Power minimization in MIMO cognitive networks using beamforming games

Diep N. Nguyen, Marwan Krunz

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


We consider a multi-channel multi-user cognitive radio MIMO network in which each node controls its antenna radiation directions and allocates power for each data stream by adjusting its precoding matrices. Under a noncooperative game, we optimize the set of precoding matrices (one per channel) at each node so as to minimize the total transmit power in the network. Using recession analysis and the theory of variational inequalities, we obtain sufficient conditions that guarantee the existence and uniqueness of the game's Nash Equilibrium (NE). Low-complexity distributed algorithms are also developed by exploiting the strong duality of the convex per-user optimization problem. To improve the efficiency of the NE, we introduce pricing policies that employ a novel network interference function. Existence and uniqueness of the new NE under pricing are studied. Simulations confirm the effectiveness of our joint optimization approach.

Original languageEnglish (US)
Article number6502486
Pages (from-to)916-925
Number of pages10
JournalIEEE Journal on Selected Areas in Communications
Issue number5
StatePublished - 2013


  • MIMO
  • Power/spectrum efficiency
  • beamforming
  • cognitive radio
  • noncooperative game
  • pricing

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


Dive into the research topics of 'Power minimization in MIMO cognitive networks using beamforming games'. Together they form a unique fingerprint.

Cite this