Estimating the frequencies of two sinusoids using only the phase angles of complex-valued data

The problem of estimating the frequencies of two complex sinusoids using only the phase data is addressed. Under the assumption that the amplitudes of the two signals are not equal, a computationally efficient approximate maximum likelihood estimation (AMLE) is obtained. This AMLE uses only the phase angles of the complex-valued data to estimate frequencies and uses the envelope data to resolve an inherent algebraic sign ambiguity in the difference frequency. At moderately high SNRs, satisfactory results are obtained from computer simulations. The mean-square errors of the estimates are compared with the corresponding values of the Cramer-Rao lower bounds (CRLBs)