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# Accession Number:

## ADA433623

# Title:

## Weak Duality and Iterative Beamforming Algorithms for Ad Hoc Networks

# Descriptive Note:

## Conference paper

# Corporate Author:

## CALIFORNIA UNIV SANTA BARBARA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING

# Report Date:

## 2004-12-20

# Pagination or Media Count:

##
11.0

# Abstract:

## A unicasting ad hoc network is considered, where each node i is equipped with a transmitreceive beamformer pair wsub i, gsub i. Each nodes SNR Gamma sub i satisfies Gamma sub i is greater than or equal to gamma0. It is first shown that the minimum sum power beamformers for the network satisfy a weak duality condition, in which the pairs gsub i , wsub i achieve the same sum power as the primal network. However, the optimum receive beamformer wsub i is not in general equal to the optimum gsub i , in contrast to the case of certain networks with simpler topologies. A suboptimal iterative beamforming algorithm is then proposed in which wsub i gsub i is enforced. The algorithm is shown to be an instance of the Power Algorithm in which gsub i is the maximizing eigenvector of an SNR-related objective matrix. The beamforming algorithm is also shown to have a Game Theory interpretation, in which the payoff is SNR, and the tax is related to interference caused to other nodes. The algorithm is also proven to have a Nash equilibriuma.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#