Signal Steering Vector Mismatches Research Articles

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.

Robust adaptive beamforming for MIMO radar in the presence of covariance matrix estimation error and desired signal steering vector mismatch

Owing to covariance matrix estimation error, desired signal steering vector mismatch, and the existence of target signal in training samples, most of adaptive beamforming algorithms suffer from a great performance degradation. Aim at this, this study proposes a robust adaptive beamforming algorithm for multiple-input-multiple-output radar. To be specific, the sample covariance matrix is replaced by the reconstructed covariance matrix, to narrow the difference between the maximum and minimum noise eigenvalues. In addition, the diagonal loading technique is applied to correct the mismatched desired signal steering vector by maximising the output signal-to-interference-plus-noise ratio of adaptive beamformer, and a simple closed-form solution to loading factor can be further obtained. Computer simulation results demonstrate that the proposed algorithm can efficiently improve the robustness of adaptive beamformer against both covariance matrix estimation error and desired signal steering vector mismatch.

Robust adaptive beamforming method based on desired signal steering vector estimation and interference‐Plus‐noise covariance matrix reconstruction

Here, the authors propose a robust adaptive beamforming method based on desired signal steering vector estimation and interference-plus-noise covariance matrix reconstruction, so as to attenuate the influences of the desired signal steering vector mismatch and the limited training snapshots on the performance of adaptive beamformer. More precisely, the desired signal steering vector is estimated by minimising the sine value of the angle between the presumed desired signal steering vector and the eigenvectors of sample covariance matrix. Besides, the sample covariance matrix is reconstructed by reducing the dispersion extent of the noise eigenvalues and eliminating the desired signal component from the sample covariance matrix. The proposed method can not only accelerate the convergence speed of adaptive beamforming algorithm, but also avoid the desired signal cancellation phenomenon when the desired signal is present in the training snapshots. Simulation results demonstrate the superiority of the proposed method.

Recursive Updating Algorithm for Robust Adaptive Beamforming in a Uniform Circular Array

When the phase-mode transformation technique is used in a uniform circular array, its output performance is known to degrade owing to the approximations applied to the formulation. In this paper, we develop a robust recursive updating algorithm based on the worst-case performance optimization and phase-mode transformation in the uniform circular array, which provides efficient robustness not only against the signal steering vector mismatches, but also against the transformation errors. The proposed algorithm belongs to the class of the diagonal loading technique and the transformation matrix belongs to a certain ellipsoid set. The weight vector is updated by the Lagrange multiplier method, in which the parameters are derived simply. The proposed algorithm has a closed-form solution, in which we analyse the reasonable ranges of two key parameters. The convergence performance and the output SINR performance are also analysed. In additional, the implementation complexity costs of the proposed algorithm and MVDR algorithm are presented in this paper. Our robust algorithm has a low implementation complexity cost and achieves the mean output array SINR consistently close to the optimal one. Simulation results are presented to compare the performances of our algorithm with the conventional algorithms.

Low‐complexity robust adaptive beamforming method for MIMO radar based on covariance matrix estimation and steering vector mismatch correction

In this study, the authors consider a low-complexity robust adaptive beamforming problem in a collocated multiple-input multiple-output (MIMO) radar. This study is motivated by the fact that in practical applications, the conventional adaptive beamforming algorithm for MIMO radar requires a large computational complexity and suffers from a great performance degradation because of the finite number of training snapshots, the desired signal steering vector mismatch and the corruption of training data by the desired signal. Since the dimension of the virtual steering vector of the MIMO radar is relatively large, the proposed method can estimate the covariance matrix by using a low-complexity method to effectively improve the computational efficiency of the adaptive beamforming algorithm and the robustness of the beamformer against the covariance matrix uncertainty. Besides, based on the estimated covariance matrix, the proposed method can also correct the desired signal steering vector mismatch to efficiently prevent the desired signal cancellation phenomenon. Simulation results demonstrate that the performance of the proposed method is always close to that of the optimal processing in a wide range of signal-to-noise ratio or of the number of training snapshots.

Robust Adaptive Beamforming Using Noise Reduction Preprocessing-Based Fully Automatic Diagonal Loading and Steering Vector Estimation

Diagonal loading provides a powerful and effective way to improve the robustness of the standard Capon beamformer. Several parameter-free robust adaptive beamformers (RAB) are considered in this paper. We reveal that the performances of them have somewhat degradation when the number of snapshots or that of sensors is large. To solve this problem, we emphatically study the well-known generalized linear combination-based method, the performance of which may degrade severely when the number of sensors increases, and propose a novel parameter-free technique, which is a combination of noise reduction preprocessing technique and truncated minimum mean square error criterion. As most of the parameter-free RAB techniques are very sensitive to the desired signal steering vector mismatch, this paper further proposes to construct a series connection between these RAB techniques and a steering vector estimation (SVE) method, where the SVE is implemented by a convex optimization technique. Simulation results show that the proposed method can achieve a promising performance in comparison with the competing methods.

Low‐complexity robust adaptive beamforming algorithms exploiting shrinkage for mismatch estimation

This study proposes low-complexity robust adaptive beamforming (RAB) techniques based on shrinkage methods. The authors first review a low-complexity shrinkage-based mismatch estimation batch algorithm to estimate the desired signal steering vector mismatch, in which the interference-plus-noise covariance matrix is also estimated by a recursive matrix shrinkage method. Then they develop low-complexity adaptive recursive versions of stochastic gradient and conjugate gradient to update the beamforming weights, resulting in low-cost robust adaptive algorithms. An analysis of the effect of shrinkage on the estimation procedure is developed along with a computational complexity study of the proposed and existing algorithms. Simulations are conducted in local scattering scenarios and comparisons to existing RAB techniques are provided.

Performance of the SMI beamformer with signal steering vector errors in heterogeneous environments

In this paper, the performance of the sample matrix inversion (SMI) beamformer in heterogeneous environments is examined by taking into account mismatches in the signal steering vector. In a heterogeneous environment, the test and training data have different covariance matrices. An approximate expression for the expectation of the normalized output signal-to-interference-plus-noise ratio (SINR) (i.e., the average SINR loss) is derived with the consideration of both the signal steering vector mismatch and environmental heterogeneity. Simulation results show that the analytical results are very close to the results obtained by using Monte Carlo techniques. This theoretical expression can be used to facilitate the performance evaluation of the SMI beamformer in real scenarios where the mismatch and heterogeneity cannot be neglected.

Robust Adaptive Beamforming against Signal Steering Vector Mismatch and Jammer Motion

Since adaptive beamformer suffers from output performance degradation in the presence of interference nonstationarity and signal steering vector mismatch, a novel robust null broadening adaptive beamforming is proposed. The proposed method is realized by the combination of projection transform and diagonal loading techniques. First, a new projection matrix with null broadening ability is constructed and then projects the array received data onto the projection matrix. With the diagonal loading technique, a new sample covariance matrix is obtained. The theoretical analysis shows that the projection transform operation can expand the incident direction of the interference and improve orthogonality between the signal-plus-interference and the noise subspaces; thus the proposed beamformer can effectively broaden the jammer null and enhance the null depth. The analytical expressions of the proposed algorithm are also provided, which are efficient and easily solved. Simulation results are presented and demonstrated that the proposed beamformer can provide strong robustness against signal steering vector mismatch and jammer motion.

Robust Recursive Algorithm under Uncertainties via Worst-Case SINR Maximization

The performance of traditional constrained-LMS (CLMS) algorithm is known to degrade seriously in the presence of small training data size and mismatches between the assumed array response and the true array response. In this paper, we develop a robust constrained-LMS (RCLMS) algorithm based on worst-case SINR maximization. Our algorithm belongs to the class of diagonal loading techniques, in which the diagonal loading factor is obtained in a simple form and it decreases the computation cost. The updated weight vector is derived by the descent gradient method and Lagrange multiplier method. It demonstrates that our proposed recursive algorithm provides excellent robustness against signal steering vector mismatches and the small training data size and, has fast convergence rate, and makes the mean output array signal-to-interference-plus-noise ratio (SINR) consistently close to the optimal one. Some simulation results are presented to compare the performance of our robust algorithm with the traditional CLMS algorithm.

An adaptive robust fuzzy beamformer for steering vector mismatch and reducing interference and noise

This paper presents an efficient beamformer design that accounts for both signal steering vector mismatches and the trade-off between interference and noise reduction. The empirical results show that substantial performance degradation occurs when the exact signal steering vector for the desired signal is not known. Furthermore, total rejection of interference may increase noise, and vice versa. Therefore, an adaptive robust fuzzy beamformer was designed by adopting the method of fuzzy systems to modify both the value of the signal steering vector and the interference-to-noise ratio. This method uses the first-order Taylor expansion of the object function to modify the mismatches of the signal steering vector, and uses the signal covariance matrix eigendecomposition to adjust the ratio of interference reduction to noise reduction. Simulations confirm that the proposed scheme performance is substantially improved and more robust if the effects of the signal steering vector mismatches and the interference to noise ratio are considered in the beamformer design which is based on expert knowledge.

Doubly Constrained Robust Blind Beamforming Algorithm

We propose doubly constrained robust least-squares constant modulus algorithm (LSCMA) to solve the problem of signal steering vector mismatches via the Bayesian method and worst-case performance optimization, which is based on the mismatches between the actual and presumed steering vectors. The weight vector is iteratively updated with penalty for the worst-case signal steering vector by the partial Taylor-series expansion and Lagrange multiplier method, in which the Lagrange multipliers can be optimally derived and incorporated at each step. A theoretical analysis for our proposed algorithm in terms of complexity cost, convergence performance, and SINR performance is presented in this paper. In contrast to the linearly constrained LSCMA, the proposed algorithm provides better robustness against the signal steering vector mismatches, yields higher signal captive performance, improves greater array output SINR, and has a lower computational cost. The simulation results confirm the superiority of the proposed algorithm on beampattern control and output SINR enhancement.

Robust Adaptive Beamformer for Speech Enhancement Using the Second-Order Extended <formula formulatype="inline"> <tex Notation="TeX">$H_{\infty}$</tex></formula> Filter

This paper presents a novel approach to implement the robust minimum variance distortionless response (MVDR) beamformer. The robust MVDR beamformer is based on the optimization of worst-case performance and provides an excellent robustness against an arbitrary but norm-bounded desired signal steering vector mismatch. For real-time consideration, the beamformer was formulated into state-space observer form and the second-order extended (SOE) Kalman filter was derived. However, the SOE Kalman filter assumes an accurate system dynamic and statistics of the noise signals. These assumptions limit the performance under uncertainties. This paper develops the SOE H∞ filter for the implementation of the robust MVDR beamformer. The estimation criterion in the SOE H∞ filter design is to minimize the worst possible effects of the disturbance signals on the signal estimation errors without a prior knowledge of the disturbance signals statistics. Experimental results demonstrate the performance of the proposed algorithm in a noisy and reverberant environment and show its superiority of the robustness against mismatches over the robust MVDR beamformer based on the SOE Kalman filter.

Modified projection approach for robust adaptive array beamforming

A novel modified projection method is proposed in this paper, which is robust against the signal steering vector mismatch and covariance matrix uncertainty. First, an enhanced covariance matrix estimate based on a shrinkage method is obtained. Then, the desired signal subspace is estimated from the eigenvectors of the enhanced covariance matrix, and a calibrated steering vector of the desired signal is obtained in sequence by projecting the presumed one onto the new estimated desired signal subspace. Finally, the robust adaptive beamformer weight is obtained from the estimated covariance matrix and the calibrated steering vector. Compared with the traditional projection method, the proposed method can work well even at low signal-to-noise ratio. Also, it is not necessary to estimate the number of sources. Simulation results demonstrate the efficiency of the proposed robust method compared with some of the existing ones.

Robust Least Squares Constant Modulus Algorithm to Signal Steering Vector Mismatches

The linearly constrained least squares constant modulus algorithm (LSCMA) may suffer significant performance degradation and lack robustness in the presence of the slight mismatches between the actual and assumed signal steering vectors, which can cause the serious problem of desired signal cancellation. To account for the mismatches, we propose a doubly constrained robust LSCMA based on explicit modeling of uncertainty in the desired signal array response and data covariance matrix, which provides robustness against pointing errors and random perturbations in detector parameters. Our algorithm optimizes the worst-case performance by minimizing the output SINR while maintaining a distortionless response for the worst-case signal steering vector. The weight vector can be optimized by the partial Taylor-series expansion and Lagrange multiplier method, and the optimal value of the Lagrange multiplier is iteratively derived based on the known level of uncertainty in the signal DOA. The proposed implementation based on iterative minimization eliminates the covariance matrix inversion estimation at a comparable cost with that of the existing LSCMA. We present a theoretical analysis of our proposed algorithm in terms of convergence, SINR performance, array beampattern gain, and complexity cost in the presence of random steering vector mismatches. In contrast to the linearly constrained LSCMA, the proposed algorithm provides excellent robustness against the signal steering vector mismatches, yields improved signal capture performance, has superior performance on SINR improvement, and enhances the array system performance under random perturbations in sensor parameters. The on-line implementation and significant SINR enhancement support the practicability of the proposed algorithm. The numerical experiments have been carried out to demonstrate the superiority of the proposed algorithm on beampattern control and output SINR enhancement compared with linearly constrained LSCMA.

Robust blind adaptive beamforming under double constraints

In practical complex communication environments, the performance of linearly constrained constant modulus algorithm (CMA) is known to degrade severely in the presence of even slight signal steering vector mismatches. To overcome the mismatches, a novel robust CMA is proposed for blind adaptive beamforming via the worst-case performance optimization and the oblique projection of signal steering vector, which is based on double constraints on explicit modeling of uncertainties in the desired signal array in this paper. To improve robustness, the weight vector is optimized to involve minimization of a constant modulus algorithm objective function with penalty for the worst-case signal steering vector. The theoretical analysis for our proposed algorithm in terms of SINR and convergence performance is presented in this paper. The proposed robust constrained CMA resolves the problem of interference capture, provides excellent robustness against the signal steering vector mismatches, and improves array output performance. Simulation results are presented to show the excellence of this technique and the main parameters of concern to evaluate the performance are analyzed.

Efficient Robust Blind Beamforming Algorithm

Because blind adaptive beamforming algorithms do not depend on any reference signal, they have found numerous important applications in signal processing. However, the conventional constrained constant modulus algorithm (CMA) may suffer significant performance degradation in the presence of the slight mismatches between the actual and assumed signal steering vectors. In this paper, to combat the mismatches, a novel robust constrained CMA is proposed for implementing double constraints with recursive method updating, which is based on explicit modeling of uncertainties in the desired signal array response. The proposed robust constrained CMA provides an improved robustness against the signal steering vector mismatches, enhances the array system performance under random perturbations in sensor parameters and makes the mean output array SINR consistently close to the optimal one. The performance of the proposed algorithm is compared with that of linear constrained CMA algorithm by computer simulations, the results of which demonstrate a marked improvement in the robustness against signal steering vector mismatches.

Robust Constrained CMA Based on a Bayesian Approach under Quadratic Constraint

CMA has been known as blind adaptive beamforming because it requires no knowledge about the signal except that the transmitted signal waveform has a constant envelope. But in practical applications, the constrained CMA degrades in the presence of both signal steering vector errors and interference nonstationarity. In this paper, we propose robust constrained CMA based on a Bayesian approach under the quadratic constraint, which improves the output performance in nonideal situations. The quadratic constraint on the weight can provide excellent robustness to signal steering vector mismatches and to random perturbations in sensor parameters. It is found that robust constrained CMA under quadratic constraint can reduce successfully the output power of internal noise while cancelling the interference enough. The Lagrange multipliers are updated and added at each step. The proposed algorithm offers faster rate, has better interference suppression, and yields higher SINR and better signal capture performance than the constrained CMA. Via computer simulation, it is show that the proposed algorithm achieves a substantially improved performance.

Robust adaptive beamforming for MIMO radar

In this paper, a new robust adaptive beamforming method is developed for MIMO radar in the presence of unknown mismatches of the desired signal steering vectors. Explicit models of uncertainties in both transmitted and received signal steering vectors are considered. It is shown that the robust adaptive beamforming problem for MIMO radar can be solved by minimizing a convex quadratic cost function based on the optimization of worst-case performance when full DOFs of MIMO radar are used. Whereas, we reformulate the quadratic cost function into a bi-quadratic cost function by adopting a separable form for the weight vector and the minimum point of the new cost function can be efficiently found by combining bi-iterative algorithm (BIA) with second-order cone programming (SOCP). The proposed beamformer has lower computational complexity and faster convergence rate comparable with that of the traditional robust adaptive beamforming algorithms with full DoFs, while, at the same time, it provides better robustness to the non-ideal cases and reduces the training samples required. Numerical experiments with the frequently encountered types of signal steering vector mismatches are provided to demonstrate the effectiveness of the proposed robust adaptive beamforming algorithm as compared with the other robust adaptive beamforming algorithms.

Adaptive beamforming with joint robustness against covariance matrix uncertainty and signal steering vector mismatch

A novel adaptive beamforming algorithm that is robust against covariance matrix uncertainty and the signal steering vector mismatch is proposed. Based on the optimisation of the diagonal loading covariance matrix in the sense of minimum mean square error, the mismatch vector between the actual steering vector and the presumed one is estimated iteratively by solving a quadratic convex optimisation problem, which is then used to update the steering vector to obtain the optimal beamformer.