Quadratically Constrained Beamforming Robust Against Direction-of-Arrival Mismatch

It is well known that the performance of the minimum variance distortionless response (MVDR) beamformer is very sensitive to steering vector mismatch. Such mismatches can occur as a result of direction-of-arrival (DOA) errors, local scattering, near-far spatial signature mismatch, waveform distortion, source spreading, imperfectly calibrated arrays and distorted antenna shape. In this paper, an adaptive beamformer that is robust against the DOA mismatch is proposed. This method imposes two quadratic constraints such that the magnitude responses of two steering vectors exceed unity. Then, a diagonal loading method is used to force the magnitude responses at the arrival angles between these two steering vectors to exceed unity. Therefore, this method can always force the gains at a desired range of angles to exceed a constant level while suppressing the interferences and noise. A closed-form solution to the proposed minimization problem is introduced, and the diagonal loading factor can be computed systematically by a proposed algorithm. Numerical examples show that this method has excellent signal-to-interference-plus-noise ratio performance and a complexity comparable to the standard MVDR beamformer

Efficient Covariance Matrix Reconstruction with Iterative Spatial Spectrum Sampling

This work presents a cost-effective technique for designing robust adaptive beamforming algorithms based on efficient covariance matrix reconstruction with iterative spatial power spectrum (CMR-ISPS). The proposed CMR-ISPS approach reconstructs the interference-plus-noise covariance (INC) matrix based on a simplified maximum entropy power spectral density function that can be used to shape the directional response of the beamformer. Firstly, we estimate the directions of arrival (DoAs) of the interfering sources with the available snapshots. We then develop an algorithm to reconstruct the INC matrix using a weighted sum of outer products of steering vectors whose coefficients can be estimated in the vicinity of the DoAs of the interferences which lie in a small angular sector. We also devise a cost-effective adaptive algorithm based on conjugate gradient techniques to update the beamforming weights and a method to obtain estimates of the signal of interest (SOI) steering vector from the spatial power spectrum. The proposed CMR-ISPS beamformer can suppress interferers close to the direction of the SOI by producing notches in the directional response of the array with sufficient depths. Simulation results are provided to confirm the validity of the proposed method and make a comparison to existing approachesComment: 14 pages, 8 figure

URGLQ: An Efficient Covariance Matrix Reconstruction Method for Robust Adaptive Beamforming

The computational complexity of the conventional adaptive beamformer is relatively large, and the performance degrades significantly due to both the model mismatch errors and the unwanted signals in received data. In this paper, an efficient unwanted signal removal and Gauss-Legendre quadrature (URGLQ)-based covariance matrix reconstruction method is proposed. Different from the prior covariance matrix reconstruction methods, a projection matrix is constructed to remove the unwanted signal from the received data, which improves the reconstruction accuracy of the covariance matrix. Considering that the computational complexity of most matrix reconstruction algorithms are relatively large due to the integral operation, we proposed a Gauss-Legendre quadrature-based method to approximate the integral operation while maintaining the accuracy. Moreover, to improve the robustness of the beamformer, the mismatch in the desired steering vector is corrected by maximizing the output power of the beamformer under a constraint that the corrected steering vector cannot converge to any interference steering vector. Simulation results and prototype experiment demonstrate that the performance of the proposed beamformer outperforms the compared methods and is much closer to the optimal beamformer in different scenarios.Comment: 11 pages, 16 figure

Study of Robust Adaptive Beamforming Algorithms Based on Power Method Processing and Spatial Spectrum Matching

Robust adaptive beamforming (RAB) based on interference-plus-noise covariance (INC) matrix reconstruction can experience performance degradation when model mismatch errors exist, particularly when the input signal-to-noise ratio (SNR) is large. In this work, we devise an efficient RAB technique for dealing with covariance matrix reconstruction issues. The proposed method involves INC matrix reconstruction using an idea in which the power and the steering vector of the interferences are estimated based on the power method. Furthermore, spatial match processing is computed to reconstruct the desired signal-plus-noise covariance matrix. Then, the noise components are excluded to retain the desired signal (DS) covariance matrix. A key feature of the proposed technique is to avoid eigenvalue decomposition of the INC matrix to obtain the dominant power of the interference-plus-noise region. Moreover, the INC reconstruction is carried out according to the definition of the theoretical INC matrix. Simulation results are shown and discussed to verify the effectiveness of the proposed method against existing approaches.Comment: 7 pages, 2 figure

Minimum Sensitivity Based Robust Beamforming with Eigenspace Decomposition

An enhanced eigenspace-based beamformer (ESB) derived using the minimum sensitivity criterion is proposed with significantly improved robustness against steering vector errors. The sensitivity function is defined as the squared norm of the appropriately scaled weight vector and since the sensitivity function of an array to perturbations becomes very large in the presence of steering vector errors, it can be used to find the best projection for the ESB, irrespective of the distribution of additive noises. As demonstrated by simulation results, the proposed method has a better performance than the classic ESBs and the previously proposed uncertainty set based approach