Study On Spatial Spectrum Estimation Algorithms Of Wideband Array Signals

Wideband spatial spectrum estimation stands as a significant area within the realm of array signal processing research.In comparison to narrowband signals,the utilization of wideband signals yields heightened advantages across a diverse spectrum of sectors including military,industrial,medical,and daily life.However,due to challenges such as spectral broadening and envelope delay inherent to wideband signals,conventional narrowband signal processing techniques are no longer applicable.Recent years,the problem of spatial spectrum estimation for wideband signals has gained widespread attention.Nevertheless,existing algorithms for wideband spatial spectrum estimation still have limitations and room for improvement in terms of estimation precision,computational intricacy,and scope of applicability.This dissertation focuses on the aforementioned issues and conducts research on wideband signal spatial spectrum estimation algorithms,which mainly consist of the following three parts:The first part of the study investigates the problem of wideband signal spatial spectrum estimation based on sparse recovery theory.Two Direction of Arrival(DOA)estimation algorithms are proposed from the perspectives of single-snapshot and multiple-snapshot scenarios.For the single-snapshot frequency domain model,the model is transformed into a Multiple Measurement Vectors(MMV)sparse recovery problem through focusing operations to reduce dictionary dimensions.An improved Feedback Hard Thresholding(FHT)algorithm called Adaptive Feedback Hard Thresholding(AFHT)is introduced and extended to the MMV case,resulting in the MMV Adaptive Feedback Hard Thresholding(M-AFHT)algorithm.Simulation results indicate that the proposed algorithm slightly lags behind the Block Sparse Bayesian Learning(BSBL)algorithm in terms of estimation accuracy,it exhibits faster computational speeds,which is highly advantageous for practical applications.Addressing the multi-snapshot frequency domain problem,the concept of a joint covariance matrix is first constructed.Building upon covariance matrix fitting theory,a fitting criterion for the joint covariance matrix multi-snapshot scenario is derived,leading to the proposal of the Joint Covariance Matrix Fitting(JCMF)algorithm.The Holder’s inequality is used to relax the optimization problem and promote the block sparsity,and the closed-form solution is deduced.Simulation results reveal that although the computational speed of the proposed algorithm is slower,it has significantly higher estimation accuracy compared to traditional subspace-based algorithms.The second part of this study addresses the problem of wideband signal spatial spectrum estimation in multipath environments.Estimation algorithms are proposed for two scenarios:uncorrelated wideband sources and mixed wideband sources in multipath environment.For the case of multipath uncorrelated wideband non-circular signals,a Focused based Off-Grid Wideband Non-Circular(FOGWNC)estimation algorithm is presented.The joint sparsity between wideband signals and grid errors is utilized,the covariance matrix and pseudocovariance matrix are jointly represented using block sparsity constraints,and the problem is transformed into a Single Measurement Vector(SMV)problem using the focusing technique,thereby the computational complexity is reduced.In comparison to existing subspacebased wideband non-circular DOA estimation algorithms,the proposed method demonstrates higher accuracy under low signal-to-noise ratio and limited snapshots.For mixed wideband signals with correlated components in a multipath environment,a novel time-domain algorithm is presented.The signal model using envelope compensation techniques is constructed and uncorrelated signals are estimated using a rank reduction algorithm.Then the uncorrelated components are eliminated through matrix transformations and the correlated signals are estimated by the spatially smooth rank reduction.Using linear search techniques,the computational speed is significantly enhanced.In comparison to existing DOA algorithms for correlated wideband sources,the proposed method demonstrates significantly improved estimation accuracy and is capable of separating uncorrelated and correlated components.The third segment of this study addresses the problem of wideband signal spatial spectrum estimation in near-field environments.Initially,utilizing the Fresnel approximation and the specific structure of a symmetric Uniform Linear Array,the angle information is separated from the covariance matrix.Subsequently,Taylor expansion is employed to mitigate model errors,and the DOA estimation problem is represented as a SMV sparse recovery problem for individual frequency bins.The estimation error of the sampled covariance matrix is approximated using an asymptotic complex Gaussian distribution fitting.A joint Sparse Bayesian Learning(SBL)framework is proposed for near-field wideband angle estimation,incorporating the Generalized Approximate Message Passing(GAMP)algorithm for computational acceleration.Next,a time-domain envelope compensation approach is utilized for distance estimation.Using the angle values obtained from SBL estimation as prior information,delay compensation is applied to each distance unit.A linear search strategy is employed to reduce computational complexity.In comparison to existing near-field wideband localization algorithms,the proposed method achieves higher estimation accuracy and improved resolution.Moreover,it doesn’t require a prior information or pre-estimated parameters.Additionally,due to the utilization of joint sparsity across subbands,the proposed algorithm has a more relaxed requirement on the inter-element spacing without ambiguity,the spacing can be set as half-wavelength.This reduces the impact of array aperture loss and mutual coupling effects.