## Date of Award

12-1994

## Document Type

Thesis

## Degree Name

Master of Science in Electrical Engineering

## Department

Department of Electrical and Computer Engineering

## First Advisor

Michael P. Clark, PhD

## Abstract

It is well known that an antenna array with N degrees of freedom (DOF) can cancel N - 1 interferers if they approach the array from directions other than that of the desired signal. It has been shown that there are cases in which it is possible for an array with N DOF to effectively cancel more than N - 1 interferers. Specifically, we show how this can be done when there is incident upon an N-element array not only the desired signal and a jammer signal, but more than N - 1 Doppler-shifted multipath copies of the jammer signal as well. In this situation the received signal is nonstationary; therefore, updates of the weight vector must use only as many samples as correspond to the time interval over which the signal can be considered locally stationary. In this frequency-dispersive environment, it is desirable to recalculate the weight vector often; in some cases, we would like to do so every sample. However, recalculating the weight vector involves estimating and inverting the covariance matrix of the received signal; using traditional methods, this is an O(N3) process, where N represents the degrees of freedom in the array. For large N this becomes timeprohibitive. In this paper we examine the application of eigenvalue decomposition and rank-one updating of the covariance matrix to reduce the computation required. By exploiting the structure of the matrix we find that we are able to decrease the time required for its estimation and inversion from 0(N3) to 0(N). Using these techniques, we can update the weight vector every sample, enabling us to operate effectively in a frequency-dispersive environment.

## AFIT Designator

AFIT-GE-ENG-94D-22

## DTIC Accession Number

ADA289206

## Recommended Citation

Murray, David A., "Adaptive Beamforming in Frequency-Dispersive Multipath Environments" (1994). *Theses and Dissertations*. 6420.

https://scholar.afit.edu/etd/6420

## Comments

The author's Vita page is omitted.