Study Of Super-Resolution Spatial Spectrum Estimation And Robust Beamforming

With the development of technology and the reduction of cost,array signal processing has been developed rapidly in recent decades.Being two important research branches of array signal processing,super resolution spatial spectrum estimation(SR-SPE)and robust adaptive beamforming(RAB)are widely used in military and civil fields owing to their superior performance.However,confronted with the increasing complexity of the signal propagation environment,both SR-SPE and RAB have been facing greater challenges recently.This dissertation focuses on the problem of SR-SPE and RAB under non-ideal conditions,which has two purposes: The first is to improve the angle estimation accuracy and the angle resolution of SR-SPE algorithms under conditions of small number of snapshots,low signal-to-noise ratio(SNR)and/or highly correlated sources.The second goal is to enhance the robustness of RAB algorithms over model mismatches.Several theoretically and practically valued algorithms are proposed and derived in this dissertation,and the correctness and effectiveness of these algorithms are verified by a series of computer simulations.Throughout this dissertation,the main contributions can be summarized as follows:1.This dissertation studies the subspace-based SPE algorithms,and proposes to construct a virtual multidimensional structure in any type of the harmonic signal.Moreover,exploiting the virtual multidimensional structure,two subspace based SPE algorithms are developed.In essence,the multidimensional structure of the multidimensional harmonic signal denotes the Kronecker product structure of the signal steering vector,upon which the signal subspace can be estimated via a Kronecker structured projection,namely higher-order singular value decomposition(HOSVD).Compared with singular value decomposition(SVD),HOSVD can fully exploit the multidimensional structure of the multidimensional harmonic signal to improve the estimation accuracy of the signal subspace.Therefore,the performance of the multidimensional subspace based SPE algorithms can be enhanced by HOSVD instead of SVD,particularly in the case of low SNR values and/or small number of snapshots.To apply HOSVD to the problem of the 1-dimensional(1-D)subspace based SPE algorithms,we propose to construct a virtual multidimensional structure in the 1-D harmonic signal.Furthermore,the idea of constructing a virtual multidimensional structure is also introduced to the R-D(R?2)harmonic signal.In conjunction with its inherent multidimensional structure,the virtual multidimensional structure of the R-D harmonic signal can be exploited to further improve the angle estimation accuracy and the angle resolution of the subspace-based SPE algorithms.2.This dissertation studies the maximum likelihood(ML)based low angle tracking algorithms,and derives the theoretical mean square error(MSE)of elevation angle estimates of the refined model based maximum likelihood(RML)algorithm,upon which a frequency-agile RML algorithm is proposed.The RML algorithm is an improved version of the traditional ML algorithm in the model of low angle tracking.Affected by multipath effects,it has a special characteristic: Increasing the operating frequency of radar does not always reduce the MSE of elevation angle estimates.In order to improve the elevation angle estimation accuracy,the proposed algorithm attempts to optimize the operating frequency of radar by utilizing the predicted value of the elevation angle under the principle of minimum mean square error(MMSE).The proposed algorithm actually follows the idea of the cognitive detection and tracking.Although numerous existing elevation angle estimation algorithms have been developed for the low-angle target tracking problem,most of them only focus on the signal processing of the receiver and relatively few investigations allow for the transmitter.Here,the online information on elevation angles is exploited to control the operating frequency of radar at each frame to improve the quality of the low-angle tracking.3.This dissertation studies the RAB algorithms in the model of a point source,and proposes two novel RAB algorithms for the point source model.As is well known,the training sample is an important resource for array signal processing.Although large sample size(i.e.the number of snapshots)can improve the system stability,the sample size will not be very large in the case that the dimension of the training sample is relatively high or that the adaptive beamformer is required to respond quickly to changes in the external environment.However,small sample size will cause a serious mismatch in the array covariance matrix,eventually leading to the performance degradation of adaptive beamformers.To improve the robustness of adaptive beamformers in the case of small sample size,this dissertation proposes a new RAB algorithm which is based on the correction of array covariance matrix and the estimate of steering vector.Reduceddimension operation is another important way to improve the robustness of adaptive beamformers over the mismatch of the array covariance matrix caused by sample size.Meanwhile,it can also reduce the amount of computation complexity.Since large computational burden will bring great difficulty to the online implementation of adaptive beamformers,this dissertation proposes a variable loading based reduceddimension beamforming algorithm.Compared with the existing variable loading based beamforming algorithms,the proposed algorithm not only balances both the robustness and the adaptiveness of the beamformer,but also greatly reduces the computational burden.4.This dissertation studies the RAB algorithms in the model of a general-rank source model,and proposes a novel RAB algorithm for the general-rank source model.The proposed RAB algorithm not only considers the uncertainties in the covariance matrices(including the desired signal covariance matrix and the array covariance matrix),but also includes an additional positive semidefinite constraints on the covariance matrices.In this way,the proposed RAB algorithm is robust against the model mismatches of covariance matrices,and avoids the conservative result caused by the negative-definite worst-case covariance matrix of the desired signal.Furthermore,a closed-form solution is derived based on the principle of the worst-case performance optimization,resulting in the simple implementation of the beamformer with low computational cost.