Adaptive beamforming and DOA estimation using uniform concentric spherical arrays with frequency invariant characteristics

Abstract

This paper proposes a new digital beamformer for uniform concentric spherical array (UCSA) having nearly frequency invariant (FI) characteristics. The basic principle is to transform the received signals to the phase mode and remove the frequency dependency of the individual phase mode through the use of a digital beamforming network. It is shown that the far field pattern of the array is determined by a set of weights and it is approximately invariant over a wide range of frequencies. FI UCSAs are electronic steerable in both the azimuth and elevation angles, unlike their concentric circular array counterpart. The frequency invariant characteristic of the FI UCSA also makes it possible to design separately the compensation network and beamformer weighting coefficients. The design of the compensation network is formulated as a second order cone programming (SOCP) problem and is solved optimally for minimax criterion. Thanks to the frequency invariant characteristic, traditional narrow band adaptive beamforming algorithms such as minimum variance beamforming (MVB) can be applied to the FI UCSA. Also, traditional narrow band 2-D direction of arrival (DOA) estimation algorithms such as unitary ESPRIT can be extended to broadband DOA estimation using FI UCSA. Simulation results show that the proposed adaptive beamformer using FI UCSA can obtain a higher output signal to inference plus noise ratio over the conventional tapped-delay line approach. Simulation results also show that FI UCSA has uniform beampattern and resolution around 360°in both azimuth and elevation angles, unlike FI uniform concentric circular array. The usefulness of the proposed UCSA-FIB in broadband 2-D DOA estimation is also verified by computer simulation. © Springer Science+Business Media, LLC 2007.