祁和陳提出一個具有高運算效率的快速峰度最大化演算法(Fast Kurtosis Maximization Algorithm, FKMA)，並將其應用於盲蔽波束成型(Blind Beamforming)、盲蔽最大比值合併(Blind Maximum Ratio Combining)及盲蔽訊號分離(Blind Source Separation)或獨立成份分析(Independent Component Analysis)。而該演算法必須假設單一訊號源本身為非高斯獨立相同分佈程序(Non-Gaussian Independent Identically Distributed Process)且不同的訊號源之間在統計上是互相獨立的。

針對正交分頻多工(Orthogonal Frequency Division Multiplexing, OFDM)結合陣列天線(Antenna Arrays)之上傳模式系統的前置快速傅立葉轉換(Pre-FFT)和後置快速傅立葉轉換(Post-FFT)波束成型接收器(Beamforming Receivers)，我們各自建立一個離散時間多重輸入多重輸出(Multi-input Multi-output)訊號模型。對於前者而言，因爲原始訊號源在傳送端經過反快速傅立葉轉換的處理，使得接收到之時域(Time-domain)訊號源在統計上趨近高斯分佈，進而導致快速峰度最大化演算法的效能嚴重地衰減。而對於後者而言，因為在接收端的每一根天線上會先經過快速傅立葉轉換的處理，因此，等效頻域(Frequency-domain)訊號源為非高斯獨立非相同分佈程序，且在多路徑傳輸的環境下，不同的訊號源之間在統計上並非互相獨立。

一般而言，在演算法(例如：快速峰度最大化演算法)的分析上，我們利用統計平均(Ensemble Average)去估測訊號的統計量。然而，在後置快速傅立葉轉換波束成型接收器中，我們發現在時間平均(Time Average)的計算下，所有的等效頻域訊號源彼此都是互相正交的。因此，在多路徑傳輸的環境下，我們以時間平均分析快速峰度最大化演算法並將其應用於後置快速傅立葉轉換波束成型接收器中，此外，我們也進一步地提出一個盲蔽波束成型演算法(Blind Beamforming Algorithm, BBA)。最後，我們呈現一些模擬結果以驗證所提出之盲蔽波束成型演算法的效能。

Chi and Chen proposed a fast kurtosis maximization algorithm (FKMA) with computationally efficient for blind beamforming, blind maximum ratio combining, and blind source separation or independent component analysis. The FKMA assumes that each source signal is non-Gaussian independent identically distributed process and statistically independent with each other.

In uplink orthogonal frequency division multiplexing (OFDM) systems with antenna arrays, we establish a discrete-time multi-input multi-output signal model for pre-FFT and post-FFT beamforming receiver, respectively. For the former, due to the IFFT process at the transmitter, the received time-domain source signals are approximate Gaussian distributed statistically such that the performance of the FKMA degrades seriously. For the latter, due to the FFT process at each antenna of the receiver, the equivalent frequency-domain source signals are non-Gaussian independent non-identically distributed and mutually dependent statistically in multipath.

In general, we utilize ensemble average to estimate the source statistic for analyses of an algorithm such as FKMA. However, in the post-FFT beamforming receiver, we observe that the equivalent frequency-domain source signals are mutually orthogonal using the calculation of time average. Therefore, we analyse the FKMA by time average and apply the FKMA to the post-FFT beamforming receiver in multipath; and further, we propose a blind beamforming algorithm (BBA). Finally, some simulation results are presented to support the efficacy of the proposed BBA.

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