**Time:** Tuesday, Dec 02, 2014 05:00PM-06:00PM

**Location:** SC 3401

**Hosts:** SIGArt

Speaker: Dr. Gary F. Hatke, MIT Lincoln Laboratory

Abstract

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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 that 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 multidimensional (e.g., planar), this search can become computationally expensive, as the source direction parameters are now also multidimensional. 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 multidimensional arrays because these arrays naturally generated a polynomial in multiple variables, which does not have discrete roots.

This seminar introduces a method for generalizing the rooting technique to multidimensional 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 more closely than a Rayleigh beamwidth, the resolution properties of the new polynomial algorithms are shown to be better than those of the search technique algorithms.