Sensitivity analysis under model perturbation for weighted eigenspace methods

Eigenspace based spectral methods comprise an important class of direction-of-arrival (DOA) estimates. The authors carry out a sensitivity analysis of weighted eigenspace methods (WEM) via a generalized approach using a particular Taylor series expansion of the cost function under model phase and gain perturbation. The multiple signal classification (MUSIC) algorithm is treated as one example of this general weighted eigenspace class of spectral methods. Central to this study is the second order analysis of WEM. General bias and variance expressions for DOA estimates are derived, which are applicable to a variety of DOA estimation algorithms. Concise and accurate bias and variance expressions for MUSIC are derived. These expressions are valid over a wide range of gain and phase errors. Simulation results are included to validate the analytical results.<>