On the Convergence of the Fast Iterative Interpolated Beamformer

The estimation of the direction of arrival (DOA), or equivalently of the frequency, of multiple sources is a fundamental problem in a number of applications including in radar, sonar communications and global navigation satellite systems. With large arrays increasing in popularity, the need for a fast yet accurate algorithms is pressing. Estimators such as MUSIC and ESPRIT incur a heavy computational cost and become impractical with increasing number of antennas. The recently proposed Fast Iterative Interpolated Beamformer (FIIB), on the other hand, is computationally fast while enjoying a performance that is better than the traditional high-resolution estimators. In this work, we examine at the convergence properties of the algorithm and study the number of iterations needed. We elucidate the behaviour of the interpolator and propose a new strategy for terminating the iterations in order to minimise the computational cost while maintaining the algorithms full performance. Extensive simulation results demonstrate the superiority of the proposed strategy.