Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels

Sriram Vishwanath, Nihar Jindal, Andrea Goldsmith

Research output: Contribution to journalArticlepeer-review

1342 Scopus citations


We consider a multiuser multiple-input multiple-output (MIMO) Gaussian broadcast channel (BC), where the transmitter and receivers have multiple antennas. Since the MIMO BC is in general a nondegraded BC, its capacity region remains an unsolved problem. In this paper, we establish a duality between what is termed the "dirty paper" achievable region (the Caire-Shamai achievable region) for the MIMO BC and the capacity region of the MIMO multiple-access channel (MAC), which is easy to compute. Using this duality, we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the MIMO BC. We also show that the dirty paper achievable region achieves the sum-rate capacity of the MIMO BC by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the MIMO BC.

Original languageEnglish (US)
Pages (from-to)2658-2668
Number of pages11
JournalIEEE Transactions on Information Theory
Issue number10
StatePublished - Oct 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Broadcast channel (BC)
  • Channel capacity
  • Dirty paper coding
  • Duality
  • Multiple-input multiple-output (MIMO) systems


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