On the Cramér-Rao Bound and the Number of Resolvable Sources in the Presence of Nonuniform Noise for Underdetermined DOA Estimation

In this paper, the closed-form stochastic Cramér-Rao Bound (CRB) expression for underdetermined direction-of- arrival (DOA) estimation is derived in the presence of nonuniform noise. By examining the information regularity condition and the number-of-equations condition, it is found that the number of resolvable uncorrelated sources exploiting sparse arrays is upper bounded by the number of positive sensor positions in the virtual difference co-array, which is identical to those in the presence of uniform noise. This indicates that the redundant sensor positions in the difference co-array can provide extra degrees of freedoms (DOFs) for identifiability of more unknown parameters associated with the covariance matrix of the noise, without sacrificing the number of resolvable sources.