1987/10/01 by H. Cox, Henry Cox, R. Zeskind +3 · 1,661 citations
Computer Science · Engineering · Mathematics · #Adaptive beamformer #Advanced Adaptive Filtering Techniques #Algorithm #Artificial intelligence #Beamforming #Computer science #Constraint (computer-aided design) #Control theory (sociology) #Direction-of-Arrival Estimation Techniques #Mathematical analysis #Mathematical optimization #Mathematics #Noise (video) #Projection (relational algebra) #Quadratic equation #Quadratic programming #Robustness (evolution) #Speech and Audio Processing #Statistics #Subspace topology
paper · doi:10.1109/tassp.1987.1165054
published in IEEE Transactions on Acoustics Speech and Signal Processing 35(10), 1365-1376 (Institute of Electrical and Electronics Engineers)
openalex publication_date 1987/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.