Research On Low Complexity And Robust Adaptive Array Signal Processing Algorithms With High Dimensional And Small Samples

In recent years,array signal processing techniques have been widely used in radar,sonar,satellite remote sensing,astronomy,wireless communication,speech signal processing,medical imaging and many other areas.More and more sensors were configured in the modern array radar system which equips with many advantages,such as higher resolution,stronger interference suppression ability,more accurate target identification ability,farther detection distance and better reliability.Hence,in real applications,the large-scale array radar system is the inevitable trend of radar development.However,it is difficult to efficiently handle the signal processing task of the modern array radar since the computational complexity of the traditional array signal processing algorithms is very high.Moreover,mismatches,such as propagation distortions,location perturbations,sensor gain errors,phase fluctuations,multipath propagation,and mutual coupling,will significantly impact array radar techniques.In addition,due to the limitations of system working environments and hardware level,the number of independent and identically distributed training samples does not increase synchronously as the number of elements.In order to overcome the problems,we should improve the convergence rate and computational complexity of adaptive angle estimation algorithm and robust beamforming algorithm.In order to overcome the problem of modern array system,The specific research achievements and main contributions of this dissertation are as follows:1.When adaptive beamformers are applied to actual problems,various model mismatches are present between the real signal steering vector(SSV)and presumend SSV,which severely deteriorates the performance of the beamformer.To address this issue,we develop a robust adaptive beamforming(RAB)algorithm in which the weight vector is a linear combination of the presumed steering vector and basis vectors of the orthogonal supplement subspace of the steering vector and constrain the norm of the given steering vector to be one.Then,we convert the common constrained optimization problem into an unconstrained one to establish a new beamformer.Moreover,we use damped singular value decomposition regularization,which employs the L-curve method to adaptively determine the regularized factor(loading level),for suppressing the effects of model mismatches.In addition,we perform simulations of the proposed algorithm and other existing beamforming algorithms by considering several commonly encountered mismatches(e.g.,the directionof-arrival mismatch,sensor gain,phase error and location perturbation,coherent local scattering,and mutual coupling),and demonstrate the superior performance of the new beamforming algorithm.In addition,the proposed algorithm requires free prior information of signal and is simple to implement.2.The adaptive beamformer of a large-scale sensor array mainly suffers from two limits.One limit is an insufficient number of training snapshots,which usually results in an illposed sample covariance matrix in many real applications.The other limit is the high computational complexity of the beamformer that severely restricts its online processing.Under complex white noise case,considering that,the optimal beamformer based on the minimum variance distortionless response criterion is located in the low-dimensional signal subspace(the subspace composed of interested SSV and interference array manifold).To overcome these two limits,we proposed two fast RAB algorithms in this dissertation,which refer to the linear kernel approaches,formulates the weight vector as a linear combination of the training samples and the SSV.The proposed algorithms only need to calculate a lowdimensional combination vector instead of the high-dimensional adaptive weight vector,which remarkably reduce the computational complexity.Moreover,regularization techniques are utilized to suppress the excessive variation of the combination vector caused by an underdetermined estimation of the Gram matrix.Experimental results show that the proposed algorithms achieve better performance and lower computation complexity than algorithms in the literature.In addition,we derive a fast version of the proposed beamformer which is suitable for scanning mode.Especially,like the kernel approaches,the proposed algorithms achieve good performance under the small sample case.3.The classical multiple signal classification(MUSIC)mainly suffers from two limits.One limit is an insufficient number of snapshots,which usually causes an ill-posed sample covariance matrix in many real applications.The smallest eigenvalues of the ill-posed sample covariance matrix are severely non-uniform,and the boundary between noise subspace and signal subspace is blurred.The other limit is the intense space-colored and time-white noise that also breaks the separability between signal and noise subspaces.The signal components of the non-zero delay sample covariance matrix,where the space-colored and time-white noise components are suppressed by the temporal method,are very little or inexistence in the case of the insufficient sample.Hence,the sufficient non-zero delay sample covariance matrices ensure that enough signal components are used for signal subspace estimation.The noise subspace is removed by the pre-projection technique which runs iteratively.An improved signal subspace is attained in this study and a more efficient MUSIC is derived.In this study,partial column vectors of the left singular matrix of the nonzero delay sample covariance matrices are used as the initial value to accelerate the convergence of the algorithm.The proposed subspace estimation algorithm only needs three to five iterations to meet the condition of convergence and the minimum description length(MDL)can accurately estimate the number of far-field targets by using non-zero delay sample covariance matrix.Experiment results exhibit the significantly improved performance of the proposed algorithm in comparison with other existing methods.4.Adaptive angle estimation from small samples has considerable significance for realworld applications.However,in the case of large arrays and small samples,the classical signal subspace finding may suffer from two prominent limitations.One limit is that insufficient samples usually make the sample covariance matrix underestimated and illconditioned.In such an underestimated covariance matrix,two undesirable cross-product terms between signals and noises are usually not ignored,and the sample covariance matrix of pure noises is not the diagonal matrix with the same diagonal entries.This affects the separability between the signal subspace and the noise subspace,and may invalidate the subspace-based techniques.Another limitation is that these algorithms have high computational complexity that may severely restrict their applications in practical engineering where real-time processing is urgently needed.To overcome the above two limitations,an efficient signal subspace finding method is proposed in this dissertation.The proposed method depends on the linear kernel matrix derived by formulating all the basis vectors of the signal subspace as a linear representation of the received sample matrix.Meanwhile,when the received samples only contain spatial-temporal white Gaussian noises,if the number of sources is much smaller than that of snapshots and the number of samples is far less than that of array elements,it is found theoretically that the pure-signal term in the underestimated covariance matrix can be implicitly fully estimated.Also,it is theoretically proved that there is a correspondence between the signal subspace of the high-dimensional sample covariance matrix and the signal subspace of the low-dimensional Gram matrix.Further,it is proved that two cross-product terms and a pure-noise term in the lowdimensional Gram matrix can be fully estimated.Interestingly,unlike the underestimated covariance matrix,such a low-dimensional Gram matrix keeps the separability between the signal subspace and the noise subspace.Therefore,the signal subspace can be found indirectly and efficiently by eigenvalue decomposition(EVD)of the low-dimensional Gram matrix.Such EVD significantly reduces the computation load for finding signal subspace.Once the signal subspace is obtained,the noise subspace can be easily obtained,and the angle parameters can be effectively searched via classical spatial-spectral estimation techniques such as MUSIC and root-MUSIC.The proposed method has low computational complexity,and simulation results demonstrate that it achieves good performance for a largescale array under the case of small samples.