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

• Published in: IEEE transactions on signal processing Vol. 54; no. 5; pp. 1716 - 1726
• Main Authors: Luzhou Xu, Stoica, P., Li, Jian
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Amplitude and phase estimation; Amplitude estimation; Amplitudes; Apes; Applied sciences; Asymptotic properties; Capon; complex amplitude estimation; Computer aided software engineering; Data models; Detection, estimation, filtering, equalization, prediction; Estimators; Exact sciences and technology; growth-curve model; Information, signal and communications theory; Interference; Interference suppression; least squares; Least squares approximation; Mathematical models; maximum likelihood; Maximum likelihood estimation; minimum variance distortionless response; Noise; Phase distortion; Phase estimation; Sensor arrays; Signal and communications theory; Signal, noise; Symmetric matrices; Telecommunications and information theory; Waveforms; Space time correlation; growth-curve model; Parameter estimation; Approximate method; complex amplitude estimation; Response amplitude; Spatial correlation; Correlated noise; Capon; Statistical method; Accuracy; Minimal variance; Phase estimation; least squares; Amplitude and phase estimation; Numerical simulation; Robustness; Amplitude estimation; Maximum likelihood; minimum variance distortionless response
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2006.872605

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.