Recursive Extended Instrumental Variable-based LCMV Beamformers for Planar Radial Coprime Arrays under Spatially Colored Noise

This article proposes a new recursive linearly constrained minimum variance (LCMV) beamformer based on the extended instrumental variable (EIV) method for planar radial coprime arrays (PRCAs) under spatially colored noise. The proposed recursive LCMV beamformer is able to deal with multiple constraints with high precision and low complexity and can be applicable to various array geometrical configurations. Taking advantage of the EIV vector, the proposed beamformer can effectively combat the additive color noise with unknown noise covariance matrix. We develop our recursive LCMV beamformer based on the square-root (SR) EIV algorithm due to its improved numerical stability than the conventional EIV-based algorithms. Furthermore, we studied a class of planar arrays called PRCAs, which consists of a set of linear coprime arrays arranged radially at various azimuth angles. The coprime array property is utilized to enlarge the array aperture leading to higher resolution and stronger interference rejection and it offers additional flexibility in the tradeoffs between array complexity and performance. Simulation results demonstrate that the proposed recursive SREIV-based LCMV beamformer outperforms the conventional QR decomposition based LCMV beamformers in the resolution and suppression of interferences under various scenarios. The PRCAs tested outperform the uniform rectangular arrays with the same number of elements. Moreover, better performance can be achieved with more linear subarrays at the expense of increased complexity.