可適性天線陣列波束成型於非完美環境下之效能特徵

Abstract

在過去數十年中，可適性陣列波束成型技術由於其卓越的干擾消除能力已被廣泛地應用及討論。當接收信號的自相關矩陣及所欲信號的指引向量已知時，波束成型器可根據最小變異無失真響應(minimum variance distortionless response, MVDR)準則，以使陣列輸出之信噪比最大化。然而在實際應用上，這兩項資訊通常無法精確得知並且需估計而求得，當接收信號之自相關矩陣是以有限資料點估計求得時，陣列的效能可能會因此衰減，這種現象我們稱之為有限資料點效應。 在本論文中，我們假設所欲信號的指引向量已知，並探討有限資料點效應對可適性陣列天線效能的影響。首先，我們分析傳統上常用之最小變異無失真響應與廣義旁瓣消除式(generalized sidelobe canceller)波束成型器的效能，由此分析可看出有限資料點效應對傳統波束成型器之影響。接著，我們分析一些現有改進傳統陣列效能之方法 – 信號消除法(signal blocking)與對角線負載(diagonal loading)，並探討為何這兩種方法可減緩傳統波束成型器之有限資料點效應。此外，我們也討論數種基於特徵空間之減秩技術(eigenspace-based reduced-rank techniques)應用於可適性波束成型下的效能並且比較它們的優缺點。最後，我們討論兩種寬頻波束成型器 – 時域型波束成型器與頻域型波束成型器於有效資料點效應下之能力，並提出有效的方法改善時域型波束成型器之效能。

Adaptive array beamforming has been utilized in a variety of fields in the past decades due to its superior anti-interference ability and high resolution. When the correlation matrix of the received data vector and the steering vector of the desired signal are known exactly, the beamforming weight vector can be obtained by the minimum variance distortionless response (MVDR) solution yielding the maximum output signal to interference-plus-noise ratio (SINR). However, these two quantities are usually unknown and have to be estimated in practical situation. The performance degradation due to the estimation of the correlation matrix of the received data vector is commonly referred to as the finite sample effect in adaptive beamforming. In this dissertation, we assume the steering vector of the desired signal is known precisely and discuss the finite sample effect on different beamforming techniques. First, the output SINR of the MVDR beamformer under finite sample effect is derived. The equivalence of the generalized sidelobe canceller (GSC) and the MVDR beamformer under finite samples is also proved. In this work, we formulate the problem of the MVDR beamformer with deficient sample size theoretically. Next, the performances of MVDR beamformers with signal blocking and diagonal loading are analyzed. The effects of using signal blocking and diagonal loading techniques on the MVDR beamformer are discussed in detail. Several eigenspace-based reduced-rank techniques including the principal component inverse (PCI), cross-spectral metric (CSM), and modified cross-spectral metric (MCSM) considering finite sample effect are compared. The reasons why the PCI and CSM methods deteriorate in performance and how the MCSM alleviates the finite sample effect are investigated. Finally, the performances of the broadband tapped delay-line (TDL) and discrete Fourier transform (DFT) beamformers with and without finite sample effect are evaluated and compared. The capabilities of the broadband beamformers to address the broadband signals are examined through this work.