Power-controlled feedback and training for two-way MIMO channels

Vaneet Aggarwal, Ashutosh Sabharwal

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Most communication systems use some form of feedback, often related to channel state information. The common models used in analyses either assume perfect channel state information at the receiver and/or noiseless state feedback links. However, in practical systems, neither is the channel estimate known perfectly at the receiver and nor is the feedback link perfect. In this paper, we study the achievable diversity multiplexing tradeoff using i.i.d. Gaussian codebooks, considering the errors in training the receiver and the errors in the feedback link for frequency division duplex (FDD) systems, where the forward and the feedback are independent multiple input multiple output (MIMO) channels. Our key result is that the maximum diversity order with one-bit of feedback information is identical to systems with more feedback bits. Thus, asymptotically in ${\ssr SNR}$, more than one bit of feedback does not improve the system performance at constant rates. Furthermore, the one-bit diversity-multiplexing performance is identical to the system which has perfect channel state information at the receiver along with noiseless feedback link. This achievability uses novel concepts of power controlled feedback and training, which naturally surface when we consider imperfect channel estimation and noisy feedback links. In the process of evaluating the proposed training and feedback protocols, we find an asymptotic expression for the joint probability of the $ {\ssr SNR}$ exponents of eigenvalues of the actual channel and the estimated channel which may be of independent interest.

Original languageEnglish (US)
Article number5484975
Pages (from-to)3310-3331
Number of pages22
JournalIEEE Transactions on Information Theory
Issue number7
StatePublished - Jul 2010


  • Channel state information
  • Diversity multiplexing tradeoff
  • Feedback
  • Multiple access channel
  • Outage probability
  • Power-controlled
  • Training

ASJC Scopus subject areas

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


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