We consider the problem of estimating the angles of arrival (AOAs) of multiple sources from a single snapshot obtained by a set of non-coherent sub-arrays, i.e., while the antenna elements in each sub-array are coherent, each sub-array observes a different unknown phase offset. Previous relevant works are based on eigendecomposition of the sample covariance, which requires a large number of snapshots, or on combining the sub-arrays using non-coherent processing. In this paper, we propose a technique to estimate the sub-arrays phase offsets for a given AOAs hypothesis, which facilitates approximate maximum likelihood estimation (MLE) of the AOAs from a single snapshot. We derive the Cramér-Rao lower bound (CRLB) for the problem at hand, and analytically show that for a single source it may suffice to use a simple non-coherent AOA estimation. However, as we demonstrate by computer simulations, for multiple sources the proposed approach clearly outperforms the non-coherent estimator, and even attains the CRLB in various scenarios. Furthermore, the performance of the proposed method is often close to the performance of MLE in the coherent case, and the gap between the estimators is unavoidable, as implied by the gap between the CRLB for the coherent and non-coherent cases.
- Angle of arrival
- Cramér-Rao lower bound
- array processing
- maximum likelihood estimation
- single snapshot