An Adaptive Beamforming Algorithm Based On The Unitary ESPRIT DOA Estimation

InstructionIn the area of array signal processing, the meaning of beamforming isreforming the source signal through the obtained array information. In anotherwords, it means to satisfy the target function through adjusting weights of theantenna. Generally speaking, traditional beamforming needs direction informationand blind beamforming reforms the source signal without any directioninformation.Compared with the traditional beamforming, the blind beamforming has largererror, slower convergence speed and more complexity. Although DOA (Directionof arrival) based adaptive beamforming algorithm is easy to analyze, but it has aheavy computation burden as it is consisted of DOA estimation and beamforming.How to improve the algorithm performance while reduce the complexity andaccelerate the convergence is a meaningful task.After the above consideration and analysis, this paper provides an adaptivebeamforming algorithm based on the Unitary ESPRIT DOA estimation. TheUnitary ESPRIT algorithm could increase the effective data twice times, improvethe performance of the algorithm and at the same time reduce the computationburden through effective measures. As the Unitary ESPRIT algorithm is sensitiveto the changes of the SNR level, a modified algorithm to overcome this problem isproposed. In the beamforming section, GSC (Generalized Sidelobe Canceller)based beamformer is used. By change constrained optimization problem tounconstrained one, at the mean time, using the modified adaptive LMS algorithm,fast convergence can obtained.1. The modified beam-space based Unitary ESPRIT algorithmThe Unitary ESPRIT algorithm is used for the complex data. As the complexdata is different from its conjugate one which also contains useful information, wecould use both of them to estimate the information of the source signals. Thismethod improves the estimation performance under uncorrelated and correlatedinterference. Through construction of Centrohermitian and skew-centrohermitianmatrices, the SVD (Single-Value Decomposition) of complex matrix is transformedinto the SVD of real matrix and reduce the computation burden.The next step is the beam-space based pretreatment which combines severalsensors into one or more beam called beam-space transform. The Unitary ESPRITalgorithm is sensitive to the change of SNR (Signal Noise Radio) level, so DCT(Discrete Cosine Transform) to remove the data with little energy for thecancellation of noise is used, and the beam-space transform to lessen the rank ofthe correlated matrix is introduced to reduce the computation complexity and lowerthe SNR gate.2. The improved GSC based adaptive beamforming algorithmAccording to weights chosen criterion, beamformer can be classified into dataindependent beamformer and statistic optimum beamformer. The data independentbeamformer chooses appropriate weights to approach the desired response. Thisresponse is independent to the array data and the statistic data. The statisticoptimum beamformer chooses weights according to the data statistic properties. Ingenerally, the purpose of statistic optimum beamformer is to optimize the outputsignals to contain least interference and noise.GSC is another expression of LCMV (Linearly Constrained MinimumVariance) beamformers, it changes the constrained optimum problems intounconstrained ones. The LMS (Least Mean Square) algorithm is used in theprocess of weights updating. The feedback error signals contain desired signals, sothe MMSE (Minimum Mean Square Error) is large. As the excess MSE (MeanSquare Error) is proportional to the resultant MMSE and the step size used, theconvergence of the conventional LMS based GSC is slow. a new decision feedback(DF) technique to overcome this problem is proposed by using large step size toimprove the convergence performance.3. Simulation and conclusionMany MATLAB simulations prove that in the DOA estimation section, underboth white noise and colored noise background, the proposed algorithm attainslower SNR gate, less computation burden with good performance than those of theUnitary-ESPRIT algorithm. And in the beamforming section, the proposedfeedback (DF) filter can also reduce the excess MSE, increase convergence speedand improve the performance of the conventional GSC.