A fundamental assumption for most direction finding algorithms is that the spatial correlation structure of the background noise (i.e., the correlation from sensor to sensor) is known to within a multiplicative scalar. In practive, this is often achieved by measuring the array covariance when no signals are present, a procedure which is unavoidably subjected to errors. The presence of undetected weak signals gives rise to similar perturbations. In this paper, the effect of such modeling errors on parametric estimation techniques is examined. First-order expressions for the mean square error (MSE) of the parameter estimates are derived for the deterministic and stochastic maximum likelihood methods and the weighted subspace fitting technique. The spatial noise correlation structures that lead to maximum performance loss are identified under different assumptions. In case of high signal-to-noise ratio, it is found that the MSE can be increased by a factor equal to the number of sensors in the array, as compared to spatially white noise. Furthermore, it is demonstrated that the presence of a relatively weak (- 15 dB) undetected signal can result in a large bias (≈1°) on the estimates of the other signal directions. © 1993.
Viberg, M. (1993). Sensitivity of parametric direction finding to colored noise fields and undermodeling. Signal Processing, 34(2), 207–222. https://doi.org/10.1016/0165-1684(93)90163-5