用於同調干擾環境之資料預處理適應性波束形成器

Abstract

傳統之波束形成器在干擾和目標訊號之間無相關性且能預先地獲得正確 之目標源指向向量的情況下，其方能有效地濾除強干擾。但是，當存在同 調干擾或指向向量誤差較大時，將導致目標訊號濾除現象，而使傳統波束 形成器之效能明顯衰降。為了解決目標訊號濾除現象，目前已有許多研究 紛紛提出各種補救之方法。在本論文中，吾人提出一類資料預處理適應性 波束形成架構，用以解決同調干擾問題，並增強對指向向量誤差之強韌性 。首先，吾人針對一具有相同子陣列之陣列幾何，利用振幅比較法中之 和/差技巧發展出一波束形成架構，並透過效能分析及電腦模擬顯示所提 之和/差波束形成器之效能。接著，吾人利用後級組合觀念，發展出一用 於矩形陣列之二階段二維波束形成器。此波束形成器首先結合二維空間平 滑技巧以破壞同調干擾之相關性，然後再使用一互補轉換以緩和因指向向 量誤差所造成之目標訊號濾除現象。根據空間平滑-互補轉換子陣列可建 構出一組最佳子陣列權重，使每一個干擾源方向可產生一零點，若將此權 重作用在任一相同之子陣列，就能產生一組``干擾濾除波束形成器元件'' 。最後，吾人根據最大化輸出訊號雜訊比和訊號雜訊雜訊比準則，將所有 干擾濾除元件利用第二階段組合還原為全口徑陣列之波束形成器。在一適 當假設下，吾人推導並分析以最大化訊號雜訊比準則建構出之波束形成器 之輸出訊號干擾雜訊比，並以數組數值模擬驗證所提二階段二維波束形成 器之效能。其次，對於任意陣列幾何結構下之同調干擾問題，吾人則提出 利用預先估測之訊號源方向建構出新穎波束形成器來解決之。首先，利用 一內差轉換技巧得到數個相同之子陣列，而得以採用空間平滑技巧以破壞 訊號間之相關性，再根據空間平滑子陣列求得最佳子波束形成器，並結合 維度還原轉換將其還原為全口徑陣列波束形成器。藉由電腦模擬可驗證所 提之內差波束形成器之效能。吾人又提出互補轉換最小變異波束形成器， 先利用預先估計之同調訊號源方向建構一轉換子將目標訊號濾除並保留干 擾訊號，再將僅含干擾和雜訊之轉換資料送至一正規之最小變異無損響應 波束形成器，以得到一組具有最大化輸出訊號干擾雜訊比之權重向量。所 提互補轉換最小變異波束形成器對方向估計誤差之效能，可由分析得到並 已由電腦模擬驗證其正確性。由所得到的結果可證明吾人所提之波束形成 器優於傳統多重限制最小變異波束形成器。此外，吾人還提出區域保存- 互補轉換最小變異波束形成器，以彌補由於較大方向估計誤差所造成互補 轉換最小變異波束形成器之效能衰降。使用區域保存-互補轉換之波束形 成器可降低對同調訊號源方向估計誤差之敏感度，並可免於發生目標訊號 濾除現象。在此以數值模擬驗證所提區域保存-互補轉換最小變異波束形 成器之效能。在本論文最後，吾人提出一波束形成架構以同時接收同調訊 號。此架構包含三步驟：先利用預先估計之同調訊號源方向求得其合成目 標指向向量，其次建構一轉換子以濾除同調訊號並保留無相關之干擾及雜 訊，最後再根據合成目標指向向量及僅含無相關干擾及雜訊之轉換資料， 建構出一最佳波束形成器。吾人以理論分析和數值模擬驗證所提之指向向 量回復波束形成器之效能，由其中可發現所提之架構能有效地組合同調訊 號，並可達到接近於最佳之理論輸出訊號干擾雜訊比。 Conventional adaptive beamformers are found to be effective in suppressingstrong interferers so long as an accurate steering vector associated withthe desired source is obtained {\it a priori} and the interferers areuncorrelated with the desired source. However, their performance degradessignificantly in the presence of coherent interferers and/or large steeringvector errors. In these cases, the beamformer breaks down as aresult of desired signal cancellation. The effects of desired signalcancellation has been widely investigated and various remedies have beenproposed. In this dissertation, we present a class of data preprocessedadaptive beamforming schemes for combating coherent interference. Methodsfor enhancing the robustness against steering vector errors will also bedeveloped as by-products.Firstly, for arrays consisting of multiple identical subarrays, we developa beamforming scheme based on the sum-and-difference technique employed inamplitude-comparison monopulse radars. Performance analysis and simulationresults demonstrate the efficacy of the sum-and-difference beamformer. As anextension, we exploit the post-combining concept to develop a two-stagetwo-dimensional (2-D) beamformer for rectangular arrays. The beamformerfirst incorporates 2-D spatial smoothing to decorrelate the possiblecorrelated interferers. A complemental transformation is then employed toalleviate desired signal cancellation due to steering vector errors. Thespatially smoothed-complementally transformed data correlation matrix is usedto compute the optimum weights which produce a null in each of theinterfering directions for the subarray beamformer. This set of weights canbe applied back to any of the identical subarrays, leading to a set of``interference cancellation beamformer elements''. Finally, a full aperturebeamformer is constructed via a secondary combining of the interference freeelements in accordance with the maximum output signal-to- noise ratio (MSNR)and maximum signal-plus-noise-to-noise ratio (MSNNR) criterion. As atheoretical evaluation, the performance of the proposed beamformer employingthe MSNR combiner is analyzed in terms of the output SINR under moderateassumptions. Several sets of numerical examples are provided demonstratingthe behavior of the beamformer with respect to relevant parameter settings.Subsequently, beamformers based on estimates of source directions-of-arrival(DOA's) are proposed for combating multiple coherent interferers with anarray of arbitrary geometry. Among them, an interpolation scheme is employedto synthesize multiple virtual subarrays allowing for the use of spatialsmoothing from a real array of arbitrary geometry. After interpolation, theoptimum spatially smoothed subarray beamformer can be constructed. Adimension recovery transformation then follows to restore the full arraybeamformer. The efficacy of the proposed interpolated beamformer is assessedwith computer simulations. Next, a complementally transformed minimumvariance (CTMV) beamformer is presented. The beamformer first constructs atransformation to remove the desired signal and retain the interference,using estimates of coherent source DOA's available. The transformed data,which contain only the interference and noise, are then sent to a regularminimum variance distortionless response (MVDR) beamformer to compute theweight vector yielding the maximum output signal-to-interference-plus-noiseratio (SINR). To verify the efficacy of the proposed CTMV beamformer, atheoretical analysis is given to describe its behavior in the presence of DOAestimation errors. Simulations then follow to confirm the analysis resultsand demonstrate the advantages of the CTMV beamformer over the conventionalmultiply constrained minimum variance (MCMV) beamformer. The CTMV beamformeris found to exhibit a certain degradation due to large DOA errors. As aalternative and remedy, the region preserved-complementally transformedminimum variance (RP-CTMV) beamformer is suggested. With the aid of regionpreserved-complemental transformation, the beamformer is insensitive tocoherent source DOA's, and thus immune to desired signal cancellation. Theefficacy of the RP- CTMV beamformer is examined with some numerical examples. Finally, a beamforming scheme is proposed for simultaneous reception ofmultiple coherent signals. The scheme consists of three stages. Firstly,estimates of coherent source DOA's are used to restore the correspondingcomposite steering vector (CSV). Secondly, a transformation matrix isconstructed for removing the coherent signal group, while retaining theuncorrelated interference and noise. Finally, optimum beamforming isperformed based on the CSV and transformed array data containing onlyuncorrelated interference and noise. By performance analysis and numericalexamples, it is demonstrated that the proposed steering vector restoral(SVR) beamformer effectively combines the coherent signals and achieves anSINR performance approaching the theoretical optimum results.