Signal Steering Vector Research Articles

Adaptive detection in the presence of signal mismatch

The problem of adaptive detection in the situation of signal mismatch is considered; that is, the actual signal steering vector is not aligned with the nominal one. Two novel tunable detectors are proposed. They can control the degree to which the mismatched signals are rejected. Remarkably, it is found that they both cover existing famous detectors as their special cases. More importantly, they possess the constant false alarm rate (CFAR) property and achieve enhanced mismatched signal rejection or improved robustness than their natural competitors. Besides, they can provide slightly better matched signals detection performance than the existing detectors.

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.

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.

A blind beamforming algorithm for multitarget signals based on time-frequency analysis

The existing blind beamforming methods are effective only under the condition that the source signals have some special statistical or structural characteristics. Additionally, the structure of cascade model is complicated and the stability of parallel model is poor when dealing with multi-target signals. To address these problems, a novel blind beamforming algorithm for multi-target signals based on time-frequency (TF) analysis is proposed in this paper. The received array signals are first transformed into time-frequency domain by using quadratic time-frequency distributions (TFDs). Then, the single-source auto-term TF points which show energy concentration at a single signal are extracted through three operations:(i) removing noise points by setting a reasonable threshold, (ii) separating auto-term TF points from cross-term points, and (iii) selecting the single-source auto-term TF points from the auto-term ones. Moreover, these single-source auto-term TF points are classified by the principal eigenvector of their spatial time-frequency distribution matrixes. For each class of TF points, the uncertain set of signal steering vector is given, whose radius is defined as the ultimate range between the center and the elements in the class. Within the uncertain set, an optimization algorithm is provided to get the optimal estimation of the signal steering vector. Finally, the blind beamforming for multi-target signals is achieved based on the Capon method, which can enhance the desired signals and suppress the noise and interference signals. In addition, the influence of parameters selection, the clustering method of unknown source number, and the computational complexity of the proposed algorithm are analyzed. The proposed algorithm can achieve parallel output of multi-target signals under the condition that the array manifold and the direction of arrival (DOA) are unknown. Also, the complex iterative solving processing may be avoided and special limitations on signal characteristics are unnecessary. As a result, it has wide applicability and superior stability compared with the existing blind beamforming methods. Simulations illustrate that the proposed algorithm can well separate multi-target signals which are TF-nondisjoint to a certain extent. It can achieve a higher output signal to interference plus noise ratio (SINR) compared with the constant modulus algorithm (CMA), the independent component analysis (ICA) algorithm, and the joint approximate diagolization of eigenmald (JADE) algorithm. Furthermore, the output performance of the proposed algorithm is close to the optimal Capon beamformer.

Detection of a distributed target with direction uncertainty

In this study, the authors deal with the problem of detecting a distributed target in coloured noise with unknown covariance matrix. The target echoes are all assumed to come from the same direction. However, the exact direction is unknown a priori. Precisely, the signal steering vector lies in a certain known subspace, but with unknown coordinate. They derive the Wald test and two-step Wald test and also show that there is no meaningful Rao test or its two-step variation. Moreover, it is found that the two-step Wald test is equivalent to an existing direction detector. Additionally, it is shown that the Wald test possesses the constant false alarm rate property. Some numerical examples are given to compare the detection performance of the novel direction detector with its counterparts, both in the cases of matched and mismatched signals.

Fully automatic robust adaptive beamforming using the constant modulus feature

The diagonal loading (DL) technique is the most widely used method to improve the robustness of the Capon beamformer in the presence of imprecise knowledge of the covariance matrix and the desired signal's steering vector. The selection of the DL level is challenging in practice and might depend on some user-defined parameters which are possibly hard to be determined. A fully automatic and training-free method for the DL level selection is herein presented to extract the desired signal with constant modulus, which is a common feature for communication signals. Simulated results of the beamforming performance have demonstrated the efficacy of the proposed method.

A robust adaptive beamforming method based on the matrix reconstruction against a large DOA mismatch

A novel adaptive beamforming algorithm against large direction-of-arrival (DOA) mismatch without using optimization toolboxes is proposed. In contrast to previous works, this new beamformer employs two reconstructed matrices, the interference-plus-noise covariance matrix and the desired signal-plus-noise covariance matrix, instead of their real sample covariance matrix, respectively. These reconstructed covariance matrices are used to obtain an orthogonal subspace, which is orthogonal to the interference subspace and contains the desired signal subspace. Without estimating the desired signal steering vector, an optimal weight can finally be solved by rotating this orthogonal subspace based on the output power of the desired signal maximization. This novel beamformer is able to keep a steady and outstanding performance when DOA mismatch has a large uncertainty level. Moreover, this algorithm overcomes the problem of the desired signal self-cancelation at high signal-to-noise ratio (SNR) while maintaining the good performance at low SNR.

Precise calibration of a GNSS antenna array for adaptive beamforming applications.

The use of global navigation satellite system (GNSS) antenna arrays for applications such as interference counter-measure, attitude determination and signal-to-noise ratio (SNR) enhancement is attracting significant attention. However, precise antenna array calibration remains a major challenge. This paper proposes a new method for calibrating a GNSS antenna array using live signals and an inertial measurement unit (IMU). Moreover, a second method that employs the calibration results for the estimation of steering vectors is also proposed. These two methods are applied to the receiver in two modes, namely calibration and operation. In the calibration mode, a two-stage optimization for precise calibration is used; in the first stage, constant uncertainties are estimated while in the second stage, the dependency of each antenna element gain and phase patterns to the received signal direction of arrival (DOA) is considered for refined calibration. In the operation mode, a low-complexity iterative and fast-converging method is applied to estimate the satellite signal steering vectors using the calibration results. This makes the technique suitable for real-time applications employing a precisely calibrated antenna array. The proposed calibration method is applied to GPS signals to verify its applicability and assess its performance. Furthermore, the data set is used to evaluate the proposed iterative method in the receiver operation mode for two different applications, namely attitude determination and SNR enhancement.

Uni-Vector-Sensor Dimensionality Reduction MUSIC Algorithm for DOA and Polarization Estimation

This paper addresses the problem of multiple signal classification- (MUSIC-) based direction of arrival (DOA) and polarization estimation and proposes a new dimensionality reduction MUSIC (DR-MUSIC) algorithm. Uni-vector-sensor MUSIC algorithm provides estimation for DOA and polarization; accordingly, a four-dimensional peak search is required, which hence incurs vast amount of computation. In the proposed DR-MUSIC method, the signal steering vector is expressed in the product form of arrival angle function matrix and polarization function vector. The MUSIC joint spectrum is converted to the form of Rayleigh-Ritz ratio by using the feature where the 2-norm of polarization function vector is constant. A four-dimensional MUSIC search reduced the dimension to two two-dimensional searches and the amount of computation is greatly decreased. The theoretical analysis and simulation results have verified the effectiveness of the proposed 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.

Maximally Robust Capon Beamformer

The standard Capon beamformer (SCB) achieves the maximum output signal-to-interference-plus-noise ratio in the error-free case. However, estimation errors of the signal steering vector and the array covariance matrix can result in severe performance deteriorations of the SCB, especially if the training data contains the desired signal component. A popular technique to improve the robustness against model errors is to compute the Capon beamformer with the maximum output power, considering an uncertainty set for the signal steering vector. However, maximizing the total beamformer output power may result in an insufficient suppression of interferers and noise. As an alternative approach to mitigate the detrimental effect of model errors, we propose to compute the Capon beamformer with the minimum sensitivity, considering the uncertainty set for the signal steering vector. The proposed maximally robust Capon beamformer (MRCB) is at least as robust as the maximum output power Capon beamformer with the same uncertainty set for the signal steering vector. We show that the MRCB can be implemented efficiently using Lagrange duality. Simulation results demonstrate that the MRCB outperforms state-of-the-art robust adaptive beamformers in many scenarios.

Using Single-Cycle-Related Electromagnetic Vector Sensors to Estimation DOA and Polarization Parameters

This paper proposes a new algorithm for joint estimation of Directions-Of-Arrival (DOA’s) and polarization parameters of the single electromagnetic vector sensor. Based on the cyclostationary properties of the signal,the algorithm uses minimum norm method to strike the signal steering vector solution, and then gets the estimation of DOA and polarization parameters. Besides limiting the distribution of additional stationary noise and interference signals on various frequencies, this algorithm also restraints the estimation error of the noise subspace singular vector with outstanding results. Computer simulation verified the effectiveness of the algorithm.

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.

Self-Contained Antenna Array Calibration using GNSS Signals

Antenna array processing techniques require calibration algorithms that often rely on the availability of signal sources at known locations, a good knowledge of the array manifold, or a reference antenna. An alternative is provided by GNSS signals that provide the location of their sources as part of their navigation data. In this paper, a projection methodology using GNSS signals is proposed for the calibration of antenna arrays. The Gram Schmidt process is used along with the properties of the signal steering vectors to determine linear relationships between the recovered signals and the calibration parameters. The obtained system of equations is then solved in the Minimum Mean Square Error (MMSE) sense leading to the estimated calibration parameters. The proposed algorithm accounts for signal gain/phase mismatches and mutual coupling between array elements. Finally, the effectiveness of the proposed technique and its suitability for beamforming and Direction-of-Arrival (DoA) applications is supported by several experiments performed using live GPS signals and a GNSS software receiver. Copyright © 2012 Institute of Navigation.

Robust Adaptive Beamforming Based on Steering Vector Estimation With as Little as Possible Prior Information

A general notion of robustness for robust adaptive beamforming (RAB) problem and a unified principle for minimum variance distortionless response (MVDR) RAB techniques design are formulated. This principle is to use standard MVDR beamformer in tandem with an estimate of the desired signal steering vector found based on some imprecise prior information. Differences between various MVDR RAB techniques occur only because of the differences in the assumed prior information and the corresponding signal steering vector estimation techniques. A new MVDR RAB technique, which uses as little as possible and easy to obtain imprecise prior information, is developed. The objective for estimating the steering vector is the maximization of the beamformer output power, while the constraints are the normalization condition and the requirement that the estimate does not converge to any of the interference steering vectors and their linear combinations. The prior information used is only the imprecise knowledge of the antenna array geometry and angular sector in which the actual steering vector lies. Mathematically, the proposed MVDR RAB is expressed as the well known non-convex quadratically constrained quadratic programming problem with two constraints, which can be efficiently and exactly solved. Some new results for the corresponding optimization problem such as a new algebraic way of finding the rank-one solution from the general-rank solution of the relaxed problem and the condition under which the solution of the relaxed problem is guaranteed to be rank-one are derived. Our simulation results demonstrate the superiority of the proposed method over other previously developed RAB techniques.

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.

Adaptive Beamforming for Uniform Linear Arrays With Unknown Mutual Coupling

This letter proposes a new adaptive beamforming algorithm for uniform linear arrays (ULAs) with unknown mutual coupling. It 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 sensor elements is inversely related to their separation, and hence it is negligible when they are separated by a few wavelengths. Taking advantage of this specific structure of the MCM, a new approach to calibrate the signal steering vector is proposed. By incorporating this improved steering vector estimate with a diagonally loaded robust beamformer, a new adaptive beamformer for ULA with unknown mutual coupling is obtained. Simulation results show that the proposed steering vector estimate considerably improves the robustness of the beamformer in the presence of unknown mutual coupling. Moreover, with appropriate diagonal loading, it is found that the proposed beamformer can achieve nearly optimal performance at all signal-to-noise ratio (SNR) levels.

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.