智慧型天線技術在第四代無線通訊的底層物理層中有著一個非常重要的優勢。但是為了量測智慧型天線的效能，通常得透過實際的場測來得到天線效能的資訊，所以我們提出一個數學分析的方法，用以快速且準確地分析。儘管許多文獻都有討論分析方法，但是應用的環境是有限的。
而我們的方法在參考了WINNER模擬參數後， 可以適用至少四種的環境中。我們也針對了均勻線性陣列(Uniform Linear Array; ULA)和均勻圓形陣列(Uniform Circular Array; UCA)做了分析，結果顯示數值方法和蒙特卡羅模擬非常吻合。而在最後我們也利用此分析方法提出了設計建議。因此如果在未來使用此數學分析方法，除了能夠加速智慧型天線的開發週期外，也提供了新的研究分析方式。

Smart antenna technology is advantages for physical layer in 4th generation wireless communications.
In order to measure the performance of the smart antennas, we usually get through actual field trials. Here,we propose a mathematical analysis method. There are many related literatures, but the application
environments are limited. However, our proposed method can be applied at least four environments. In the simulation results, it showed that the numerical analysis are matching to the Monte Carlo simulation on both
uniform linear array (ULA) and uniform circular array (UCA) cases. We also propose the design suggestion based on the mathematical analysis method. Therefore, this proposed mathematical analysis method could be helpful for shorten development period and research for smart antenna systems.