Coprime beamforming: Fast estimation of more sources than sensors

Abstract

In radar, the minimisation of redundancies within the sensing array can lead to significant hardware computational savings. Arrays with a coprime-pair configuration enjoy increased degrees of freedom and can detect more sources than sensors. To achieve this, a virtual array (VA) consisting of the full complement of lags is usually constructed and subspace-based algorithms are then employed to obtain the direction-of-arrival (DOA) or frequency estimates. However, the application of the subspace techniques to the VA incurs a significant computational cost and requires spatial smoothing. The authors propose and analyse the application of the fast iterative interpolated beamformer (FIIB) to the coprime DOA estimation problem. The FIIB enjoys a computational complexity of the same order as the fast Fourier transform and does not require spatial smoothing. They consider two implementations that construct the VA differently with the first selecting a single estimate for each lag and the other employing averaged values of the lag estimates. They present a comprehensive study of the estimation performance as a function of signal-to-noise ratio, number of snapshots and source separation. The results clearly show that the FIIB delivers high-fidelity frequency estimates that consistently outperform the high-resolution subspace-based methods.