Frequency Invariant Uniform Concentric Circular Arrays with Directional Elements

A new approach for designing frequency invariant (FI) uniform concentric circular arrays (UCCAs) with directional elements is proposed, and their applications to direction-of-arrival (DOA) estimation and adaptive beamforming are studied. By treating the sensors along the radial direction of the UCCA as linear subarrays and using appropriately designed beamformers, each subarray is transformed to a virtual element with appropriate directivity. Consequently, the whole UCCA can be viewed as a virtual uniform circular array (UCA) with desired element directivity for broadband processing. By extending the approach for designing FI-UCAs, the frequency dependency of the phase modes of the virtual UCA is compensated to facilitate broadband DOA and adaptive beamforming. Both the linear array beamformers (LABFs) and compensation filters can be designed separately using second-order cone programming (SOCP). Moreover, a new method to tackle the possible noise amplification problem in such large arrays by imposing additional norm constraints on the design of the compensation filters is proposed. The advantages of this decoupled approach are 1) the complicated design problem of large UCCAs can be decoupled into simpler problems of designing the LABFs and compensation filters, and 2) directional elements, which are frequently encountered, can be treated readily under the proposed framework. Numerical examples are provided to demonstrate the effectiveness and improvement of the proposed methods in DOA estimation, adaptive beamforming, and elevation control over the conventional FI-UCCA design method.