On the sensitivity of orthogonal beamforming

Orthogonal beamforming is the name of high-resolution methods for estimating the angle spectra of a wavefield received by an array of sensors. The methods, e.g. Pisarenko´s or Owsley´s peak estimates, use the eigenvalues and eigenvectors of the spectral density matrix of the sensor outputs. The problem is the behavior of such methods when only an estimate of the matrix is known. If the spectral density matrix is estimated by one of the classical technics, some asymptotic distributional properties of peak estimators can be found, However, they cannot be calculated since the exact spectral density matrix is unknown. We therefore develop bounds for the deviation of the peak estimates which only use weak knowledge about that matrix by applying some results about perturbation of hermitian operators. Extensive simulations with random matrices were executed to evaluate the new bounds.