Research Of Parameter Estimation And Beamforming Algorithm Based On Tensor Operations

Array signal processing is of great significance in many applications such as satellite navigation,wireless communication,radar,sonar,seismic exploration,radio astronomy,and biomedical engineering,etc.However,the complexity of the electromagnetic environment and the scarcity of spectrum resources available make it important to fully explore and utilize the multidimensional characteristic information of signals with the purpose of improving the processing capacity of related information systems.In fact,research on the multi-dimensional signal processing technology,a field that has drawn a lot of attention in recent years,are abundant now.In spite of this,there are still many hot topics worthy of discussion,such as how to make full use of the multi-dimensional features of signals and how to improve the robust performance of information processing systems,the capabilities of signal detection and resolution,as well as the accuracy of parameters estimation.Meanwhile,it is worth noting that research on the tensor theory,which effectively provides new technical ways and approaches to discuss these questions,has important scientific significance and application values.Based on the application of the tensor theory in parameter estimation and beamforming,this paper focuses on three main tasks which are expanding the multi-dimensional observation aperture of the signal,improving the estimation performance of the multi-dimensional parameters of the signal and improving the robust performance of adaptive filtering in the case of array steering mismatch.Details of this paper’s innovative work are as follows.(1)According to the multi-dimensional characteristics of the signal model received by the polarization sensitive array,a multi-dimensional parameter estimation method based on tensor decomposition is proposed,which avoids the estimation of subspace and the search of spectral peak,preserves the observation dimension of the polarization domain of the signal,and effectively improves the estimation accuracy of the signal parameters.The proposed algorithm establishes a third-order tensor signal model of the polarization sensitive array,and performs the matrix expansion on the tensor to obtain slice matrix pairs.Furthermore,the polarization domain array manifold and the spatial domain array manifold are estimated by performing Generalized Eigenvalue Decomposition(GEVD)on slice matrix pairs,and the closed-form solutions of the parameters in the spatial and polarization domains are given by algebraic operations.The simulation results show that the proposed GEVD tensor decomposition algorithm effectively improves the accuracy of parameter estimation compared to matrix-based parameter estimation methods.In addition,in order to further improve the accuracy of parameters estimation and reduce the calculation time,a hierarchical CGLS(HCGLS)algorithm for decomposing the third-order tensor signal model is proposed.By improving the conjugate gradient least squares(CGLS)model and introducing a layering strategy,the decoupling of the polarization domain and spatial domain array manifolds is further achieved,which effectively reduces the calculation time.(2)The reconstructing theory of tensor model under polarization sensitive array is proposed to explore the multi-dimensional parameters estimation of the coherent signal,which avoids the loss of array aperture,makes the space configuration of array elements flexible and improves the accuracy of parameters estimation.The proposed algorithm analyzes conditions of the unique decomposition of tensors.In the case of coherent signals,the signal tensor characteristics are studied when at least one of the spatial array manifold and the polarization array manifold meets the requirement of the column full rank.Furthermore,the signal array manifolds are estimated by reconstructing the signal tensor model.The theoretical analysis andsimulation results show that the proposed algorithm can not only realize the decoupling of multi-dimensional parameters of coherent signals,but also have the ability to resolve similar or even identical signals in the spatial domain when the signals have obvious polarization differences.(3)In order to explore robust beamforming of polarization sensitive arrays when array manifolds mismatch,we propose the tensor multi-linear decomposition beamforming algorithms in which interferences are suppressed in multiple dimensions of space,effectively improving the robustness of beamformers and the effectiveness of interference suppression.Specifically,a high-order tensor model of the signal is firstly established for the polarization sensitive array with spatial multi-rotationally invariant property,and then the TD-MVDR beamforming algorithm is proposed.The proposed algorithm implements sub-array Minimum Variance Distortionless Response(MVDR)beamforming through high-order tensor multilinear decomposition,and implements global filtering through iteration.In order to further solve the problem of error accumulation caused by independent filtering between sub-arrays,the TDICGLS beamforming algorithm is proposed by improving the CGLS method.The TD-ICGLS beamformer takes the output of the upper-level sub-array as the reference input for the nextlevel sub-array filtering,and then achieves global filtering by implementing the sub-array iterative strategy.At the same time,in order to improve the robust performance of the proposed beamformers,a variable diagonal loading strategy for the tensor beamformer is proposed by analyzing the changing characteristics of the covariance matrix of each order subarray during the iteration.Additionally,in the case of spatial large-aperture arrays,the tensor decomposition filtering method provides new technical means and approaches for dimensionality reduction.