Topic: “Computational Model for Eigenvalue Density Function of Cylindrically Isotropic Noise”
Presenter: Mr. Saurav R. Tuladhar, ECE Ph.D. Student, University of Massachusetts Dartmouth
Advisor: Dr. John R. Buck
Adaptive beamforming (ABF) rely on the knowledge of measurement covariance which is usually unknown a priori. It is commonly estimated from the measurement by computing the sample covariance matrix (SCM). But in a limited sample size case, the SCM no longer converges to the ensemble quantity. Further, the performance of the ABF is related to the behavior of the eigenstructure of the SCM. In this setting, Random Matrix Theory (RMT) provides the necessary framework to analyze the asymptotic behavior of the eigenstructure of the SCM. This work presents a method to compute the asymptotic eigenvalue density function (EDF) of the SCM for a cylindrically isotropic noise field. The EDF of the noise ECM is shown to behave as a spiked covariance model. The method exploits the properties of free multiplicative convolution to model the EDF of the noise ECM as an atomic density with fewer impulses than the ECM size. The reduced order atomic density model resutls in a substantial computational savings when computing the EDF of the noise SCM. The Polynomial Method is used to numerically compute the EDFs. The approximate EDF thus obtained are in agreement with histograms of eigenvalues obtained from simulation. The knowledge of EDF of the noise SCM could lead to a bearing dependent threshold setting for detection problems.
Saurav R. Tuladhar completed his undergraduate studies in Electronics and Communication Engineering from Pulchowk Campus, Institute of Engineering, Tribhuvan University in 2007 in Nepal. He received his M.S. degree in Electrical Engineering (Signal Processing) in 2011 from UMassD under the guidance of Dr. John Buck. Currently, he is a Ph.D. student at University of Massachusetts Dartmouth. His research interests include digital and statistical signal processing with applications to sensor arrays and communications.
The seminar is open to the public free of charge.