Virtual array design for array interpolation using differential geometry

In array interpolation, the optimal design of the virtual array geometry is still an open question. It is usually done heuristically by placing a virtual ULA into the center of the original array and fitting orientation and aperture by rule of thumb. In this paper, we parameterize the array manifold by its arc length and use this representation for the design of a virtual array manifold that optimally matches the directional properties of the original array. We verify the advantages of our new design method by simulation results and give some deeper understanding about the interrelation between the interpolation error, the condition number of the interpolation matrix and the DOA estimation bias.