Weak Duality and Iterative Beamforming Algorithms for Ad Hoc Networks

Abstract

A unicasting ad hoc network is considered, where each node i is equipped with a transmit/receive beamformer pair (w(sub i), g(sub i)). Each node's 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 (g(sub i) *, w(sub i) *) achieve the same sum power as the primal network. However, the optimum receive beamformer w(sub i) is not in general equal to the optimum g(sub i) *, in contrast to the case of certain networks with simpler topologies. A suboptimal iterative beamforming algorithm is then proposed in which w(sub i) = g(sub i) * is enforced. The algorithm is shown to be an instance of the Power Algorithm in which g(sub 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 equilibrium(a).

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Document Details

Document Type
Technical Report
Publication Date
Dec 20, 2004
Accession Number
ADA433623

Entities

People

  • Ronald A. Iltis
  • Seung-jun Kim

Organizations

  • University of California, Santa Barbara

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Ad Hoc Networks
  • Algorithms
  • Beam Forming
  • Convergence
  • Cooperative Games
  • Eigenvectors
  • Engineering
  • Game Theory
  • Iterations
  • Mesh Networks
  • Networks
  • Non-Cooperative Games
  • Point Theorem
  • Steering
  • Systems Engineering
  • Universities

Fields of Study

  • Engineering

Readers

  • Analytical Mechanics
  • Operations Research
  • Phased Array Antenna Design.