Complex amplitude estimation in the known steering matrix and generalized waveform case

We consider a special growth-curve (SGC) model with a known steering matrix and generalized waveform in the presence of unknown interference and noise. Several estimators of the complex amplitude based on this model are derived, including the methods of approximate maximum likelihood (AML), minimum variance distortionless response (MVDR), and amplitude and phase estimation (APES). We analyze the statistical properties of these estimators and show that in the presence of temporally white but spatially correlated noise and interference, AML is asymptotically statistically efficient for a large snapshot number while MVDR and APES are asymptotically equivalent but not statistically efficient. Via several numerical examples, we also show that when the noise and interference are both spatially and temporally correlated, the APES estimator can achieve better estimation accuracy and exhibit greater robustness than the other methods.