Quality of service and Max-min fair transmit beamforming to multiple cochannel multicast groups

Eleftherios Karipidis, Nicholas D. Sidiropoulos, Zhi Quan Luo

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490 Scopus citations


The problem of transmit beamforming to multiple cochannel multicast groups is considered, when the channel state is known at the transmitter and from two viewpoints: minimizing total transmission power while guaranteeing a prescribed minimum signal-to-interference-plus-noise ratio (SINR) at each receiver; and a "fair" approach maximizing the overall minimum SINR under a total power budget. The core problem is a multicast generalization of the multiuser downlink beamforming problem; the difference is that each transmitted stream is directed to multiple receivers, each with its own channel. Such generalization is relevant and timely, e.g., in the context of the emerging WiMAX and UMTS-LTE wireless networks. The joint problem also contains single-group multicast beamforming as a special case. The latter (and therefore also the former) is NP-hard. This motivates the pursuit of computationally efficient quasi-optimal solutions. It is shown that Lagrangian relaxation coupled with suitable randomization/ cochannel multicast power control yield computationally efficient high-quality approximate solutions. For a significant fraction of problem instances, the solutions generated this way are exactly optimal. Extensive numerical results using both simulated and measured wireless channels are presented to corroborate our main findings.

Original languageEnglish (US)
Pages (from-to)1268-1279
Number of pages12
JournalIEEE Transactions on Signal Processing
Issue number3
StatePublished - Mar 2008

Bibliographical note

Funding Information:
Manuscript received March 17, 2007; revised July 31, 2007. Original version submitted to the IEEE TRANSACTIONS ON SIGNAL PROCESSING on July 4, 2006. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Erik G. Larsson. The work of E. Karipidis was supported in part by the E.U. under FP6 506790 project U-BROAD and by National and Community Funds (75% from E.U.-European Social Fund and 25% from the Greek Ministry of Development - General Secretariat of Research and Technology) under 03ED918 research project, implemented within the framework of the Reinforcement Programme of Human Research Manpower (PENED). The work of N. D. Sidiropoulos was supported in part by the U.S. ARO under ERO Contract N62558-03-C-0012 and by the E.U. under FP6 project NEWCOM. The work of Z.-Q. Luo was supported in part by the National Science Foundation by Grant DMS-0312416. An earlier version of part of this work appears in conference form in the Proceedings of the 1st IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Puerto Vallarta, Mexico, December 13–15, 2005, pp. 109–112.


  • Broadcasting
  • Convex optimization
  • Downlink beamforming
  • Multicasting
  • Semidefinite relaxation


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