Fast and accurate covariance matrix reconstruction for adaptive beamforming using Gauss-Legendre quadrature

Most of the reconstruction-based robust adaptive beamforming(RAB)algorithms require the covariance matrix reconstruction(CMR)by high-complexity integral computation.A Gauss-Legendre quadrature(GLQ)method with the highest algebraic precision in the interpolation-type quadrature is proposed to reduce the complexity.The interference angular sector in RAB is regarded as the GLQ integral range,and the zeros of the threeorder Legendre orthogonal polynomial is selected as the GLQ nodes.Consequently,the CMR can be efficiently obtained by simple summation with respect to the three GLQ nodes without integral.The new method has significantly reduced the complexity as compared to most state-of-the-art reconstruction-based RAB techniques,and it is able to provide the similar performance close to the optimal.These advantages are verified by numerical simulations.

Frequency-invariant robust adaptive beamforming based on interference covariance matrix reconstruction

Consider the problems of frequency-invariant beampattern optimization and robustness in broadband beamforming.Firstly,a global optimization algorithm,which is based on phase compensation of the array manifolds,is used to construct the frequency-invariant beampattern.Compared with some methods presented recently,the proposed algorithm is not only available to get the global optimal solution,but also simple for physical realization.Meanwhile,a robust adaptive broadband beamforming algorithm is also derived by reconstructing the covariance matrix.The essence of the proposed algorithm is to estimate the space-frequency spectrum using Capon estimator firstly,then integrate over a region separated from the desired signal direction to reconstruct the interference-plus-noise covariance matrix,and finally caleulate the adaptive beamformer weights with the reconstructed matrix.The design of beamformer is formulated as a convex optimization problem to be solved.Simulation results show that the performance of the proposed algorithm is almost always close to the optimal value across a wide range of signal to noise ratios.

Oversample Reconstruction Based on a Strong Inter-Diagonal Matrix for an Optical Microscanning Thermal Microscope Imaging System

Based on a strong inter-diagonal matrix and Taylor series expansions,an oversample reconstruction method was proposed to calibrate the optical micro-scanning error. The technique can obtain regular 2 ×2 microscanning undersampling images from the real irregular undersampling images,and can then obtain a high spatial oversample resolution image. Simulations and experiments show that the proposed technique can reduce optical micro-scanning error and improve the system＇s spatial resolution. The algorithm is simple,fast and has low computational complexity. It can also be applied to other electro-optical imaging systems to improve their spatial resolution and has a widespread application prospect.

Reduced-complexity multiple parameters estimation via toeplitz matrix triple iteration reconstruction with bistatic MIMO radar

In this advanced exploration, we focus on multiple parameters estimation in bistatic Multiple-Input Multiple-Output(MIMO) radar systems, a crucial technique for target localization and imaging. Our research innovatively addresses the joint estimation of the Direction of Departure(DOD), Direction of Arrival(DOA), and Doppler frequency for incoherent targets. We propose a novel approach that significantly reduces computational complexity by utilizing the TemporalSpatial Nested Sampling Model(TSNSM). Our methodology begins with a multi-linear mapping mechanism to efficiently eliminate unnecessary virtual Degrees of Freedom(DOFs) and reorganize the remaining ones. We then employ the Toeplitz matrix triple iteration reconstruction method, surpassing the traditional Temporal-Spatial Smoothing Window(TSSW) approach, to mitigate the single snapshot effect and reduce computational demands. We further refine the highdimensional ESPRIT algorithm for joint estimation of DOD, DOA, and Doppler frequency, eliminating the need for additional parameter pairing. Moreover, we meticulously derive the Cramér-Rao Bound(CRB) for the TSNSM. This signal model allows for a second expansion of DOFs in time and space domains, achieving high precision in target angle and Doppler frequency estimation with low computational complexity. Our adaptable algorithm is validated through simulations and is suitable for sparse array MIMO radars with various structures, ensuring higher precision in parameter estimation with less complexity burden.

Reciprocity evaluation based adaptive CCM reconstruction in FDD multi-antenna systems

In view of the difficulty of obtaining downlink channel state information,partial reciprocity based channel covariance matrix(CCM)reconstruction has attracted a lot of attention in frequency division duplex(FDD)multi-antenna systems.Taking both the impact of CCM reconstruction on system performance and design complexity,we investigate an adaptive CCM reconstruction in this paper.Specifically,to effectively evaluate the validity of the reciprocity,we firstly analyze the characteristics of the partial reciprocity and define a reciprocity evaluation criterion.Then,we propose a partial antenna based angular power spectrum(APS)estimating algorithm to further reduce the complexity of the CCM reconstruction.Finally,simulation results demonstrate the superiority of our proposed schemes.

Binary Image Reconstruction Based on Prescribed Numerical Information

The problem of reconstruction of a binary image in the field of discrete tomography is a classic instance of seeking solution applying mathematical techniques. Here two such binary image reconstruction problems are considered given some numerical information on the image. Algorithms are developed for solving these problems and correctness of the algorithms are discussed.

Robust generalized sidelobe canceller based on eigenanalysis and a MaxSINR beamformer

A robust generalized sidelobe canceller is proposed to combat direction of arrival(DOA)mismatches.To estimate the interference-plus-noise(IPN)statistics characteristics,conventional signal of interest(SOI)extraction methods usually collect a large number of segments where only the IPN signal is active.To avoid that collection procedure,we redesign the blocking matrix structure using an eigenanalysis method to reconstruct the IPN covariance matrix from the samples.Additionally,a modified eigenanalysis reconstruction method based on the rank-one matrix assumption is proposed to achieve a higher reconstruction accuracy.The blocking matrix is obtained by incorporating the effective reconstruction into the maximum signal-to-interferenceplus-noise ratio(MaxSINR)beamformer.It can minimize the influence of signal leakage and maximize the IPN power for further noise and interference suppression.Numerical results show that the two proposed methods achieve considerable improvements in terms of the output waveform SINR and correlation coefficients with the desired signal in the presence of a DOA mismatch and a limited number of snapshots.Compared to the first proposed method,the modified one can reduce the signal distortion even further.