- 學位論文
於空時系統中具有非均勻線性陣列之MVDR波束構成
MVDR Beamforming with Nonuniform Linear Array for Time-Space Systems
摘要
本篇論文探討一個於空時系統中具有非均勻線性陣列之基於最小變異無失真響應(minimum variance distortionless response, MVDR)之到達方向(direction of arrival, DOA)和波束構成(beamforming)技術。在適應性陣列系統中天線陣列一般均假設是均勻線性陣列(uniform linear array, ULA)，但由於應用環境之需要，採用非均勻的線性陣列(nonuniform linear array, NULA)仍有其必要性。首先，在傳統的DOA估測器中，基於MVDR的 DOA估測器可以提供優良的DOA估測能力，但是因為要頻譜掃描，故執行MVDR估測器所需之計算複雜度較高，為了降低搜尋之計算複雜度，對均勻線性陣列可採用多項式求根(polynomial rooting)的方法，但是由於非均勻陣列之方向向量元素間並不具有Vandermonde之結構，故無法直接使用此求根方法。接著，對於波束構成當所欲訊號發生DOA估測誤差時，MVDR波束構成器會將所欲訊號視為干擾而抑制(null)掉，因而造成性能驟降，為了發揮MVDR波束構成的優點，正確估測訊號之DOA是必要的，於是為了在低計算複雜度下擁有高解析之DOA估測，本論文先對基於MVDR的 DOA估測器實施粗估，再經由泰勒級數展開(Taylor series expansion)法實施細估，最後使用快速迭代(fast iteratively)的方法對殘餘的角度誤差做微調，也就是說藉由入射角度的粗估到細估到微調，以提高到訊號入射角度估測的精確度。因此，訊號入射角度可以獲得正確的估測，保證當使用MVDR波束構成器時，即使是在有許多干擾源的情況下所欲訊號也不會被視為是干擾而被抑制。最後，本篇論文也提出了許多模擬的結果用以印證所提出方法的有效性。
並列摘要
This thesis deals with directional of arrival (DOA) and beamforming technique based on minimum variance distortionless response (MVDR) for nonuniform linear array (NULA) for time-space systems. Most of research topics, the array configuration always be assumed as uniform linear array (ULA) for adaptive antenna array. Due to the application requirement, the use of NULA is still necessary. Although this traditional searching-based MVDR estimator can offer more accuracy DOA estimation under the NULA scenario, it is computationally quite expensive. Moreover, the complexity and the estimation accuracy strictly depend on the grid size that is used during the search. It is well known that the conventional polynomial rooting method can be used to replace the conventional spectrum searching method to reduce the computational load for ULA. Under the NULA, the steering vectors of the signal sources do not have the Vandermonde structure. Therefore, the polynomial rooting method can be used directly. The MVDR beamformer has better resolution and much better interference rejection capability than the conventional beamformer. But it is well known that this method may suffer from significant performance degradation when there is even a small DOA estimate error of antenna array. However, more accuracy DOA estimate is necessary for MVDR beamforming. To cure this problem, a DOA estimate approach with high resolution and low computational load is presented in this thesis. A coarse DOA estimate is first determined from a MVDR estimator. Next, the preliminary DOA estimate is then sent to the Taylor series expansion based estimator to form fine-estimation. The last step is to fine-tune the residual angle error by using the fast iterative estimate method, which can provide more accuracy estimate value for MVDR beamformer to protect desired signal while to obtain better interference rejection capability. Finally, several simulation results are provided for illustrating the effectiveness of the proposed approach.