Simultaneous DOA Estimation of Fully
Correlated and Uncorrelated

Gaussian Sources in Nonuniform Linear Antenna Arrays

**Yuri Abramovich and Nick Spencer
CSSIP
Mawson Lakes, South Australis
Email: yuri.abramovich@cssip.edu.au**

**Abstract****
**In many applications, such
as passive source location or jammer mapping, the true directions of sources should be
discriminated from multipath directions for some relatively small number of multipath
sources embedded in a substantial number of single-mode propagated sources [Nickel]. The
main problem here is to select a supporting antenna array geometry and corresponding
signal processing technique. Indeed, DOA estimation of fully correlated sources advocates
significant redundancy in array geometry, ultimately preferring a uniform array and
standard spatial smoothing. Conversely, given a particular number of antenna sensors M
(eg. in HF radar), sparse arrays are preferable for uncorrelated Gaussian sources because
larger aperture means better resolution; moreover, sparse arrays allow estimation of a
"superior" number of sources, impossible with a uniform array.

For some small number of multipath sources, we have introduced a special class of nonuniform geometry with embedded "partial arrays," and a corresponding generalised spatial smoothing (GSS) algorithm [Abromovich and Spencer]. We now incorporate this approach into a more general iterative technique.

For a "conventional" total number of sources (m<M), we firstly identify m_UC uncorrelated sources using standard MUSIC applied to the direct data covariance (DDC) matrix. A power-fitting method (based on linear programming) estimates the uncorrelated-source covariance matrix. Secondly, we subtract this from the DDC matrix and apply GSS to obtain multimode DOA estimation. We then find the corresponding complex amplitudes by calculating the "maximum" eigenvector of the "intersource" covariance matrix [Bohme], then iterate with uncorrelated MUSIC estimates using the eigen-decomposition of the updated covariance correction matrix. Further iterations result in separately identified DOA’s for all uncorrelated and fully correlated sources. This paper contains simulation results that demonstrate the efficiency of this algorithm with nonuniform PA geometries. Though demonstrated for linear arrays (typical of HF OTHR applications), this technique could be applied to arbitrary subarrays of a fully filled multifunction array radar.