Analysis of the combined effects of finite samples and model errors on array processing performance

Abstract

Abstract-The principal sources of estimation error in sensor array signal processing applications are the finite sample effects of additive noise and imprecise models for the antenna array and spatial noise statistics. While the effects of these errors have been studied individually, their combined effect has not yet been rigorously analyzed. In this paper, we undertake such an analysis for the class of so-called subspace Jitfing algorithms. In addition to deriving first-order asymptotic expressions for the estimation error, we show that an overall optimal weighting exists for a particular array and noise covariance error model. In a companion paper, the optimally weighted subspace fitting method is shown to be asymptotically equivalent with the more complicated maximum a posteriori estimator. Thus, for the model in question, no other method can yield more accurate estimates for large samples and small model errors. Numerical examples and computer simulations are included to illustrate the obtained results and to verify the asymptotic analysis for realistic scenarios.

On the Angular Resolution Limit for Array Processing in the Presence of Modeling Errors

“…Using the results given in the appendix, the Smith's criterion for the considered model is given (13) Finally, criterion (13) can be rewritten as a third-order polynomial: (14) We also use the same property as in deriving the ARL based on the Lee's criterion: if is the solution of the Smith equation, then is also a solution. Let be the other root, we have Finally, the ARL based on the Smith's criterion is given by (15) where and are given in (7).…”

Capon algorithm mean-squared error threshold SNR prediction and probability of resolution

“…The Capon asymptotic MSE of the estimate in the presence of mismatch is given by (41) where the asymptotic bias can be written (42) Regarding the threshold region of MSE performance, the lesson learned in Section III-A is that the correct weights governing the transition of MSE performance from the no information region to the asymptotic region are those given by the interval error probabilities relative to the local interval of the global maximum of the ambiguity function. Thus, the total MSE for this Capon parameter estimate can be approximated by (43) where the interval error probabilities are approximated by the dominant pairwise error probability of the UB sum (44) Note that the estimation error is with respect to the assumed true target angle , but the error probabilities are with respect to the location of the true global maximum of the ambiguity function . Equations (41)-(44) represent the first generalization of MIE MSE prediction to encompasses signal model mismatch.…”

“…The goal of this analysis is to accurately predict the threshold SNR point for the Capon algorithm, as well as the threshold region of the MSE curve, accounting for finite sample effects [9], [21] and colored noise. Some consideration is given to the issue of signal model mismatch [10], [43], [44] that, in practice, often limits achievable performance. It is also desired to provide a measure of the probability of resolution for the Capon algorithm that accounts for finite sample effects, colored noise, and signal model mismatch.…”

Complex-valued ICA utilizing signal-subspace demixing for robust DOA estimation and blind signal separation

“…During the last decade, there are several array processing techniques proposed in the literatures [5], [7][8][9] to reduce the array sensitivity for radio source localization in the presence of unknown array model perturbations. Optimal weightings that ignore the finite sample effects of noise have been developed for MUSIC [5] and the the weighted subspace fitting technique [7] A more general analysis in [8] includes the effects of noise and presents a weighted subspace fitting method whose DOA estimates asymptotically achieve the Cramér-Rao bound for general array error models. The statistical DOA properties of MUSIC and ESPRIT under the combined effects of finite samples and model errors have been studied in [9].…”