Title :
Detection-estimation of more uncorrelated Gaussian sources than sensors in nonuniform linear antenna arrays .I. Fully augmentable arrays
Author :
Abramovich, Yuri I. ; Spencer, Nicholas K. ; Gorokhov, Alexei Y.
Author_Institution :
Cooperative Res. Centre for Sensor Signal & Inf. Processing, Adelaide, SA, Australia
fDate :
5/1/2001 12:00:00 AM
Abstract :
Previous studies dealing with direction-of-arrival (DOA) estimation for uncorrelated planes waves incident on nonuniform M-sensor arrays assumed that the number of signal sources m was known or had already been estimated. In the “conventional” case (m<M), traditional detection techniques such as Akaike´s information criterion (AIC) and minimum description length (MDL) that are based on the equality of several smallest eigenvalues in the covariance matrix may be applied, although we demonstrate that these results can be misleading for nonuniform arrays. In the “superior” case (m⩾M), these standard techniques are not applicable. We introduce a new approach to the detection problem for “fully augmentable” arrays (whose set of intersensor differences is complete). We show that the well-known direct augmentation approach applied to the sample covariance matrix is not a solution by itself since the resulting Toeplitz matrix is generally not positive definite for realistic sample volumes. We propose a transformation of this augmented matrix into a positive definite Toeplitz matrix Tμ with the proper number of equal minimum eigenvalues that are appropriate for the candidate number of sources μ. Comparison of the results of these best-fit transformations over the permissible range of candidates then allows us to select the most likely number of sources mˆ using traditional criteria and yields uniquely defined DOAs. Simulation results demonstrate the high performance of this method. Since detection techniques for superior scenarios have not been previously described in the literature, we compare our method with the standard AIC and MDL techniques in a conventional case with similar Cramer-Rao bound (CRB) and find that it has a similar detection performance
Keywords :
Gaussian processes; Toeplitz matrices; array signal processing; covariance matrices; direction-of-arrival estimation; eigenvalues and eigenfunctions; linear antenna arrays; signal detection; Akaike´s information criterion; Cramer-Rao bound; DOA; DOA estimation; MDL; augmented matrix; detection performance; detection-estimation; direct augmentation approach; direction-of-arrival estimation; eigenvalues; fully augmentable arrays; minimum description length; nonuniform M-sensor arrays; nonuniform linear antenna arrays; positive definite Toeplitz matrix; sample covariance matrix; sensors; signal sources; simulation results; uncorrelated Gaussian sources; uncorrelated planes waves; Antenna arrays; Array signal processing; Covariance matrix; Direction of arrival estimation; Eigenvalues and eigenfunctions; Linear antenna arrays; Sensor arrays; Signal detection; Signal processing; Vectors;
Journal_Title :
Signal Processing, IEEE Transactions on