Interference-plus-noise Covariance Matrix 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.

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.

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.

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.

A Novel Robust Adaptive Beamforming Algorithm Based on Subspace Orthogonality and Projection

Recently, it has been extensively researched about designing robust adaptive beamforming (RAB) algorithms to deal with model mismatch issues. In this paper, a RAB algorithm is proposed to estimate the steering vectors (SVs) of the incident sources and reconstruct the interference-plus-noise covariance matrix (INCM). First, we construct the error SVs in the noise subspace, which correct the nominal SVs by iterative updates to obtain more accurate estimation of SVs. Then the projection matrix is constructed utilizing the estimated SV of the signal of interest (SOI), and the interference powers are estimated by projecting the sampled covariance matrix (SCM). Furthermore, two virtual interferences are added on both sides of each estimated interference direction to widen the nulls in the corresponding directions of the interferences. Finally, the INCM can be constructed and utilize the estimated SV of the SOI to calculate the weight vector of the beamformer. The proposed method has less computational complexity and the simulation results show that the proposed method is more robust to various types of mismatches in comparison to previous algorithms.

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.

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.

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.

A novel beamforming technique using mmWave antenna arrays for 5G wireless communication networks

Millimeter wave (mmWave) multiple-input multiple-output (MIMO) and beamforming technologies are most likely the integral parts and the key enablers of 5G-and-Beyond (5G-B) wireless communication systems. From that perspective, this manuscript proposes an efficient digital beamforming technique for 5G applications. The suggested approach is formulated based on a reliable sampling technique that effectively samples the interference-plus-noise covariance matrix (IPNCM) to construct an efficient projection matrix (PM). The proposed technique is therefore named interference-plus-noise PM (IPNPM) beamformer. Next, a compact-size rectangular microstrip antenna operating at 49.3 GHz having 1.7 GHz potential bandwidth is designed using CST microwave studio. The designed antenna is subsequently used to model a 32-element uniform linear array (ULA) representing a typical 5G base station. The elements of the modeled ULA are then manually fed with the complex-weights generated from the proposed beamformer to produce high-power beams and deep nulls toward the desired and undesired locations, respectively. To further improve the beamformer performance in terms of minimizing radiating power within undesired regions, an iterative sidelobe level (SLL) suppression technique is developed and integrated with the proposed beamformer. The conducted theoretical analysis justifies that the IPNPM beamformer requires less arithmetic operations than the well-known beamforming approaches. To reveal the benefits of the proposed technique, the array radiation pattern based on the proposed beamformer is plotted and compared with those for the three widely used approaches. An intensive Monte Carlo simulation is also carried out in which the IPNPM beamformer performance is systemically compared with the popular approaches based on the output signal to interference-plus-noise ratio (SINR) criterion. The achieved results demonstrate that the proposed approach is superior and surpasses the rival algorithms in terms of generating deeper nulls, enhanced output SINR, and lower execution time. It is also demonstrated that, unlike the existing SLL reduction techniques, the newly developed SLL suppressor reduces the SLLs of the proposed beamformer to a predefined threshold value (i.e., −24 dB) after few iterations.

A Robust Beamforming Suppressing Deceptive Jamming Method Based On FDA-MIMO Radar

In comparison to phased array (PA) radar that just transmits a beampattern with angle-dependent, frequency diverse array (FDA) radar with adding a feature of distance dimension performs well in main-beam deceptive jamming suppression domain. However, in practical conditions, estimating an inaccuracy of the covariance matrix(CM) has a significant negative impact on algorithm performance, also as a mismatch of target SV has. Hence, a robust adaptive beamforming technique comes up in this article that selects the principal eigenvector to get accurate signal steering vectors (SV), further gets the reconstruction interference-plus-noise CM (IPNCM). According to experiments, the proposed algorithm keeps a robust and good performance under non-ideal circumstances.

Oblique Projection-Based Covariance Matrix Reconstruction and Steering Vector Estimation for Robust Adaptive Beamforming

Adaptive beamforming can efficiently contract interference and noise. Due to high sensitivity of the beamformer to model mismatch, the capability of interference reduction will critically degrade when the signal model mismatch occurs, particularly when the sampling sequence contains the desired signal. For the purpose of enhancing the robustness of beamformers to signal model mismatch, we propose a new robust adaptive beamforming (RAB) method. Firstly, the precise steering vector (SV) associating with the desired signal is estimated by employing the minimum norm of subspace projection (MNSP) approach. Secondly, the nominal interference SVs are estimated via the maximum entropy power spectrum. Subsequently, the corrected interference SVs and powers are obtained by oblique projection. Finally, the interference-plus-noise covariance matrix (INCM) is reconstructed, and the proposed RAB is obtained. Multiple simulations are carried out and demonstrate the robustness of the proposed RAB method.

Robust Adaptive Beamforming Based on Sparse Bayesian Learning and Covariance Matrix Reconstruction

Sparse Bayesian learning (SBL) exploits sparse information from a Bayesian perspective by making sparse prior assumptions about the signal. It has good flexibility in modeling sparse signals and can also achieve good estimation results when the number of samples is low. In this letter, we propose a robust adaptive beamforming (RAB) method based on interference-plus-noise covariance matrix (INCM) reconstruction using SBL. This method derives the fixed point iteration formula of the signal under the Laplace prior distribution by maximizing the marginal likelihood function of the data received by the array. Then the sampling position of the coarse grid in the SBL model is regarded as an adjustable parameter, and it is refined through iteration. By using the superiority of SBL in modeling sparse signals, the steering vectors and power of the source signals are precisely estimated, and an accurate INCM is reconstructed to obtain a high output SINR. The only prior knowledge required is imprecise angular sector knowledge of the desired signal (DS). Simulation results demonstrate that our proposed method achieves near-optimal output SINR over a wide range of input SNR and a limited number of snapshots and even achieves good performance in the single snapshot situation.

Robust Adaptive Beamforming Algorithm for Sparse Subarray Antenna Array Based on Hierarchical Weighting

Sparse antenna arrays based on subarrays have more and more broad application prospects for the limitation of array space, real-time algorithm and hardware costs. Aiming at the beamforming technology of sparse antenna arrays based on subarrays, this paper proposes a robust adaptive beamforming algorithm based on hierarchical weighting. The algorithm performs conventional beamforming to calculate the weights of each element in the subarray, then the synthetic signals output by each subarray are used as sparse array metadata. The Interference-plus-Noise Covariance Matrix (INCM) is reconstructed by integration in two-dimensional space, and a convex optimization model of a multi-constraint array containing the signal pointing error was established to estimate the real guide vector. Finally, using the reconstructed INCM and the estimation of the guide vector, we obtain a weighted vector between the subarrays and output signal for the whole array. The simulation results show that the proposed algorithm has better Signal-to-Interference-and-Noise Ratio (SINR) and robustness compared with other algorithms for sparse subarray antenna array beamforming.

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.

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.

Robust adaptive null broadening beamforming based on subspace projection

ABSTRACT When the rapid moving interference exists, especially in the presence of look direction mismatch, coherent local scattering and so on, the output performance of beamformer will degrade dramatically. To solve this problem, a novel robust adaptive null broadening beamforming method based on subspace projection is proposed. First, the proposed beamformer requires a priori information, that is, the spatial sector where the desired signal and interference may locate, so as to construct the signal-plus-noise covariance matrix (SPNCM) and interference-plus-noise covariance matrix (IPNCM). Then, the desired signal steering vector (SV) is calibrated twice. The desired signal SV is estimated from the SPNCM and subsequently calibrated by using the uncertainty set optimisation method. Next, we construct the null broadening projection matrix by tapering the interference subspace got from IPNCM. Finally, the sample covariance matrix is processed by projection technology and diagonal loading technology. The optimal weight vector is obtained by the new covariance matrix and calibrated desired signal SV. Simulation results show that the proposed method can form wide null in the incident direction of interference and prevent interference from moving out of the null when the rapid moving interference exists. The proposed method outperforms other existing methods.

Robust Adaptive Beamforming Algorithm for Sparse Array Based on Covariance Matrix Reconstruction Technology

When the array structure of the sparse arrays (SA) cannot be determined, the existing beamforming algorithms designed according to specific formations such as coprime arrays (CA), nested arrays (NA), etc. will fail. To solve this problem, we propose two algorithms that are suitable for a variety of SA. In the first method, assuming that the desired signal is a non-Gaussian signal, the desired signal direction vector (DSDV) is estimated using the fourth-order cumulant, and then the interference plus noise covariance matrix (INCM) is reconstructed by integrating the area outside the desired signal. When the desired signal is a Gaussian signal, we propose the second method. The second method estimates the power and direction of arrival (DOA) of the signals by performing eigenvalue decomposition on the sampled covariance matrix (SCM) and finally calculates the weight vector. However, this method needs to estimate the DOA of the signals, so it has certain requirements for the SA structure design. The simulation results show that the proposed method has good performance and strong robustness under different SA.

A Robust Digital Beamforming on Receive in Elevation for Airborne MIMO SAR System

The echo separation issue for multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) is usually regarded as a more technical challenge. Spotlighted as a promising solution to the echo separation, the well-known short-term shift-orthogonal (STSO) beamforming scheme has become increasingly popular. However, for airborne MIMO SAR systems, the digital beamforming (DBF) involved in the STSO scheme usually encounters more issues, e.g., the direction of arrival (DOA) mismatch induced by topography variation. Up to now, relatively less research on robust DBF processing has been conducted for airborne MIMO SAR systems. In this respect, an adaptive DBF technique, based on interference plus noise covariance matrix (IPNCM) reconstruction and desired signal steering vector estimation, has been proposed in this paper. IPNCM reconstruction and steering vector estimation can not only cope with the DOA mismatch problem, but also remove the desired signal component in the training data cells to increase the beamformer convergence rates. Consequently, the proposed approach really improves the array output signal-to-interference-plus-noise ratio (SINR). Moreover, numerous discussions and simulations are carried out to prove the effectiveness of proposed DBF technique under various disturbance environments. Compared with the current DBF techniques, the proposed method provides a bright application prospect for the STSO scheme.

Adaptive beamforming algorithm for coprime array based on interference and noise covariance matrix reconstruction

Compared with the uniform linear array (ULA) under the same physical array element, the coprime array can obtain a higher degree of freedom and a larger array aperture, so it has received extensive attention from scholars in recent years. Based on the idea of interference plus noise covariance matrix (INCM) reconstruction, this study proposed a robust adaptive beamforming algorithm using the coprime array. In the virtual array generated by the coprime array, the authors prove from the perspective of virtual signals that the constructed Toeplitz matrix is equivalent to a virtual ULA with more array elements. Subsequently, a high-resolution subspace algorithm is used to estimate the direction of arrival (DOA) of the signals, and the estimated DOA is used to reconstruct the direction vector (DV) of the coprime array. Through the eigenvalue decomposition of the reconstructed Toeplitz matrix, the corresponding relationship between the eigenvalue and the power is deduced, and the signals and noise power are estimated using the eigenvalue. Finally, combine the DV of the desired signal and the reconstructed INCM to calculate the weight vector of the proposed algorithm. The simulation results prove the superiority and effectiveness of the algorithm.