Statistical Resolution Limits of DOA for Discrete Sources

This paper examines the stochastic Cramer-Rao bound (CRB) of direction of arrival (DOA) estimates for binary phase-shift keying (BPSK), minimum shift keying (MSK) and quaternary phase-shift keying (QPSK) modulated signals in the presence of unknown nonuniform Gaussian noise. After deriving closed-form expressions of the CRB, the statistical resolution limit, defined as the source separation that equals its own CRB is given. It is shown that this highest achievable resolution is proportional to the reciprocal of the fourth root of the product of the number of snapshots by an extended signal to noise ratio (SNR), in contrast to the square root dependence for circular Gaussian sources