在不匹配情境下的可適性陣列波束成型技術

Abstract

可適性陣列波束成型能自動截取信號同時抑止干擾與雜訊，在諸多應用領域中早已深受重視。就傳統可適性波束成型技術而言，事先所必備的資訊非信號的波形即信號的指引向量。近二十幾年來，已有諸多文獻在探討利用信號循環平穩特性的可適性陣列波束成型技術。相比之下，循環可適性波束成型技術不需要信號的波形或指引向量等資訊故可用來實現盲可適性波束成型。本論文主要的目的在於發展多種有效且強健的循環可適性波束成型技術。在傳統可適性波束成型方面，吾人也提出兩種新穎強健的技術。 在本論文中，吾人探討存在有限取樣點效應之循環可適性波束成型。為了對抗有限取樣點效應，吾人首先提出一種估測誤差的模型來表示由有限取樣點效應所造成的擾動，此擾動為理想循環自相關向量與樣本循環自相關向量之間的誤差。接著，吾人提出子空間投影和基於對角線負載等方法來消除此擾動。此外，吾人也提出一種新的方案將上述方法延伸至多信號的環境。為了達到更快的收斂速度，吾人根據Capon的方法提出另一種新的循環波束成型技術，其中吾人利用一個和信號循環平穩特性相關的約束以及接收信號的自相關矩陣之信號子空間來計算權重向量。 由於實現循環可適性波束成型事先所必備的資訊只有信號的週期頻率，吾人分析週期頻率誤差對效能所產生之影響。針對週期頻率誤差，吾人提出一種補償的方法，用一個補償矩陣重建循環相關矩陣以對抗其最大奇異值之退化。在多信號的環境中，吾人提出一種高效強健的方法用以同時估測所有信號的週期頻率，也對該方法之收斂特性進行分析。另一方面，吾人建立了循環自相關向量在隨機週期頻率誤差下的統計模型。隨即發展一套強健的作法來解決隨機週期頻率誤差的問題並且進一步推導出解析公式來評估此作法之效能。 對傳統指引式波束成型器而言，其可適性權重是經由最小化波束成型器的輸出在受到陣列在信號方向的響應不變的限制條件下獲得。故此波束成型器對指引向量的精確度十非敏感。為了解決指引向量不匹配的難題，吾人提出兩種變形的對角線負載的作法，對接收信號的自相關矩陣之最不顯著的特徵值提供較大的負載因子而最顯著的特徵值則提供較小的負載因子。較之傳統對角線負載的作法，吾人所提之作法具有顯著的優點以及強健性來對抗指引向量不匹配的難題。

Adaptive array beamforming, which can automatically extract signal of interest (SOI) while suppressing signal not of interest (SNOI) and noise, has received much attention in several application areas. For conventional adaptive array beamforming, the a priori information required for adapting the weights is either the waveform or the direction of the SOI. Over the past two decades, adaptive array beamforming utilizing signal cyclostationarity has been widely presented in the literature. In contrast, the cyclostationarity-exploiting (cyclic) adaptive beamforming techniques do not require any priori information about the waveform or the direction according to the SOI and thus achieve blind adaptive beamforming. The purpose of this dissertation is mainly to develop several efficient and robust techniques for cyclic adaptive beamforming. We also present two novel robust techniques for conventional adaptive beamforming. In this dissertation, we consider the cyclic adaptive beamforming in the presence of error due to the effect of using finite data samples. To cope with the finite sample effect, we first present an estimation error model to represent the perturbation due to finite sample effect on the sample cyclic correlation vector. The sample cyclic correlation vector plays a key role required for adapting the weights of the least-squares spectral self-coherence restoral (LS-SCORE) algorithm. Then, two efficient methods, namely the subspace projection and loading-based methods, are proposed to eliminate the perturbation. Moreover, a novel scheme to extend the aforementioned methods to deal with the situation of multiple SOIs is also presented. To achieve faster convergence rate, we present a new cyclic beamforming method based on the well-known Capon method. In the proposed method, the adaptive weights are obtained by using a constraint related to the signal cyclostationarity and the signal subspace of the received data correlation matrix. Since the a priori information required by performing cyclic adaptive beamforming is only the cycle frequency of the SOI, we analyze the performance degradation of the cyclic adaptive beamforming in the presence of cycle frequency error (CFE). We present a compensation method to reconstruct the cyclic correlation matrix by using a compensation matrix to cope with the deterioration of its dominant singular value when CFE exists. To further deal with the situation of multiple SOIs with CFE, an efficient robust method is proposed to simultaneously estimate the actual cycle frequencies of the SOIs and its convergence property is also evaluated. On the other hand, we also establish the statistical model of the cyclic correlation vector under random CFE (RCFE). A robust method is developed to tackle the problem due to RCFE and analytical formulas for evaluating the performance of this robust method are further derived. For a steered-beam adaptive beamformer, the adaptive weights are calculated by minimizing the beamformer's output power subject to the constraint that forces the array to make a constant response in the direction of the SOI. Hence, the performance of the beamformer is very sensitive to the accuracy of the steering vector of the SOI. To alleviate the difficulty due to steering vector mismatch, we present two variations of the diagonal loading (DL) approaches. The proposed approaches provide large loading factors for the least significant eigenvalues of the received data correlation matrix and small ones for the most significant eigenvalues. This is a significant advantage over the conventional DL methods and achieves significant robustness against the above mentioned difficulty.