A note on CRLB formulation for underdetermined DOA estimation in circularly configured planar arrays

Abstract

This letter presents the Cramer–Rao Lower Bound (CRLB) for circularly configured planar arrays. CRLB sets a lower bound on the variance of unbiased estimators. It has been extensively studied in the field of array signal processing especially for direction-of-arrival (DOA) estimation using uniform or non-uniform linear arrays. We consider an underdetermined signal model for circularly configured planar arrays and investigate the conditions under which CRLB exist. A new closed-form expression for the CRLB is derived. We numerically compare the CRLB of uniform circular array (UCA) and nested sparse circular array (NSCA) to confirm whether the proposed formulation is effective for both uniform and non-uniform circular planar arrays.