Interference-plus-noise Covariance Research Articles

New convex approaches to general MVDR robust adaptive beamforming problems

AbstractConsider general minimum variance distortionless response (MVDR) robust adaptive beamforming problems based on the optimal estimation for both the desired signal steering vector and the interference‐plus‐noise covariance (INC) matrix. The optimal robust adaptive beamformer design problem is an array output power maximization problem, subject to three constraints on the steering vector, namely, a (convex or nonconvex) quadratic constraint ensuring that the direction‐of‐arrival (DOA) of the desired signal is separated from the DOA region of all linear combinations of the interference steering vectors, a double‐sided norm constraint, and a similarity constraint; as well as a ball constraint on the INC matrix, which is centered at a given data sample covariance matrix. To tackle the nonconvex problem, a new tightened semidefinite relaxation (SDR) approach is proposed to output a globally optimal solution; otherwise, a sequential convex approximation (SCA) method is established to return a locally optimal solution. The simulation results show that the MVDR robust adaptive beamformers based on the optimal estimation for the steering vector and the INC matrix have better performance (in terms of, e.g., the array output signal‐to‐interference‐plus‐noise ratio) than the existing MVDR robust adaptive beamformers by the steering vector estimation only.

Covariance matrix reconstruction with iterative mismatch approximation for robust adaptive beamforming

The covariance matrix reconstruction based robust adaptive beamforming (RAB) methods overcome the performance degradation due to the imprecise knowledge of the steering vector and the covariance matrix. However, high complexity limits the application of them. In this paper, we proposed a new RAB method based on interference plus noise covariance (INC) matrix reconstruction and desired signal steering vector estimation. In this method, nominal interference steering vectors are estimated by the Capon spatial spectrum, as well as noise power. Subsequently, the iterative mismatch approximation algorithm based on maximizing the beamformer output power is proposed to estimate all the incident signal steering vectors and powers, and the INC matrix is reconstructed. Finally, the beamformer is determined by the estimated INC matrix and desired signal steering vector. Simulation results indicate that the proposed method obtains better performance than other existed methods at both the high signal to noise ratio (SNR) and the complexity.

Robust adaptive beamforming based on virtual sensors using low-complexity spatial sampling

The performance of robust adaptive beamforming (RAB) based on interference-plus-noise covariance (IPNC) matrix reconstruction can be degraded seriously in the presence of random mismatches (look direction and array geometry), particularly when the input signal-to-noise ratio (SNR) is high. In this work, we present a RAB technique to address covariance matrix reconstruction problems. The proposed RAB technique involves IPNC matrix reconstruction using a low-complexity spatial sampling process (LCSSP) and employs a virtual received array vector. In particular, the power spectrum sampling is realized by a proposed projection matrix in a higher dimension. The essence of the proposed technique is to avoid reconstruction of the IPNC matrix by integrating over the angular sector of the interference-plus-noise region. Simulation results are presented to verify the effectiveness of the proposed RAB approach.

Robust Adaptive Beamforming with Optimal Covariance Matrix Estimation in the Presence of Gain-Phase Errors.

An adaptive beamformer is sensitive to model mismatch, especially when the desired signal exists in the training samples. Focusing on the problem, this paper proposed a novel adaptive beamformer based on the interference-plus-noise covariance (INC) matrix reconstruction method, which is robust with gain-phase errors for uniform or sparse linear array. In this beamformer, the INC matrix is reconstructed by the estimated steering vector (SV) and the corresponding individual powers of the interference signals, as well as noise power. Firstly, a gain-phase errors model of the sensors is deduced based on the first-order Taylor series expansion. Secondly, sensor gain-phase errors, the directions of the interferences, and the desired signal can be accurately estimated by using an alternating descent method. Thirdly, the interferences and noise powers are estimated by solving a quadratic optimization problem. To reduce the computational complexity, we derive the closed-form solutions of the second and third steps with compressive sensing and total least squares methods. Simulation results and measured data demonstrate that the performance of the proposed beamformer is always close to the optimum, and outperforms other tested methods in the case of gain-phase errors.

Robust Null Broadening Beamforming Based on Covariance Matrix Reconstruction via Virtual Interference Sources.

When jammers move rapidly or an antenna platform travels at high speed, interference signals may move out of the null width in the array beampattern. Consequently, the interference suppression performance can be significantly degraded. To solve this problem, both the null broadening technique and robust adaptive beamforming are considered in this paper. A novel null broadening beamforming method based on reconstruction of the interference-plus-noise covariance (INC) matrix is proposed, in order to broaden the null width and offset the motion of the interfering signals. In the moving case, a single interference signal can have multiple directions of arrival, which is equivalent to the existence of multiple interference sources. In the reconstruction of the INC matrix, several virtual interference sources are set up around each of the actual jammers, such that the nulls can be broadened. Based on the reconstructed INC and signal-plus-noise covariance (SNC) matrices, the steering vector of the desired signal can be obtained by solving a new convex optimization problem. Simulation results show that the proposed beamformer can effectively broaden the null width and deepen the null depth, and its performance in interference cancellation is robust against fast-moving jammers or array platform motion. Furthermore, the null depth can be controlled by adjusting the power parameters in the reconstruction process and, if the direction of interference motion is known, the virtual interference sources can be set to achieve better performance.

A robust STAP beamforming algorithm for GNSS receivers in high dynamic environment

In high dynamic environment, the output performance of the space-time adaptive processing (STAP) beamformer can be degraded dramatically since directions of arrival (DOAs) corresponding to interferences change rapidly. A novel robust STAP beamforming algorithm is proposed for global navigation satellite system (GNSS) receivers to broaden the nulls towards interferences and meanwhile fight against the steering vector (SV) mismatch caused by DOA estimation errors. Firstly, the received signal model in high dynamic environment is established for the STAP architecture. Then, the spatial-temporal interference plus noise covariance (INC) matrix is obtained by reconstructing the interference covariance matrix and noise covariance matrix respectively to avoid DOA estimation of GNSS signals, which can also remove the signal of interest (SOI) component from the sample covariance matrix (SCM). Furthermore, the spatial-temporal spectrum estimates around interferences are respectively reset to be the same as those of interferences, due to which the nulls towards interferences in the space domain can be widened in high dynamic environment. Finally, the constraints to solve weight vector is specially designed for GNSS signals. Simulation results show that the proposed algorithm can broaden the nulls effectively and also has a better output carrier-to-noise (C/No) ratio performance than the other involving algorithms.

Robust adaptive beamforming using a novel signal power estimation algorithm

Recently, many robust adaptive beamforming (RAB) methods based on covariance matrix reconstruction have been proposed. Motivated by the idea, in this paper, a novel and efficient signal power estimator is devised to reconstruct the interference-plus-noise covariance (INC) matrix, with the corresponding RAB algorithm proposed. Firstly, the steering vectors of the incoming sources are derived using the Capon spatial spectrum and known array geometry. Secondly, a set of linear equations is established based on the signal subspace projection, from which the powers of the incoming sources are estimated. Based on the presumed angular sector of the signal-of-interest (SOI), the steering vectors and powers of the SOI and interferences are distinguished, and the INC matrix is then reconstructed. Finally, the beamformer is determined by the estimated INC matrix and SOI steering vector. The proposed algorithm is computationally more efficient than other reconstruction-based methods because there are closed-form solutions for the signal powers. Simulation results indicate that our proposed algorithm performs better than the existing methods at high signal-to-noise ratios (SNRs), and achieves nearly optimal performance across a wide range of SNR.

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.

Sum-MSE Gain of DFT-Based Channel Estimator Over Frequency-Domain LS One in Full-Duplex OFDM Systems

In this paper, we make an investigation on the sum-mean-square-error (Sum-MSE) performance gain in full-duplex orthogonal frequency-division multiplexing (OFDM) systems in the presence of colored interference-plus-noise (IPN). This gain is defined as the ratio of Sum-MSE of frequency-domain least-square (LS) channel estimator to that of DFT-based LS one. The closed-form formula of the gain is derived. And, its simple upper and lower bounds are given using inequalities of matrix eigenvalues. The exact value of Sum-MSE gain depends heavily on the correlation factor of the IPN covariance matrix. More importantly, we also find that the Sum-MSE performance gain grows from 1 to $N/L$ as the correlation factor gradually decreases from 1 to 0, where $N$ and $L$ denote the number of total subcarrier and the length of cyclic prefix, respectively. Also, via theoretical analysis, the exact Sum-MSE gain degenerates into 1 and $N/L$ in two extreme scenarios: fully-correlated and white, respectively. The former 1 means there is no performance gain, while the latter $N/L$ corresponds to the maximum Sum-MSE performance gain achievable. Numerical simulation further validates the above results. Additionally, the derived lower bound is shown to be closer to the exact value of Sum-MSE gain compared to the upper bound.

Covariance Matrix Reconstruction With Interference Steering Vector and Power Estimation for Robust Adaptive Beamforming

To ensure link reliability and signal receiving quality, robust adaptive beamforming (RAB) is vital important in mobile communications. In this paper, we propose a new RAB algorithm based on interference-plus-noise covariance (INC) matrix reconstruction and steering vector (SV) estimation. In this method, the INC matrix is reconstructed by estimating all interferences SVs and powers, as well as the noise power. The interference SVs are estimated by using the Capon spatial spectrum together with robust Capon beamforming principle, subsequently the interference powers are estimated based on the orthogonality between different signal SVs. On the other hand, the desired signal SV is estimated via maximizing the beamformer output power by solving a quadratic convex optimization problem. The proposed algorithm only needs to know in advance the array geometry and angular sector, in which the desired signal lies. Simulation results indicate that the proposed algorithm outperforms the existing RAB techniques in terms of the overall performance in cases of various mismatches.

Robust Adaptive Beamforming Against Mutual Coupling Based on Mutual Coupling Coefficients Estimation

In an adaptive beamforming system, the mutual coupling effects among the array elements can seriously degrade the system performance. In this paper, we propose a robust adaptive beamforming algorithm using a uniform linear array (ULA) to mitigate the mutual coupling effects. The proposed algorithm is based on the fact that the mutual coupling matrix (MCM) of a ULA can be approximated as a banded symmetric Toeplitz matrix as the mutual coupling between two sensors is inversely related to their separation and is negligible for a few wavelengths away. By exploiting the structural characteristics of the MCM, a subspace-based method is used to estimate the mutual coupling coefficients of the ULA that yield a closed-form solution, and the MCM is further constructed. Then, the constructed MCM and array received data are used to reconstruct the interference-plus-noise covariance (INC) matrix. Finally, the robust adaptive beamformer is created through using the Capon principle and the reconstructed INC matrix. Unlike most of the existing algorithms, the proposed algorithm only requires prior knowledge of the array geometry. Simulation results indicate that our approach outperforms the compared algorithms in the presence of unknown mutual coupling and can achieve a performance close to the theoretical optimal value.

Interference-plus-Noise Covariance Matrix Reconstruction via Spatial Power Spectrum Sampling for Robust Adaptive Beamforming

Recently, a robust adaptive beamforming (RAB) technique based on interference-plus-noise covariance (INC) matrix reconstruction has been proposed, which utilizes the Capon spectrum estimator integrated over a region separated from the direction of the desired signal. Inspired by the sampling and reconstruction idea, in this paper, a novel method named spatial power spectrum sampling (SPSS) is proposed to reconstruct the INC matrix more efficiently, with the corresponding beamforming algorithm developed, where the covariance matrix taper (CMT) technique is employed to further improve its performance. Simulation results are provided to demonstrate the effectiveness of the proposed method.

Robust adaptive beamforming based on the effectiveness of reconstruction

The beamformers by joint estimation of the steering vector (SV) and the reconstructed interference-plus-noise covariance (INC) matrix have been investigated. However, few of them concerned about the effectiveness of reconstruction. In this paper, a novel beamformer is proposed, which introduces the improve factor (IF) to evaluate the improvement scale of output signal-to-interference-plus-noise ratio (SINR) with and without reconstruction. By exploiting the relationship between the IF and input signal-to-noise ratio (SNR), it can be made a trade off between the extent of the performance improved and computational load that reconstruction required. Therefore, the SV is estimated at first, and then the level of SNR determines whether the INC matrix is required to reconstruct. During the implementation, a spherical uncertainty set and the sparsity of interference direction are used. Simulation results indicate that the proposed beamformer has better performance compared with existing adaptive beamforming algorithms.

Robust Adaptive Beamforming Using a Low-Complexity Shrinkage-Based Mismatch Estimation Algorithm

In this work, we propose a low-complexity robust adaptive beamforming (RAB) technique which estimates the steering vector using a Low-Complexity Shrinkage-Based Mismatch Estimation (LOCSME) algorithm. The proposed LOCSME algorithm estimates the covariance matrix of the input data and the interference-plus-noise covariance (INC) matrix by using the Oracle Approximating Shrinkage (OAS) method. LOCSME only requires prior knowledge of the angular sector in which the actual steering vector is located and the antenna array geometry. LOCSME does not require a costly optimization algorithm and does not need to know extra information from the interferers, which avoids direction finding for all interferers. Simulations show that LOCSME outperforms previously reported RAB algorithms and has a performance very close to the optimum.