Interference Covariance Matrix Research Articles

Advanced Interference Mitigation Method Based on Joint Direction of Arrival Estimation and Adaptive Beamforming for L-Band Digital Aeronautical Communication System

The L-band digital aeronautical communication system (LDACS) is one of the candidate technologies for future broadband digital aeronautical communications, utilizing the unused L-band spectrum between distance measuring equipment (DME) channels. However, the higher signal power of DME complicates LDACS implementation. This paper proposes an advanced DME mitigation approach for the LDACS, integrating joint direction of arrival (DOA) estimation with adaptive beamforming techniques. The proposed method begins by exploiting the cyclostationary characteristics of signals, accurately obtaining the preliminary direction of the LDACS signal using the Cyclic-MUSIC method. Subsequent precise steering vectors (SVs) are selected through Capon spectrum search, followed by the reconstruction of the interference plus noise covariance matrix (INCM). Using the obtained SV and INCM, the weight vector is calculated and beamforming is performed. Simulation results validate that the proposed method not only accurately estimates the direction of LDACS signal but also efficiently mitigates DME interference, demonstrating a superior performance and reduced algorithmic complexity, even in scenarios with lower signal-to-noise ratios (SNRs) and the presence of DOA estimation errors. Additionally, the proposed method achieves a low bit error rate (BER), further validating its ability to ensure communication quality and enhance the reliability of LDACS.

Adaptive beamforming for maximum SINR in the presence of correlated interferences

The conventional steering vector (SV) based beamformers such as the minimum variance distortionless response (MVDR) can suffer from severe performance degradation due to the signal cancellation in the presence of correlated interferences. A partially correlated interference can be decomposed into two components, the coherent component and the other uncorrelated with the desired signal. The SVs of the desired signal and the coherent interference components compose the composite steering vector (CSV). In this paper, a beamforming method is presented that can achieve the maximum signal-to-interference-plus-noise ratio (SINR) via the use of the CSV and the interference covariance matrix (ICM) formed by the uncorrelated interference components only. The estimates of the CSV and the ICM are extracted from the sample matrix through oblique projections. In the estimation process, neither the interference powers nor the desired signal power is estimated, though the direction estimation is carried out using the multiple signal classification (MUSIC). We make theoretical performance analysis, which shows that the CSV based method is more effective as the correlation between the desired signal and the interferences increases and as the desired signal power becomes small. Simulation results demonstrate that it not only converges very quickly to the maximum SINR but also is robust to pointing errors.

A novel semi-blind source separation framework towards maximum signal-to-interference ratio

For the independence-based blind source separation (BSS) methods, effective modeling of the source signals is important. When applying the auxiliary function techniques, different source models normally result in different forms of the weighted covariance matrices, which in turn are used to compute the demixing filters. This paper proposes a new algorithmic framework termed minimum variance independent component analysis (MVICA), which is rigorously derived from the conventional BSS methods by determining the weighted covariance matrices with the maximum signal-to-interference ratio (SIR) criterion.The maximum-SIR weighted covariance matrix is approximately proved to be the interference covariance matrix. A deep neural network-supported implementation of the proposed MVICA algorithm is subsequently presented. Furthermore, we give a revealing insight into the relationships between MVICA and the existing speech separation approaches including conventional BSS methods and several mainstream beamforming techniques. Experimental results show the superiority of MVICA over the state-of-the-art BSS techniques and beamformers under various conditions, in terms of not only SIR but also signal-to-distortion ratio, speech intelligibility and perceptual quality and automatic speech recognition accuracy.

Virtual covariance matrix reconstruction-based adaptive beamforming for small aperture array.

Recently, many robust adaptive beamforming (RAB) algorithms have been proposed to improve beamforming performance when model mismatches occur. For a uniform linear array, a larger aperture array can obtain higher array gain for beamforming when the inter-sensor spacing is fixed. However, only the small aperture array can be used in the equipment limited by platform installation space, significantly weakening beamforming output performance. This paper proposes two beamforming methods for improving beamforming output in small aperture sensor arrays. The first method employs an integration algorithm that combines angular sector and gradient vector search to reconstruct the interference covariance matrix (ICM). Then, the interference-plus-noise covariance matrix (INCM) is reconstructed combined with the estimated noise power. The INCM and ICM are used to optimize the desired signal steering vector (SV) by solving a quadratically constrained quadratic programming (QCQP) problem. The second method proposes a beamforming algorithm based on a virtual extended array to increase the degree of freedom of the beamformer. First, the virtual conjugated array element is designed based on the structural characteristics of a uniform linear array, and received data at the virtual array element are obtained using a linear prediction method. Then, the extended INCM is reconstructed, and the desired signal SV is optimized using an algorithm similar to the actual array. The simulation results demonstrate the effectiveness of the proposed methods under different 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.

Adaptive Target Detection With Polarimetric FDA-MIMO Radar

The problem of adaptive radar detection with a polarimetric Frequency Diverse Array Multiple-Input Multiple-Output (FDA-MIMO) radar is addressed in this paper. At the design stage, the target detection problem is formulated as a composite hypothesis test, with the unknowns given by the target angle, incremental range (target displacement with respect to the center of the occupied range cell), and scattering matrix, as well as the interference covariance matrix. The formulated detection problem is handled by resorting to sub-optimal design strategies based on the Generalized Likelihood Ratio (GLR) criterion. The resulting detectors demand, under the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\mathrm{{1}}$</tex-math></inline-formula> hypothesis, the solution of a box-constrained optimization problem for which several iterative techniques, i.e., the Linearized Array Manifold (LAM), the Gradient Projection Method (GPM), and the Coordinate Descent (CD) algorithms, are exploited. At the analysis stage, the performance of the proposed architectures, which ensure the bounded CFAR property, is evaluated via Monte Carlo simulations and compared with the benchmarks in both white and colored disturbance.

Designing FDA Radars Robust to Contaminated Shared Spectra

This paper considers the problem of jointly designing the transmit waveforms and weights for a frequency diverse array (FDA) in a spectrally congested environment in which unintentional spectral interferences exist. Exploiting the properties of the interference signal induced by the processing of the multi-channel mixing and low-pass filtering FDA receiver, the interference covariance matrix structure is derived. With this, the receive weights are formed using the minimum variance distortionless response (MVDR) method for interference cancellation. Owing to the fact that the resulting output signal-to-interference-plus-noise ratio (SINR) is a function of the transmit waveforms and weights, as well as due to the ever-greater competition for the finite available spectrum, a joint design scheme for the FDA transmit weights and the spectrally compatible waveforms is proposed to efficiently use the available spectrum while maintaining a sufficient receive SINR. The performance of the proposed technique is verified using numerical simulations in terms of the achievable SINR, spectral compatiblity, as well as several aspects of the synthesized waveforms.

Robust Mainlobe Interference Suppression Based on Joint Oblique Projection for Dual Polarization Conformal Array

In this paper, a robust mainlobe interference suppression algorithm is proposed in a space-polarization joint domain based on a dual-polarized conformal array. An oblique projection filter can eliminate the interference while retaining the desired signal information. However, little deviation in signal parameters will lead to significant performance degradation. To solve such problems, the joint steering vector of the desired signal is corrected by solving the quadratic convex optimization problem. Parameters of interferences are first estimated by using multiple signal classification (MUSIC) joint spectrum, and then, the interference covariance matrix can be reconstructed individually to further estimate the interference steering vector. After that, the joint oblique projection operator can be established by the estimated steering vectors. Consequently, an antijamming beamformer can be obtained by the joint oblique projection filter to achieve robustness on the interference parameter estimation deviation and desired signal mismatch. Simulation experiments verify the effectiveness of the proposed method.

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 Based on Covariance Matrix Reconstruction via Steering Vector Estimation

The performance of the sample matrix inverse (SMI) beamformer degrades greatly when the signal-to-noise ratio (SNR) increases because the signal of interest (SOI) is mistaken as interferences and suppressed. To avoid this situation, the interference-plus-noise covariance matrix (INCM) is introduced via steering vector (SV) estimation for robust adaptive beamforming (RAB). To avoid the convex optimization for the SV estimation, a vertical error vector is constructed based on the property of subspace in the proposed method, and the SV error neighborhood table is built in advance to lower the computational complexity. Through the Capon spectrum search, the initial directions of the SOI and interference signals are estimated, and more accurate SVs are confirmed through neighborhood optimization in the table. Next, the interference covariance matrix (ICM) is generated by the estimated SVs and the noise covariance matrix (NCM) is obtained by the least-square (LS) solution based on the corrected SVs. Finally, INCM is reconstructed and the weight vector is computed for RAB. The main advantage of the proposed method is robust against unknown arbitrary-type mismatches. Simulation results demonstrate the effectiveness and robustness of the proposed method.

Space-Time Cascaded Processing-Based Adaptive Transient Interference Mitigation for Compact HFSWR

In high-frequency (HF) radar systems, transient interference is a common phenomenon that dramatically degrades the performance of target detection and remote sensing. Up until now, various suppression algorithms of transient interference have been proposed. They mainly concentrate on the skywave over-the-horizon radar on the basis of the assumption that the interference is sparse in a coherent processing interval (CPI). However, HF surface wave radar (HFSWR) often faces more complex transient interference due to various extreme types of weather, such as thunderstorm and typhoon, etc. The above algorithms usually suffer dramatic performance loss when transient interference contaminates the enormously continuous parts of a CPI. Especially for the compact HFSWR, which suffers from severe beam broadening and fewer array degrees of freedom. In order to solve the above problem, this study developed a two-dimensional interference suppression algorithm based on space-time cascaded processing. First, according to the spatial correlation of the compact array, the statistical samples of the main-lobe transient interference are estimated using a rotating spatial beam method. Next, an adaptive selection strategy is developed to obtain the optimal secondary samples based on information geometry distance. Finally, based on a quadratic constraint approximation, a precise estimation method of the optimal weight is developed when the interference covariance matrix is singular. The experimental results of simulation and measured data demonstrate that the proposed approach provides far superior suppression performance.

Robust adaptive beamforming based on covariance matrix reconstruction using Gauss–Legendre quadrature and steering vector estimation

The performance of adaptive beamforming is considerably affected by system errors in the gain and phase perturbation errors, direction of arrival mismatch, and incoherent local scattering, especially when the sample data contains the signal of interest (SOI) component. In this study, a robust adaptive beamforming approach based on interference plus noise covariance matrix (INCM) reconstruction using Gauss–Legendre quadrature (GLQ) and steering vector (SV) estimation is developed. The proposed algorithm incorporates the GLQ with the integral over the spherical uncertainty set and uses a linear combination of the integral at several angular nodes to substitute the integral of the entire interference region; consequently, the computational efficiency of reconstructing the INCM is enhanced. The SV of the SOI is represented as a linear combination of several principal eigenvectors of the SOI covariance matrix; thus, the double-constrained problem corresponding to the noise subspace is transformed into a single-constrained model, and its solution can be gained by utilizing the Lagrange multiplier method. Subsequently, the weight vector of the proposed beamformer can be calculated. Numerical simulations indicate that the proposed approach can effectively suppress interferences and exhibits superior overall performance under system errors.

Flexible Null Broadening Robust Beamforming Based on JADE

In order to flexibly and completely suppress dynamic interference, a flexible and robust beamforming based on JADE is proposed in this paper. In addition, it is insensitive to the gain–phase errors of the array. Firstly, the actual steering vector with gain–phase errors is separated from the received snapshot data by the joint approximate diagonalization of eigenmatrix (JADE) algorithm. Secondly, the direction of arrival (DOA) of interference can be estimated from the separated actual steering vector by the correlation coefficient method. Thus, the actual interference steering vector with gain–phase errors can be selected by the correlation coefficient with the nominal steering vector constructed by the estimated DOA. Then, the interference covariance matrix can be reconstructed by the actual interference steering vector, and the interference power estimated by the Capon power spectral. Finally, according to the prior information of the interference, only the dynamic interference covariance matrix is tapered by the novel covariance matrix trap (CMT), which can flexibly broaden and deepen the null. Simulation results show that the depth of the proposed beamformer is more than 10 dB deeper than that of the traditional algorithm in the non-stationary interference. In addition, it can save at least 2 degrees of freedom compared to the traditional method.

Null Broadening Robust Adaptive Beamforming Algorithm Based on Power Estimation.

In order to solve the problem of severely decreased performance under the situation of rapid moving sources and unstable array platforms, a null broadening robust adaptive beamforming algorithm based on power estimation is proposed in this paper. First of all, we estimate the interference signal power according to the characteristic subspace theory. Then, the correspondence between the signal power and steering vector (SV) is obtained based on the orthogonal property, and the interference covariance matrix (ICM) is reconstructed. Finally, with the aim of setting virtual interference sources, null broadening can be carried out. The proposed algorithm results in a deeper null, lower side lobes and higher tolerance of the desired signal steering vector mismatch under the condition of low complexity. The simulation results show that the algorithm also has stronger robustness.

Estimation of Covariance Matrix of Interference for Secure Spatial Modulation Against a Malicious Full-Duplex Attacker

In secure spatial modulation with a malicious full-duplex attacker, how to obtain the interference subspace or channel state information (CSI) is very important for Bob to reduce or even completely cancel the interference from Mallory. In this paper, different from existing work with perfect CSI, the covariance matrix of malicious interference (CMMI) from Mallory is estimated to construct the interference subspace. To improve the estimation accuracy, a CMMI rank detector relying on the Akaike information criterion (AIC) is derived first. To achieve a high-precision CMMI estimation, two methods, principal component analysis-eigenvalue decomposition (PCA-EVD) and joint diagonalization (JD) are proposed. The proposed PCA-EVD is a rank deduction method whereas the JD method is a joint optimization method with improved performance in the low jamming-to-noise ratio (JNR) region at the expense of increased complexity. Simulation results show that the proposed PCA-EVD performs much better than existing methods like sample estimated covariance matrix (SCM) and EVD in terms of normalized mean square error (NMSE) and secrecy rate (SR). Additionally, the proposed JD has achieved a better NMSE performance than PCA-EVD in the low JNR region (JNR <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\leq$</tex-math></inline-formula> 0 dB) while the proposed PCA-EVD performs better than JD in the high JNR region.

Adaptive Radar Detection in the Presence of Missing-data

This article deals with the problem of adaptive radar detection in a missing-data context, where the complete observations (i.e., downstream information loss mechanisms) are characterized by homogeneous Gaussian disturbance with an unknown but possibly structured covariance matrix. The detection problem, formulated as a composite hypothesis test, is tackled by resorting to suboptimal design strategies, leveraging the generalized likelihood ratio criterion demanding appropriate maximum likelihood estimates (MLEs) of the unknowns under both hypotheses. Capitalizing on some possible <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge about the interference covariance matrix structure, the optimization problems involved in the MLE computation are handled by employing the expectation–maximization (EM) algorithm or its expectation–conditional maximization and multicycle EM variants. At the analysis stage, the performance of the devised architectures is assessed both via Monte Carlo simulations and on measured data for some covariance matrix structures of practical interest.

Robust Adaptive Beamforming Based on Subspace Decomposition, Steering Vector Estimation and Correction

Considering that the performance of adaptive arrays is sensitive to any type of mismatches, an innovative robust adaptive beamforming method based on covariance matrix reconstruction, subspace decomposition, steering vector estimation and correction is proposed. Based on Capon spatial spectrum, a group of angle sets containing all interfering signals are determined, and the interference covariance matrix can be reconstructed with a smaller integration interval. On the other hand, the sample covariance matrix can be decomposed into signal subspace and interference-plus-noise by using the principle of maximum correlation. Based on the interference-plus-noise subspace and the reconstructed signal-plus-noise covariance matrix, a new convex optimization model is built to estimate the steering vector of the desired signal. Then, an improved projection approach based on signal subspace is designed for correction to improve the robustness against the nominal direction vector mismatches. Simulation results demonstrate that the proposed method achieves better overall performance under multiple mismatches over a wide range of input signal-to-noise ratios.

Covariance Matrix Reconstruction via a Subspace Method and Spatial Spectral Estimation for Robust Adaptive Beamforming

Several robust adaptive beamforming (RAB) algorithms based on interference plus noise covariance matrix (INCM) reconstruction have been recently proposed, which can enhance the robustness of beamforming algorithms when certain mismatches occur in the model. However, some approaches ignore the resolution of the Capon spectral estimator (CSE), leading to reconstruction errors. This paper proposes a novel RAB algorithm formulated using the subspace projection method and spatial spectral estimation (SSE), which is named INCM-SSE. First, without using the CSE, the subspace projection matrix (SPM) is obtained through the integral of the angular sector where the signal of interest (SOI) is located. Subsequently, after estimating the direction of arrival (DOA) of incident signals using the multiple signal classification (MUSIC) algorithm, we project the sample covariance matrix (SCM) onto the SPM to eliminate the SOI influence. Then, the estimation method of interference powers is derived. Moreover, the INCM is reconstructed based on the estimated powers and steering vector (SV) of interferences. The SV of the SOI is optimized by solving a quadratic convex optimization problem. The INCM-SSE algorithm not only employs SSE to improve the angular resolution but also reduces the influence of the SOI component by using SPM. Simulation results indicate that the proposed method is robust against various types of mismatches, thus achieving superior overall performance.

Sparse Covariance Matrix Reconstruction-Based Nulling Broadening for UAV 2D Antenna Arrays

Since the antennas on UAVs may have slight vibrations or the interference source is in the state of rapid movement in practice, the interference suppression performance and robustness of the traditional methods may suffer a decline. In this paper, we propose a flexible asymmetric null widening technique, which allows flexible adjustment of the null width to accommodate the variation of the interference source. This method has a good effect of spreading zero trap on the two-dimensional array and can effectively reduce the waste of degrees of freedom. Firstly, the flexible asymmetric null widening method is extended to two-dimensional arrays to accommodate 2D array antennas of UAVs. Secondly, when the SMI algorithm is applied in adaptive beamforming, the desired signal appears in sampling snapshots or using data samples, resulting in a model mismatch. To solve the model mismatch problem of UAV antenna arrays, this paper applies a sparsity-based interference plus noise covariance matrix reconstruction technique. Finally, for the application scenario that the UAV may receive signals from multiple directions, we apply the linear constrained minimum variance criterion (LCMV) to achieve the main beam gain formation in multiple directions. The simulation results show that we can generate a wide null and adjust the null width asymmetrically. The results also show that the model mismatch problem is avoided, and the performance of the adaptive beamforming is almost optimal. For the UAV antenna, we also implemented multiple beams to receive multiple signals .

Robust adaptive beamforming based on covariance matrix reconstruction with RCB principle

In this paper, a novel robust adaptive beamforming (RAB) technique based on the covariance matrix reconstruction is proposed to solve the array model mismatch. The proposed technique provides an alternative method to reconstruct the interference-plus-noise covariance matrix (IPNCM) and estimate the steering vector (SV) of the desired signal. In particular, an unknown error exists in the SV of the considered array. The proposed RAB algorithm adopts the robust Capon beamformer (RCB) principle to roughly estimate the SVs of the desired and interference signals. Based on those preliminary estimated SVs, an improved Capon power spectrum is constructed. Then the interference covariance matrix is reconstructed by utilizing the modified Capon power spectrum integrated over the union of several disjoint angular sectors. Then, the reconstructed covariance matrix is further refined by exploring the low rank property. Meanwhile, the SV of the desired signal is estimated by solving a modified quadratically constrained quadratic programming (QCQP) problem. The simulation results show that the RCB principle provides an accurate IPNCM reconstruction, and the proposed RAB algorithm outperforms the existing RAB techniques over a wide range of input signal-to-noise ratio (SNR) region under various mismatch conditions.