Communication over MIMO X channels: Interference alignment, decomposition, and performance analysis

M. A. Maddah-Ali, Abolfazl Seyed Motahari, Amir Keyvan Khandani

Research output: Contribution to journalArticlepeer-review

793 Scopus citations


In a multiple-antenna system with two transmitters and two receivers, a scenario of data communication, known as the X channel, is studied in which each receiver receives data from both transmitters. In this scenario, it is assumed that each transmitter is unaware of the other transmitter's data (noncooperative scenario). This system can be considered as a combination of two broadcast channels (from the transmitters' points of view) and two multiple-access channels (from the receivers' points of view). Taking advantage of both perspectives, two signaling schemes for such a scenario are developed. In these schemes, some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple-antenna broadcast subchannels or two noninterfering multiple-antenna multiple-access subchannels. The main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain (MG). It is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable MG. In particular, it is shown that in some specific cases, the achieved MG is the same as the MG of the system if full cooperation is provided either between the transmitters or between the receivers.

Original languageEnglish (US)
Pages (from-to)3457-3470
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2008
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received June 14, 2007; revised November 20, 2007. This work was supported by Nortel and the corresponding matching funds by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Ontario Centres of Excellence (OCE). The material in this paper was presented in part at the IEEE International Symposium on Information Theory (ISIT), Seattle, WA, July 2006 and the 10th Canadian Workshop on Information Theory (CWIT) Edmonton, AB, Canada, June 2007 and reported in the Technical Report UW-ECE 2006-12, July 23, 2006, and the Technical Report UW-ECE 2006-27, December 2006, University of Waterloo, Waterloo, ON, Canada.


  • Antenna measurements
  • Antennas
  • Base stations
  • Color
  • Communication channels
  • Computational modeling
  • Computer languages
  • Computers
  • Conferences
  • Covariance matrix
  • Data communication
  • Decoding
  • Degrees of freedom
  • Electrical engineering
  • Encoding
  • Filtering theory
  • Gain
  • Gain measurement
  • Gaussian noise
  • Information filtering
  • Information filters
  • Information theory
  • Interference
  • Interference alignment
  • Interference channels
  • Joining processes
  • Laboratories
  • Materials
  • Mathematical model
  • Matrix decomposition
  • Maximum likelihood detection
  • MIMO
  • MIMO X channels
  • Multiple-antenna systems
  • Multiple-input multiple- output (MIMO) multiuser systems
  • Multiplexing
  • Multiplexing gain
  • Noncooperative communication
  • Nonlinear filters
  • Object recognition
  • Performance analysis
  • Power measurement
  • Power offset
  • Propagation losses
  • Receivers
  • Receiving antennas
  • Relays
  • Signal to noise ratio
  • Simulation
  • Space-division multiple access
  • Transmitters
  • Transmitting antennas
  • Upper bound
  • Vectors
  • Wireless communication
  • Writing


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