在交互耦合情況下天線陣列波束成型之有效方法及其效能分析

Abstract

天線陣列信號處理之演算法分成「方位估測」及「波束成型」兩大領域，多種經典演算法早在數十年前即被提出，然而這些演算法在實際應用時卻遭遇許多非理想效應，導致輸出效能無法達到理想的水準。近來學者專家不斷研究更加強健的演算法，試圖改進這些非理想效應造成的效能惡化，許多解決方案已被提出。 近年來，天線間的交互耦合效應已逐漸受到重視，本篇論文即是針對波束成型技術在交互耦合效應下作討論。首先我們的實驗發現在交互耦合的情況下，特徵空間波束成型器（Eigenspace-based Method, ESB）較線性限制最小輸出功率波束成型器（Linear Constrained Minimum Variance Beamformer, LCMV）具有較好之效能，接者我們嘗試對這兩種波束成型器作效能分析。在分析交互耦合效應之前，我們參考[1]中分析有限取樣點之方法，並用類似之方法分析交互耦合之效應。首先推導LCMV與ESB的所欲信號、干擾信號及雜訊輸出功率，取比例後即求得兩者的輸出信號對干擾加雜訊之功率比（signal-to-interference-plus-noise ratio, SINR）。 效能分析的結果發現當這兩種演算法的輸出SINR分子正規化到相同的數值時，LCMV的輸出SINR在分母的部分比ESB多了一個非負項，因此證實了在無限取樣點下ESB法確實較LCMV法更能抵抗交互耦合效應。理論分析的結果與實驗模擬的結果在取樣點數足夠多的情況下相當吻合，說明了推導過程的正確性。 此外，我們所提供的理論分析結果可適用於任何接收信號可表達成（2.39）式之非理想效應以及任何幾何形狀之天線陣列。

Two major topics in the antenna array signal processing are bearing estimation and adaptive beamforming. Many classical algorithms have been proposed in the past decades. Because the algorithms suffer from degradation in practical applications, they cannot achieve satisfactory performance. Many scholars and experts keep looking for algorithms with robustness and the abilities to mitigate the effects in practical environments. A lot of efficient solutions have been proposed to combat the nonideal effects. Recently, the mutual coupling effects between antenna array sensors have been considered seriously. The goal of the thesis is to consider the mutual coupling effects on the adaptive beamforming. First, we found that the performance of ESB （Eigenspace-based） beamformer is superior to LCMV （Linear Constrained Minimum Variance） beamformer under mutual coupling effects. Then, we tried to analyze the performance of the two beamformers. We first referred to the steps analyzing the finite sample effects provided in [1] and then used the similar steps to analyze the mutual coupling effects. We computed the output SINR（Signal-to-Interference-plus-Noise Ratio） of the two beamformers and found that the denominator of the output SINR of LCMV beamformer is larger than that of ESB beamformer with a nonnegative term while the numerators are the same. For this reason, we confirm the ESB beamformer is more robust than the LCMV beamformer under mutual coupling environment. The theoretical results match the simulation results when the numbers of snapshot are sufficient. It also shows the validity of the theoretical results. Besides, the results are suitable for any nonideal effect under the similar received signal model and arbitrary array geometry.