MSPA to solve the problems caused by the clustered zeros. We also use realistic microwave channels to compare the performance of the algorithms. From the computer simulation, we can see that the truncated OPDA has a great improvement compared to the original algorithm when the channel has clustered zeros. And it has better performance than the high-order CMA method.