The cost of uncorrelation and noncooperation in MIMO channels

Tal Philosof*, Ram Zamir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We investigate the capacity loss for using uncorrelated Gaussian input over a multiple-input multiple-output (MIMO) linear additive-noise channel. We upper-bound the capacity loss by a universal constant C* which is independent of the channel matrix and the noise distribution. For a single-user MIMO channel with nt inputs and nr outputs C* = min {1/2, nr/2ntlog2 (1 + nt/nr bit per input dimension (or 2C* bit per transmit antenna per second per hertz), under both total and per-input power constraints. If we restrict attention to (colored) Gaussian noise, then the capacity loss is upper-bounded by a smaller constant CG= nr/2ntlog2 (nt/nr) for nr ≥ nt/e, and CG = 0.265 otherwise, and this bound is tight for certain cases of channel matrix and noise covariance. We also derive similar bounds for the sum-capacity loss in multiuser MIMO channels. This includes in particular uncorrelated Gaussian transmission in a MIMO multiple-access channel (MAC), and "flat"Gaussian dirty-paper coding (DPC) in a MIMO broadcast channel. In the context of wireless communication, our results imply that the benefit of beamforming and spatial water-filling over simple isotropic transmission is limited. Moreover, the excess capacity of a point-to-point MIMO channel over the same MIMO channel in a multiuser configuration is bounded by a universal constant.

Original languageEnglish
Pages (from-to)3904-3920
Number of pages17
JournalIEEE Transactions on Information Theory
Issue number11
StatePublished - Nov 2007


  • Capacity loss
  • MIMO broadcast channel (MIMO-BC)
  • MIMO multiple-access channel (MIMO-MAC)
  • Multiple-input multiple-output (MIMO) channel
  • Noncooperation loss
  • Robust input
  • Uncorrelation loss


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