Robust minimum variance beamforming

By Robert G. Lorenz, Stephen P. Boyd. IEEE Transactions on Signal Processing, 2005

648 citations recorded by the source corpus.

This paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response. Sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold. In our method, uncertainty in the array manifold is explicitly modeled via an ellipsoid that gives the possible values of the array for a particular look direction. We choose weights that minimize the total weighted power output of the array, subject to the constraint that the gain should exceed unity for all array responses in this ellipsoid. The robust weight selection process can be cast as a second-order cone program that can be solved efficiently using Lagrange multiplier techniques. If the ellipsoid reduces to a single point, the method coincides with Capon's method. We describe in detail several methods that can be used to derive an appropriate uncertainty ellipsoid for the array response. We form separate uncertainty ellipsoids for each component in the signal path (e.g., antenna, electronics) and then determine an aggregate uncertainty ellipsoid from these. We give new results for modeling the element-wise products of ellipsoids. We demonstrate the robust beamforming and the ellipsoidal modeling methods with several numerical examples.

Subfields: Aerospace Engineering, Civil and Structural Engineering, Signal Processing

View Paper: https://www.semanticscholar.org/paper/4d64ce87dfd8daacf12040cfc0eadf0a3bab60e1

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Citations in the corpus

Robust Adaptive Beamforming Based on Interference Covariance Matrix Reconstruction and Steering Vector Estimation (2012, methodology): “In this category, the worst-case performance optimization-based adaptive beamforming technique [2], [6]–[8] makes explicit use of an uncertainty set of the signal steering vector.”
Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem (2003, background): “Note, however, that it is not easy to use (32) directly for computing the optimal weight vector because it is not clear how to obtain the Lagrange multiplier in a closed form [26].”
Theory and Applications of Robust Optimization (2010, background): “Antenna design: Lorenz and Boyd [71] consider the problem of building an array antenna with minimum variance when the underlying array response is not known exactly.”
Principles of minimum variance robust adaptive beamforming design (2013, methodology): “An ellipsoidal uncertainty region can also be considered instead of the mentioned above spherical uncertainty [60].”
Radar-Based Breast Cancer Detection Using a Hemispherical Antenna Array—Experimental Results (2009, methodology): “The problem (6) can be solved using the Lagrange multiplier method [25], [30]”
Real-Time Convex Optimization in Signal Processing (2010, methodology): “More recently, convex optimization has been used to design array weights that are robust to variations in the signal statisti cs or array response [39], [40].”
A Consolidated Perspective on Multimicrophone Speech Enhancement and Source Separation (2017, neutral): “It is a widely-explored area in the field of array processing [369]–[371].”
Doubly constrained robust Capon beamformer (2004, methodology): “In [24], a polyhedron is used to describe the uncertainty set, whereas spherical and ellipsoidal (including flat ellipsoidal) uncertainty sets are considered in [10]–[12] and [25].”
MIMO Radar Waveform Optimization With Prior Information of the Extended Target and Clutter (2009, methodology): “In [36], similar result has been obtained for solving beamformer robust against steering vector mismatch.”
On robust Capon beamforming and diagonal loading (2003, methodology): “The solution to (5) is easily derived: (6) Using (6) in Step b) above yields the following estimate of : (7)”
A robust maximin approach for MIMO communications with imperfect channel state information based on convex optimization (2006, background): “The classical Capon’s beamformer [31] was extended to its robust version in [32]–[34] taking generic uncertainty regions and different formulations.”
Convex Optimization-Based Beamforming (2010, methodology): “The key idea of the beamformer developed in [4] and, independently, in [7], is to explicitly model the steering vector uncertainty as d ! a s2 as where a | s and as are the actual and presumed signal steering vectors, respectively; and to assume that the Euclidean norm of d is upper-bounded by a kno”