On multicast beamforming for minimum outage

Vassilis Ntranos, Nicholas D. Sidiropoulos, Leandros Tassiulas

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


The multicast beamforming problem is considered from the viewpoint of minimizing outage probability subject to a transmit power constraint. The main difference with the point-to-point transmit beamforming problem is that in multicast beamforming the channel is naturally modeled as a Gaussian mixture, as opposed to a single Gaussian distribution. The Gaussian components in the mixture model user clusters of different means (locations) and variances (spreads). It is shown that minimizing outage probability subject to a transmit power constraint is an NP-hard problem when the number of Gaussian kernels, J, is greater than or equal to the number of transmit antennas, N. Through dimensionality reduction, it is also shown that the problem is practically tractable for 2 3 Gaussian kernels. An approximate solution based on the Markov inequality is also proposed. This is simple to compute for any J and N, and often works well in practice.

Original languageEnglish (US)
Article number5089998
Pages (from-to)3172-3181
Number of pages10
JournalIEEE Transactions on Wireless Communications
Issue number6
StatePublished - Jun 2009
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received June 27, 2008; revised November 10, 2008 and February 13, 2009; accepted February 13, 2009. The associate editor coordinating the review of this paper and approving it for publication was O. Simeone. V. Ntranos and N. D. Sidiropoulos are with the Department of Electronic and Computer Engineering, Technical University of Crete, 73100 Chania - Crete, Greece (e-mail: nikos@telecom.tuc.gr; vntranos@gmail.com). L. Tassiulas is with the Department of Computer Engineering and Telecommunications, University of Thessaly, Volos, Greece (e-mail: leandros@uth.gr). N. D. Sidiropoulos was partially supported by EC project WIP and N-CRAVE. L. Tassiulas was partially supported by EC project N-CRAVE. Digital Object Identifier 10.1109/TWC.2009.080850


  • Multicast beamforming
  • Outage probability
  • Transmit power constraint


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