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Improvements in DOA estimation by array interpolation in non-uniform linear arrays

Yaşar, Temel Kaya
In this thesis a new approach is proposed for non-uniform linear arrays (NLA) which employs conventional subspace methods to improve the direction of arrival (DOA) estimation performance. Uniform linear arrays (ULA) are composed of evenly spaced sensor elements located on a straight line. ULA's covariance matrix have a Vandermonde matrix structure, which is required by fast subspace DOA estimation algorithms. NLA differ from ULA only by some missing sensor elements. These missing elements cause some gaps in covariance matrix and Vandermonde structure is lost. Therefore fast subspace DOA algorithms can not be applied in this case. Linear programming methods and array interpolation methods can be used to solve this problem. However linear programming is computationally expensive and array interpolation is angular sector dependent and requires the same number of sensor in the virtual array. In this thesis, a covariance matrix augmentation method is developed by using the array interpolation technique and initial DOA estimates. An initial DOA estimate is obtained by Toeplitz completion of the covariance matrix. This initial DOA estimates eliminates the sector dependency and reduces the least square mapping error of array interpolation. A Wiener formulation is developed which allows more sensors in the virtual array than the real array. In addition, it leads to better estimates at low SNR. The new covariance matrix is used in the root-MUSIC algorithm to obtain a better DOA estimate. Several computer simulations are done and it is shown that the proposed approach improves the DOA estimation accuracy significantly compared to the same number of sensor ULA. This approach also increases the number of sources that can be identifed.