Title: Array Signal Processing with Davies Transformation on Uniform Circular Arrays

Speaker: Buon Kiong Lau, Curtin University of Technology, Perth, Australia

Time and Place:

Friday, June 14th, at 14:00
Library, floor 2 at Magistern, Dag Hammarskjölds väg 31, Uppsala

Abstract:

Uniform circular arrays (UCAs), as a result of their two-dimensional array structure, are able to provide all azimuth coverage. Furthermore, when called for, they are able to provide 180 coverage in elevation. In comparison to uniform linear arrays (ULAs), the special features of UCAs come, however, at the cost of a less friendly steering vector: it is non-Vandermonde. It is well known that, as a direct consequence of the Vandermonde property of a ULA's steering vector, many powerful array-processing techniques have been devised. Some examples include root-MUSIC, Dolph-Chebyshev pattern synthesis, optimum beamforming and spatial smoothing/averaging. Significant efforts have been directed to bringing these techniques over to UCAs via preprocessing on the array outputs. The philosophy behind these preprocessing techniques is to transform the steering vectors of UCAs to Vandermonde form.

In this seminar, the focus is on the use of the Davies Transformation, which is essentially a spatial-DFT, to map the UCA to a virtual array. This virtual array has no physical interpretation except that its steering vector is Vandermonde. An overview will be given for the successful applications of this approach in the aforesaid ULA-based techniques. Nevertheless, the virtual arrays can be highly sensitive to array imperfections such as element position errors, mutual coupling, and gain and phase mismatches. This non-robust behaviour is the result of the Davies transformation matrix having a large norm for certain array parameters. This problem can be addressed by the use of a robust transformation matrix. The robust matrix is found by posing and solving a quadratic semi-infinite optimization problem which trades-off the Vandermonde approximation error with a matrix of lower norm.