CRLB for DOA Estimation in Gaussian and Non-Gaussian Mixed Environments

The determination of Cramer-Rao lower bound (CRLB) as an optimality criterion for the problem of Direction-of-arrival (DOA) estimation is a very important issue. Several CRLBs on DOA estimation have been derived for Gaussian noise. However, a practical channel is affected by not only Gaussian background noise but also non-Gaussian noise such as impulsive interference. This paper derives the deterministic CRLB for Gaussian and non-Gaussian mixed environments. Since non-parametric kernel method is used to build the probability density function (PDF) of non-Gaussian noise, the CRLB derived is suitable for various noise distributions with or without symmetric PDF. The relationship between the CRLB for Gaussian noise and the proposed CRLB is also investigated. Theoretical analysis shows that the proposed CRLB provides a unified representation for both the cases of Gaussian and mixed environments. Computer simulations are included to verify the derived CRLB in different noise environments.

[1]  Hao Ye,et al.  Maximum likelihood DOA estimation and asymptotic Cramer-Rao bounds for additive unknown colored noise , 1995, IEEE Trans. Signal Process..

[2]  Petre Stoica,et al.  MUSIC, maximum likelihood, and Cramer-Rao bound , 1989, IEEE Transactions on Acoustics, Speech, and Signal Processing.

[3]  Vladimir V. Lukin,et al.  Robust DFT with high breakdown point for complex-valued impulse noise environment , 2006, IEEE Signal Processing Letters.

[4]  Ying Zhang,et al.  Support Vector Regression for Basis Selection in Laplacian Noise Environment , 2007, IEEE Signal Processing Letters.

[5]  D. W. Scott,et al.  Multivariate Density Estimation, Theory, Practice and Visualization , 1992 .

[6]  C. L. Nikias,et al.  Signal processing with alpha-stable distributions and applications , 1995 .

[7]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[8]  Tatsuo Itoh,et al.  Adaptive Robust DOA Estimation for a 60-GHz Antenna-Array System , 2007, IEEE Transactions on Vehicular Technology.

[9]  Brian M. Sadler,et al.  Maximum-likelihood array processing in non-Gaussian noise with Gaussian mixtures , 2000, IEEE Trans. Signal Process..

[10]  Sergiy A. Vorobyov,et al.  Maximum likelihood direction-of-arrival estimation in unknown noise fields using sparse sensor arrays , 2005, IEEE Transactions on Signal Processing.

[11]  Anthony J. Weiss,et al.  On the Cramer-Rao Bound for Direction Finding of Correlated Signals , 1993, IEEE Trans. Signal Process..

[12]  D. Middleton,et al.  Man-Made Noise in Urban Environments and Transportation Systems: Models and Measurements , 1973, IEEE Trans. Commun..

[13]  Ljubisa Stankovic,et al.  Further results on the minimum variance time-frequency distribution kernels , 1997, IEEE Trans. Signal Process..

[14]  Erik G. Larsson,et al.  Stochastic Cramer-Rao bound for direction estimation in unknown noise fields , 2002 .

[15]  L. Davis,et al.  Background and foreground modeling using nonparametric kernel density estimation for visual surveillance , 2002, Proc. IEEE.

[16]  David W. Scott,et al.  Multivariate Density Estimation: Theory, Practice, and Visualization , 1992, Wiley Series in Probability and Statistics.

[17]  Mark S. Leeson,et al.  Intelligent systems : techniques and applications , 2008 .

[18]  P. Stoica,et al.  The stochastic CRB for array processing: a textbook derivation , 2001, IEEE Signal Processing Letters.