Research On Robust Adaptive Beamforming Algorithms

Adaptive beamforming can be used for the rapidly changing signal environments to adaptively suppress interference.Since it can greatly improve the anti-jamming performance of the electronic systems,adaptive beamforming has been widely applied in radar,communications,sonar,and other areas.There is difficulty to be solved when adaptive beamforming is applied in practical engineering applications.Adaptive beamforming is extremely sensitive to covariance matrix uncertainty and steering vector mismatch,especially when the array received signal data contains the desired signal component.This can lead to a dramatic decline in the performance of adaptive beamforming algorithm.It is an urgent problem that how to improve the robustness of adaptive beamforming against array mismatch to ensure good performance,which is needed to be solved by the current array signal processing in practical engineering applications.Although robust adaptive beamforming(RAB)algorithms have enjoyed great development during the last four decades,the performance of many RAB algorithms is still far away from the optimal performance due to their own inherent drawbacks.Based on the array mismatch problem in current engineering applications,this thesis will continue to study the robust algorithms of adaptive beamforming.The research contents and contributions mainly include the following four aspects:1.The research on robust beamforming algorithms applicable to the situation of limited snapshots.In order to effectively deal with the situation of limited snapshots,a probability-constrained diagonal loading robust adaptive beamforming algorithm based on covariance matrix uncertainty(CMU)is firstly proposed in the third chapter of this thesis.This algorithm makes full use of the randomness of CMU and studies the probability distribution of its squared Frobenius norm.Then a probability constraint is applied for CMU with a preselected probability to obtain a better and more efficient diagonal loading factor.The proposed algorithm can improve the robustness against the situation of limited snapshots.Secondly,another diagonal loading robust adaptive beamforming algorithm with joint robustness against two kinds of array mismatch is addressed in this chapter.This algorithm obtains the best estimation of covariance matrix under the minimum mean-squared error(MMSE)criterion through a modified general linear combination algorithm,which can efficiently cope with the situation of limited snapshots.Then using the best estimation,a quadratic convex optimization problem is formulated under two constraints to refine the steering vector of the desired signal,which can efficiently deal with steering vector mismatch.2.The research on robust beamforming algorithms applicable to the signal direction of arrival uncertainty.In order to deal with the signal direction of arrival uncertainty caused by direction of arrival errors or coherent scattering,a robust adaptive beamforming algorithm based on principal eigenvector for interference-plus-noise covariance matrix(IPNCM)reconstruction is firstly addressed in the fourth chapter of this thesis.This algorithm can fundamentally eliminate the desired signal component from the sample covariance matrix.Each interference covariance matrix is constructed on each angular sector of interference,and its prime eigenvector is used to accurately estimate the interference steering vector.A more precise IPNCM is reconstructed according to its definition.At the same time,a similar processing is used to estimate steering vector of the desired signal.The beamforming weight vector is designed by combining with reconstructed IPNCM,which improves the robustness of the algorithm against the signal direction of arrival errors.The proposed algorithm can almost obtain the optimal signal-to-interference-plus-noise ratio(SINR).Secondly,another robust adaptive beamforming via a novel subspace method for IPNCM reconstruction is proposed based on the algorithm above in this chapter.The intersection between the interference subspace of each interference covariance matrix and the signal-interference subspace of the sample covariance matrix is obtained by using alternating projection algorithm,and it is used as a more accurate estimate of the interference steering vector.This can further improve the robustness against the signal direction of arrival uncertainty,which is caused by both direction of arrival errors and coherent scattering,and guarantee the output SINR of the proposed algorithm to approach the optimal SINR.3.The research on robust beamforming algorithms applicable to the steering vector random errors.In order to cope with the steering vector random errors,a robust adaptive beamforming algorithm based on steering vector uncertainty sets for IPNCM reconstruction is firstly addressed in the fifth chapter of this thesis.The steering ve ctor random error of each interference is modeled as a circle uncertainty set,and the robust Capon beamforming(RCB)algorithm is used to estimate the interference steering vector.A more precise IPNCM based on these accurate estimates is reconstructed according to its definition.Meanwhile,a worst-case performance optimization(WCPO)beamformer problem,which is formulated by combining with the reconstructed IPNCM on the uncertainty set of the desired signal,is used to design the robust adaptive beamformer weight.It can improve the robustness against the steering vector rando m errors.Secondly,an annulus uncertainty set is introduced to model the steering vector random error of each interference.Each interference steering vector is accurately estimated on its own annulus uncertainty set via the subspace projection algorithm.A more precise IPNCM based on these accurate estimates is reconstructed according to its definition.Then the steering vector of the desired signal is accurately estimated as the prime eigenvector of the desired signal covariance matrix,which is calculated over its own annulus uncertainty set.The beamformer weight vector is obtained by combining with the reconstructed IPNCM to efficiently deal with the steering vector random errors.4.The research on robust beamforming algorithms with probability constraint.In order to effectively match the true steering vector random errors,a probability-constrained RCB algorithm based on steering vector uncertainty sets is firstly addressed in the sixth chapter of this thesis.Based on the original RCB algorithm,a probability constraint is applied on the squared Euclidean norm of the steering vector random error of the desired signal.This can obtain a more compact steering vector uncertainty set,which effectively matches the true steering vector mismatch norm.The proposed algorithm can highly improve the robustness against the arbitrary rando m errors of steering vector.Secondly,the idea of probability constraint is introduced in this chapter,which is on the basis of the robust adaptive beamforming algorithm based on steering vector uncertainty sets for IPNCM reconstruction proposed in the fifth chapter.A probability constraint is applied on the squared Euclidean norm of each steering vector random error of both the desired signal and the interferences.It obtains a more compact steering vector uncertainty set to match the true steering vector mismatch norm,and further improves the estimation accuracy of the steering vector to reconstruct a more precise IPNCM.The proposed algorithm holds better robustness against steering vector random errors.