DSP seminar, Wed Apr. 05 Time and location: 4:00-5:00 PM 2269 Beckman Institute

Title: Polynomial Rooting Techniques for Adaptive Array Direction Finding


Speaker: Gary Hatke
	
Dr., Assistant Leader
MIT Lincoln Laboratory


Abstract:

Array processing has many applications in modern communications, radar, and sonar  
systems. Array processing is used when a signal in space, be it electromagnetic 
or acoustic, has some spatial coherence properties which can be exploited (such 
as far field plane wave properties). The array can be used to sense the orientation 
of the plane wave, and thus deduce the angular direction to the source. Adaptive 
array processing is used when there exists an environment of many signals from 
unknown directions as well as noise with unknown spatial distribution. Under 
these circumstances, classical Fourier analysis of the spatial correlations from 
an array data snapshot (the data seen at one instance in time) is insufficient to 
localize the signal sources.

In estimating the signal directions, most adaptive algorithms require computing an 
optimization metric over all possible source directions, and searching for a maximum. 
When the array is multi-dimensional (say planar) this search can become computationally 
expensive, as the source direction parameters are now also multi-dimensional. In the 
special case of one-dimensional (line) arrays, this search procedure can be replaced 
by solving a polynomial equation, where the roots of the polynomial correspond to 
estimates of the signal directions. This technique had not been extended to 
multi-dimensional arrays because these arrays naturally generated a polynomial in 
multiple variables, which does not have discrete roots. 

This talk introduces a method for generalizing the rooting technique to multi-dimensional 
arrays by generating multiple optimization polynomials corresponding to the source 
estimation problem, and finding a set of simultaneous solutions to these equations 
which contain source location information. It is shown that the variance of this new 
class of estimators is equal to that of the search techniques they supplant. 
In addition, for sources spaced closer than a Rayleigh beamwidth, the resolution 
properties of the new polynomial algorithms are shown to be better than the search 
technique algorithms.


This work was sponsored by the Department of the Air Force under contract number 
F19628-00-C-0002. Opinions, interpretations, conclusions, and recommendations are 
those of the authors and are not necessarily endorsed by the United States Government.


Biography: 

Dr. Gary F. Hatke was born in Princeton NJ on Feb. 18, 1963. He graduated from  
Princeton Day School in 1981, received a BSEE from University of Pennsylvania 
in 1985 (Magna Cum Laude), and received the MA and PhD degrees from Princeton 
University in 1988 and 1990, respectively. Since 1990 he has been with MIT Lincoln 
Laboratory. From 1990 to 2000, he was a staff member in the Advanced Techniques group. 
Since 2000, he has been an assistant group leader, currently in the Advanced Sensor 
Techniques group. Dr. Hatke has interests in adaptive signal parameter estimation, 
array-based communications, HF propagation, polarimetric array theory, space-time 
array processing and GPS adaptive beamforming. Dr. Hatke has served as an associate 
editor for IEEE Transactions on Signal Processing. He is a senior member of the IEEE, 
and a member of Tau Beta Pi, Eta Kappa Nu, and Phi Beta Kappa.