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Decoupled Maximum
Likelihood Angle
Estimation for Signals with Known Waveforms

Jian Li
University of Florida
Department of Electrical Engineering
Gainesville, FL 32611
email: li@saturn.ee.ufl.edu
Bijit Halder
Stanford University
Information Systems Laboratory
Stanford, CA 94305
Petre Stoica
Uppsala University
Systems and Control Group
Department of Technology
P.O. Box 27, S-751 03
Uppsala, Sweden
Mats Viberg
Chalmers University of Technology
Department of Applied Electronics
S-412 96, Gothenburg, Sweden

This presentation presents a large sample decoupled maximum likelihood (DEML) angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially colored noise. The DEML estimator decouples the multidimensional problem of the exact maximum likelihood (ML) estimator to a set of one-dimensional problems and hence is computationally efficient. We derive the asymptotic statistical performance of the DEML estimator and compare the performance with its Cramér-Rao bound, i.e., the best possible performance. We show that the DEML estimator is asymptotically statistically efficient for uncorrelated signals with known waveforms. We also show that for moderately correlated signals with known waveforms, the DEML estimator is no longer a large sample ML estimator, but the DEML estimator may still be used for angle estimation and the performance degradation is small. To estimate the arrival angles of desired signals with known waveforms in the presence or interfering of jamming signals we show that modeling the interfering or jamming signals as random processes with an unknown spatial covariance matrix may give lower CRD than modeling them as unknown deterministic incident signals. Finally, several numerical examples showing the performance of the DEML estimator are presented.



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