Analytical spherical-mode-based compensation of mutual coupling in uniform circular arrays for direction-of-arrival estimation

An analytical circuit model with a limited number of parameters is presented to describe mutual coupling in uniform circular arrays. The model, which is based on a spherical-mode expansion, provides physical insight into the frequency dependence and the dependence on azimuth and elevation angle of the coupling between antenna elements. It is shown that the number of circuit elements, required to describe the open-circuit voltages and the mutual impedances at the different antenna ports, depends on the overall size of the array and not on the spacing between the antenna elements. Based on this observation, an analytical technique is described to derive a coupling matrix representing the mutual coupling effects. Relying on the phase-mode-based circuit elements, dedicated eigenstructure techniques are developed for direction-of-arrival (DOA) estimation with uniform circular arrays. By considering several synthetic reference scenarios, it is shown that even in the presence of severe mutual coupling, root-MUSIC combined with a limited number of phase-mode components gives very robust DOA estimations for the azimuth angle, when all signals are incident on the array from a fixed elevation angle.