Asymptotic analysis of Rayleigh product channels: A free probability approach

Research output: Contribution to journalArticleScientificpeer-review


Research units

  • Saarland University
  • Friedrich-Alexander University Erlangen-Nürnberg
  • University of Helsinki
  • University of Oslo


The Rayleigh product channel model is useful in capturing the performance degradation due to rank deficiency of MIMO channels. In this paper, such a performance degradation is investigated via the distribution of mutual information assuming the block fading channels and the uniform power transmission scheme. Using techniques of free probability theory, the asymptotic variance of mutual information is derived when the dimensions of the channel matrices approach infinity. In this asymptotic regime, the mutual information is rigorously proven to be Gaussian distributed. Using the obtained results, a fundamental tradeoff between multiplexing gain and diversity gain of Rayleigh product channels under the uniform power transmission can be characterized by the closed-form expression at any finite signal-to-noise ratio. Numerical results are provided to compare the outage performance between the Rayleigh product channels and the conventional Rayleigh MIMO channels.


Original languageEnglish
Article number7802604
Pages (from-to)1731-1745
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number3
Publication statusPublished - 1 Mar 2017
MoE publication typeA1 Journal article-refereed

    Research areas

  • Central limit theorem, Finite-SNR diversity-multiplexing tradeoff, Free probability theory, MIMO, Mutual information, Rayleigh product channels

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