在無線通訊系統下，分集結合技術對於降低多路徑衰落的效應而言是不可或缺的，並且分集技術被期望為可以增加系統的效能。然而在相關性通道分支的情況下，分集技術的作用力會被降低。在空間分集技術的應用上，若天線沒有被間隔至少同調頻寬以上，通道之間產生相關性的現象是時常發生的。對於無線通訊系統效能的估測而言，二階統計特性是一個重要的指標。我們所提出的方法是利用Karhunen-Loeve 展開式，將原本具有相關性的隨機變數轉換為獨立的隨機變數，則這些獨立的隨機變數可以接著以分集結合技術處理，並期望觀察通道之統計特性。 For wireless communication systems, diversity combining techniques are indispensable for reducing the multipath fading effects, and it is expected to enhance the system performance. However, diversity techniques are diminished over correlated channel branches, which are commonly occurred in space diversity if the antennas are not separated at least coherence bandwidth. Second-order statistics are crucial performance criterion to evaluate the diversity effects of fading channels, whereas the performance in a correlated diversity system must be worse than that on independent multipath fading channels. A method which is to transform the correlated diversity branches into uncorrelated ones by the Karhunen-Loeve expansion, and then the transformed independent random variables are fed into the diversity combiner, and is expected to study the statistics of the fading channels.
