Subspace topology

Mathematics

Beamforming

Noise (video)

Gene

Algorithm

Image (mathematics)

Statistics

Mathematical optimization

Quadratic equation

Mathematical analysis

Artificial intelligence

Control (management)

Chemistry

Geometry

Constraint (computer-aided design)

Adaptive beamformer

Computer science

Quadratic programming

Control theory (sociology)

Biochemistry

Projection (relational algebra)

Robustness (evolution)

IEEE Transactions on Acoustics Speech and Signal Processing

Adaptive beamforming algorithms can be extremely sensitive to slight errors in array characteristics. Errors which are uncorrelated from sensor to sensor pass through the beamformer like uncorrelated or spatially white noise. Hence, gain against white noise is a measure of robustness. A new algorithm is presented which includes a quadratic inequality constraint on the array gain against uncorrelated noise, while minimizing output power subject to multiple linear equality constraints. It is shown that a simple scaling of the projection of tentative weights, in the subspace orthogonal to the linear constraints, can be used to satisfy the quadratic inequality constraint. Moreover, this scaling is equivalent to a projection onto the quadratic constraint boundary so that the usual favorable properties of projection algorithms apply. This leads to a simple, effective, robust adaptive beamforming algorithm in which all constraints are satisfied exactly at each step and roundoff errors do not accumulate. The algorithm is then extended to the case of a more general quadratic constraint.

Robust adaptive beamforming