Coordinated beamforming for MISO interference channel: Complexity analysis and efficient algorithms

Ya Feng Liu, Yu Hong Dai, Zhi Quan Luo

Research output: Contribution to journalArticlepeer-review

158 Scopus citations


In a cellular wireless system, users located at cell edges often suffer significant out-of-cell interference. Assuming each base station is equipped with multiple antennas, we can model this scenario as a multiple-input single-output (MISO) interference channel. In this paper we consider a coordinated beamforming approach whereby multiple base stations jointly optimize their downlink beamforming vectors in order to simultaneously improve the data rates of a given group of cell edge users. Assuming perfect channel knowledge, we formulate this problem as the maximization of a system utility (which balances user fairness and average user rates), subject to individual power constraints at each base station. We show that, for the single-carrier case and when the number of antennas at each base station is at least two, the optimal coordinated beamforming problem is NP-hard for both the harmonic mean utility and the proportional fairness utility. For general utilities, we propose a cyclic coordinate descent algorithm, which enables each transmitter to update its beamformer locally with limited information exchange and establish its global convergence to a stationary point. We illustrate its effectiveness in computer simulations by using the space matched beamformer as the benchmark.

Original languageEnglish (US)
Article number5638157
Pages (from-to)1142-1157
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number3
StatePublished - Mar 2011

Bibliographical note

Funding Information:
Manuscript received April 28, 2010; revised August 22, 2010, November 05, 2010; accepted November 05, 2010. Date of publication November 15, 2010; date of current version February 09, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Aleksandar Dogandzic. This work was supported in part by the National Natural Science Foundation, Grant 10831006 and the CAS Grant kjcx-yw-s7-03, in part by the Army Research Office, Grant W911NF-09-1-0279, and in part by the National Science Foundation, Grant CMMI-0726336. This work has been presented in part at the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Dallas, Texas, March 14–19, 2010.


  • Complexity
  • MISO interference channel
  • coordinated beamforming
  • cyclic coordinate descent algorithm
  • global convergence

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