Covariance Matrix Reconstruction Research Articles

Robust adaptive beamforming via quasi-signal subspace estimation for covariance matrix reconstruction

In this paper, a novel narrowband interference-plus-noise covariance matrix (INCM) reconstruction method is proposed for robust adaptive beamforming (RAB). To enhance the effectiveness of the INCM reconstruction, we offer a prior selection of the dimension of a quasi-signal subspace (QSS) based on the signal subspace proximity employing two subsample covariance matrices (SSCMs). The QSS herein can provide estimations of all relevant factors of interference for the INCM. Moreover, by employing the eigenvectors of the SSCM, the noise power can be estimated precisely through a nonlinear regularization scheme. Finally, the signal-of-interest steering vector is corrected by an optimization problem exploiting the reconstructed INCM. The proposed RAB method can capitalize on the benefits of the QSS without prior knowledge of the number of sources. The results of the simulations demonstrate the effectiveness of the proposed method in terms of various mismatches.

IGM damping wing constraints on the tail end of reionisation from the enlarged XQR-30 sample

Abstract The attenuation of Lyα photons by neutral hydrogen in the intergalactic medium (IGM) at z ≳ 5 continues to be a powerful probe for studying the epoch of reionisation. Given a framework to estimate the intrinsic (true) Lyα emission of high-z sources, one can infer the ionisation state of the IGM during reionisation. In this work, we use the enlarged XQR-30 sample of 42 high-resolution and high-SNR QSO spectra between 5.8 ≲ z ≲ 6.6 obtained with VLT/X-Shooter to place constraints on the IGM neutral fraction. This is achieved using our existing Bayesian QSO reconstruction framework which accounts for uncertainties such as the: (i) posterior distribution of predicted intrinsic Lyα emission profiles (obtained via covariance matrix reconstruction of the Lyα and N v emission lines from unattenuated high-ionisation emission line profiles; C iv, Si IV +O IV] and C iii]) and (ii) distribution of ionised regions within the IGM using synthetic damping wing profiles drawn from a 1.63 Gpc3 reionisation simulation. Following careful quality control, we used 23 of the 42 available QSOs to obtain constraints/limits on the IGM neutral fraction during the tail-end of reionisation. Our median and 68th percentile constraints on the IGM neutral fraction are: $0.20\substack{+0.14 -0.12}$ and $0.29\substack{+0.14 -0.13}$ at z = 6.15 and 6.35. Further, we also report 68th percentile upper-limits of $\bar{x}_{\mathrm{H\, \small {I}}{}} < 0.21$, 0.20, 0.21 and 0.18 at z = 5.8, 5.95, 6.05 and 6.55. These results imply reionisation is still ongoing at 5.8 ≲ z ≲ 6.55, consistent with previous results from XQR-30 (dark fraction and Lyα forest) along with other observational probes considered in the literature.

Gridless Underdetermined DOA Estimation for Mobile Agents with Limited Snapshots Based on Deep Convolutional Generative Adversarial Network

Deep learning techniques have made certain breakthroughs in direction-of-arrival (DOA) estimation in recent years. However, most of the current deep-learning-based DOA estimation methods view the direction finding problem as a grid-based multi-label classification task and require multiple samplings with a uniform linear array (ULA), which leads to grid mismatch issues and difficulty in ensuring accurate DOA estimation with insufficient sampling and in underdetermined scenarios. In order to solve these challenges, we propose a new DOA estimation method based on a deep convolutional generative adversarial network (DCGAN) with a coprime array. By employing virtual interpolation, the difference co-array derived from the coprime array is extended to a virtual ULA with more degrees of freedom (DOFs). Then, combining with the Hermitian and Toeplitz prior knowledge, the covariance matrix is retrieved by the DCGAN. A backtracking method is employed to ensure that the reconstructed covariance matrix has a low-rank characteristic. We performed DOA estimation using the MUSIC algorithm. Simulation results demonstrate that the proposed method can not only distinguish more sources than the number of physical sensors but can also quickly and accurately solve DOA, especially with limited snapshots, which is suitable for fast estimation in mobile agent localization.

Downlink Channel Covariance Matrix Reconstruction for FDD Massive MIMO Systems With Limited Feedback

Downlink Channel Covariance Matrix Reconstruction for FDD Massive MIMO Systems With Limited Feedback

DOA estimation of coherent signals in underdetermined problems using sparse-based Toeplitz covariance reconstruction

Direction-Of-Arrival (DOA) estimation in environments with coherent sources is a challenging problem, when the number of narrowband sources is more than elements and current coherent algorithms cannot accurately overcome such underdetermined problems. In this paper, we propose the Sparse-based Toeplitz Covariance Reconstruction (STCR) algorithm, which obtains a hole-free extended-aperture array with increased Degrees of Freedom (DOF) by exploiting a minimum redundancy array. This method provides superiority in estimating coherent sources by Toeplitz covariance matrix reconstruction. Also, using a Sparse Signal Representation (SSR) framework makes the DOA estimator stronger in source detection and robust to the noise power. Numerical results show the effectiveness of the proposed method even at low SNRs for over- and underdetermined DOA estimators compared to well-known methods. Also, it has high accuracy in DOA estimation of closely-located coherent sources using a small number of snapshots.

Jammer Tracking Based on Efficient Covariance Matrix Reconstruction With Iterative Spatial Spectrum Sampling

Jammer Tracking Based on Efficient Covariance Matrix Reconstruction With Iterative Spatial Spectrum Sampling

Fast DOA Estimation Algorithms via Positive Incremental Modified Cholesky Decomposition for Augmented Coprime Array Sensors.

This paper proposes a fast direction of arrival (DOA) estimation method based on positive incremental modified Cholesky decomposition atomic norm minimization (PI-CANM) for augmented coprime array sensors. The approach incorporates coprime sampling on the augmented array to generate a non-uniform, discontinuous virtual array. It then utilizes interpolation to convert this into a uniform, continuous virtual array. Based on this, the problem of DOA estimation is equivalently formulated as a gridless optimization problem, which is solved via atomic norm minimization to reconstruct a Hermitian Toeplitz covariance matrix. Furthermore, by positive incremental modified Cholesky decomposition, the covariance matrix is transformed from positive semi-definite to positive definite, which simplifies the constraint of optimization problem and reduces the complexity of the solution. Finally, the Multiple Signal Classification method is utilized to carry out statistical signal processing on the reconstructed covariance matrix, yielding initial DOA angle estimates. Experimental outcomes highlight that the PI-CANM algorithm surpasses other algorithms in estimation accuracy, demonstrating stability in difficult circumstances such as low signal-to-noise ratios and limited snapshots. Additionally, it boasts an impressive computational speed. This method enhances both the accuracy and computational efficiency of DOA estimation, showing potential for broad applicability.

Robust Adaptive Beamforming for Interference Suppression Based on SNR

Robust adaptive beamforming (RAB) can be used to suppress interference signals while retaining the desired signals received by a sensor array. However, desired signal self-cancellation and model mismatch can affect RAB performance. In this paper, a novel interference-plus-noise covariance matrix (INCM) reconstruction method is proposed for RAB to solve these problems. The proposed method divides the desired signal into two ranges according to the input signal-to-noise ratio (SNR), namely low SNR and high SNR. In the low SNR range, INCM reconstruction directly uses the same sample covariance matrix as the sample matrix inversion (SMI) beamformer to retain the advantages of the traditional SMI algorithm. In the high SNR range, the eigenvalues of the sample covariance matrix are used to estimate the interference power and noise power. The optimized interference steering vector (SV) is obtained by solving a quadratic convex optimization problem in an interference subspace. The INCM is reconstructed from the interference SVs, interference power, and noise power. The reconstructed INCM is then used to correct the desired signal SV via maximizing the beamformer output power. This is achieved by solving a quadratically constrained quadratic programming (QCQP) problem. Analysis and simulation results are presented which demonstrate that the proposed method performs well under a variety of mismatch conditions.

Adaptive Beamforming with Small Samples and Low Complexity for Large-Scale Arrays

In this paper, we propose a novel adaptive beamforming method based on interference plus noise covariance matrix (INCM) reconstruction with few samples and low complexity. Unlike existing techniques, we make use of the fact that large-scale antenna arrays can significantly increase the spectral analysis’s resolution by estimating the steering vector (SV) and power of the interfering signal using the discrete Fourier transform (DFT). In addition, a simple spatial rotation operation is employed to resolve the power “leakage” problem of the DFT spectrum and increase estimation precision. The proposed method achieves a high output SINR by reconstructing an accurate INCM with the advantage of simple implementation and low computation complexity. Finally, we verify the effectiveness of the proposed method by numerical simulation and result analysis.

Robust Adaptive Beamforming Algorithm Based on Complex Gauss–Legendre Integral

This study addresses the poor robustness of the current beamforming algorithm for covariance matrix reconstruction and the high computational complexity in the covariance matrix reconstruction process. A robust beamforming algorithm based on the Complex Gauss–Legendre integral is proposed. The method firstly partitions the neighborhood of the interference signal and constructs the interference signal space using the complex Gauss-Legendre integral, then projects the received signal into the interference signal space to filter out the desired signal and complete the reconstruction of the interference noise covariance matrix, before finally correcting the steering vector mismatch using the improved optimal steering vector estimation method. The simulation results show that the method has good robustness and a low sidelobe in the presence of the steering vector mismatch and the presence of array perturbation. Compared with the previous works, the proposed CGL-ISV method provides a better beamforming performance.

Satellite Interference Source Direction of Arrival (DOA) Estimation Based on Frequency Domain Covariance Matrix Reconstruction.

Direction of arrival (DOA) estimation is an effective method for detecting various active interference signals during the satellite navigation process. It can be utilized for both interference detection and anti-interference applications. This paper proposes a DOA estimation algorithm for satellite interference sources based on frequency domain covariance matrix reconstruction (FDCMR) to address various types of active interference that may occur in the satellite navigation positioning process. This algorithm can estimate the DOA of coherent signals from multiple frequency points under low signal-to-noise ratio (SNR) conditions. The signals received from the array are transformed from the time domain to the frequency domain using a fast Fourier transform (FFT). The data corresponding to the frequency point of the target signal is extracted from the signal in the frequency domain. The frequency domain covariance matrix of the received array signals is reconstructed by utilizing its covariance matrix property. The spatial spectrum search method is used for the final DOA estimation. Simulation experiments have shown that the proposed algorithm performs well in the DOA estimation under low SNR conditions and also resolves coherency. Moreover, the algorithm's effectiveness is verified through comparison with three other algorithms. Finally, the algorithm's applicability is validated through simulations of various interference scenarios.

Coarray Interpolation for Direction Finding and Polarization Estimation Using Coprime EMVS Array via Atomic Norm Minimization

In this paper, we develop an efficient algorithm for direction finding and polarization estimation using coprime electromagnetic vector sensor (EMVS) array. First of all, we represent the coarray outputs of coprime EMVS array as the multiple-component form and perform interpolation on each coarray output component. Using the interpolated measurement matrix, we subsequently formulate an atomic norm minimization problem to reconstruct the noise-free covariance matrix and measurement matrix of the interpolated ULA measurements. Finally, we estimate the directions-of-arrival (DOAs) of sources by applying MUSIC on the reconstructed covariance matrix, and utilize the reconstructed measurement matrix and the estimated DOAs to derive the closed-form estimates of polarization parameters. Compared with various existing methods, the proposed algorithm can provide higher estimation accuracy. Furthermore, our algorithm is able to handle more sources and has lower computational complexity. Numerical results illustrate the superiority of the proposed algorithm over the state-of-the-art methods.

Angular Reciprocity-Based CCM Reconstruction for Downlink FDD Multi-Antenna Channels With Multiple Scattering Clusters

Angular reciprocity based downlink (DL) channel covariance matrix (CCM) reconstruction has the significant superiority of requiring no uplink feedback in frequency division duplex multi-antenna systems. In this realm, maximal angle of arrival estimation-based schemes show superior performance due to its noise-robust merit for environment with a dominant scattering cluster. To extend the scheme to multiple scattering clusters environments, we propose to decompose the DL CCM into the covariance matrix of each scattering cluster and then reconstruct each DL sub-covariance matrix utilizing the estimated angular reciprocal parameters. Simulation results verify the validity of the proposed scheme in a 3GPP standard based multiple scattering clusters channel model.

Covariance Matrix Reconstruction Based on Power Spectral Estimation and Uncertainty Region for Robust Adaptive Beamforming

In this work, a simple and effective robust adaptive beamforming technique is proposed for uniform linear arrays, which is based on the power spectral estimation and uncertainty region (PSEUR) of the interference plus noise (IPN) components. In particular, two algorithms are presented to find the angular sector of interference in every snapshot based on the adopted spatial uncertainty region of the interference direction. Moreover, a power spectrum is introduced based on the estimation of the power of interference and noise components, which allows the development of a robust approach to IPN covariance matrix reconstruction. The proposed method has two main advantages. First, an angular region that contains the interference direction is updated based on the statistics of the array data. Secondly, the proposed IPN-PSEUR method avoids estimating the power spectrum of the whole range of possible directions of the interference sector. Simulation results show that the performance of the proposed IPN-PSEUR beamformer is almost always close to the optimal value across a wide range of signal-to-noise ratios.

Design of a robust MVDR beamforming method with Low-Latency by reconstructing covariance matrix for speech enhancement

Aiming at solving the problems of the conventional minimum variance distortionless response (MVDR) beamformer in practical applications, such as the sensibility of the steering vector mismatch and beampattern distortion, a robust broadband MVDR beamforming method with low-latency by reconstructing covariance matrix is proposed and applied to speech enhancement with a linear microphone array in this paper. In this work, some important steps are optimized, and the main contribution is to consider the problem of correlation terms generated by the low latency. Firstly, the direction of arrival (DOA) is corrected and the steering vector is estimated based on the sparsity of the DOAs corresponding to the sound sources, which improves the ability of anti-mismatches in the steering vector. Secondly, the correlation terms between the sound sources and noise are estimated and eliminated by the Capon power within the eigen-subspace, and the indirect dominant method is used to eliminate the correlation terms between the sound sources, so that the covariance matrix is reconstructed to obtain a more robust MVDR beamformer. Thirdly, the problem of white noise amplification at low frequency bins is analyzed, and a white noise gain (WNG) modification method is proposed to obtain a compromise between the interference suppression and WNG. In the experiments, the TIMIT corpus is used to generate the multi-channel speech data set, and the performance of the proposed method is evaluated with different DOAs and input signal to interference plus noise ratios (SINRs). The experimental results show that the proposed method can effectively suppress the interferences and reduce the noise with strong robustness.

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.

Mainlobe Interference Suppression Based on Compressive Sensing and Covariance Matrix Reconstruction

Mainlobe Interference Suppression Based on Compressive Sensing and Covariance Matrix Reconstruction

High resolution adaptive estimator of sinusoidal based on covariance matrix reconstruction

Exponentially decaying sinusoidal signal is often observed in engineering and research fields. In some practical applications, the frequencies of multiple signals are close to each other. It would face a challenging task to resolve these crowded signals processed by discrete Fourier transformation, especially in the case of the lack of sampling time and the fast-decaying signals. The Localised Capon estimator (LoCapE) has demonstrated its advantage in improving the resolution of exponentially decaying sinusoidal signals. However, the amplitude and the frequency of each component extracted by the LoCapE are not accurate due to the effect from interference components. Here, we improve the LoCapE method by reconstructing the interference-plus-noise covariance matrix instead of the signal covariance matrix. Experimental results on simulated and real exponentially decaying sinusoidal data show that the proposed method is more accurate in extracting parameters at the lack of sampling points.

Mainlobe Interference Suppression for Radar Network via RPCA-Based Covariance Matrix Reconstruction

Radar networks can provide spatial diversity by observing targets from different perspectives with adequately separated receiving stations. This article proposes a mainlobe interference suppression approach for radar networks based on covariance matrix reconstruction. First, we formulate the mainlobe interference suppression under multiradar configuration as a multichannel signal enhancement problem and perform range and Doppler equalization to improve interferences’ spatial correlation. Then, we estimate the signal and interference covariance matrix from the sampling covariance matrix by solving a robust principal component analysis (RPCA) model. After that, we devise a time-domain-constrained (TDC) linear estimator dependent on the reconstructed covariance matrices to enhance target echo. To remove those duplicate false targets caused by signal enhancement and estimate the state of the physical targets, we establish and solve a generalized multiple measurement vector (GMMV) model based on the fact that targets have unique locations in the state space. Finally, we confirm the effectiveness of the proposed approach with numerical experiments and demonstrate better performance in comparison with the subspace projection method.

Robust adaptive beamforming via covariance matrix reconstruction with diagonal loading on interference sources covariance matrix

The majority of the existing adaptive beamforming methods utilize the interference-plus-noise covariance matrix (INCM) to prevent the signal of interest (SOI) from being suppressed. However, the removal of the SOI component will lead to a decrease in the performance at low input signal-to-noise ratio (SNR). In this paper, a novel interference sources covariance matrix (ISCM) diagonal loading method is proposed to improve the robustness of the beamformer. First of all, we employ the peaks of the Capon spectrum to calculate the corresponding nominal steering vectors (SVs), and then accurate SVs of the SOI and interferences are obtained by subspace projection. Instead of utilizing the orthogonality, the proposed method preserves the non-orthogonality between SVs to estimate an accurate signal-plus-interference sources covariance matrix (SISCM), and then obtains a reconstructed array covariance matrix (RACM). Furthermore, we conduct diagonal loading on ISCM and construct a modified array covariance matrix (MACM) to keep the interference-to-signal ratio (ISR) after loading at a proper large value. Simulation results demonstrate the robustness of the proposed method, and indicate that the proposed method not only has the low computational complexity but also performs well at both low and high input SNR.