Capacity of Rayleigh fading channels under different adaptive transmission and diversity-combining techniques

Mohamed Slim Alouini, Andrea J. Goldsmith

Research output: Contribution to journalArticlepeer-review

821 Scopus citations


We study the Shannon capacity of adaptive transmission techniques in conjunction with diversity combining. This capacity provides an upper bound on spectral efficiency using these techniques. We obtain closed-form solutions for the Rayleigh fading channel capacity under three adaptive policies: optimal power and rate adaptation, constant power with optimal rate adaptation, and channel inversion with fixed rate. Optimal power and rate adaptation yields a small increase in capacity over just rate adaptation, and this increase diminishes as the average received carrier-to-noise ratio (CNR) or the number of diversity branches increases. Channel inversion suffers the largest capacity penalty relative to the optimal technique, however, the penalty diminishes with increased diversity. Although diversity yields large capacity gains for all the techniques, the gain is most pronounced with channel inversion. For example, the capacity using channel inversion with two-branch diversity exceeds that of a single-branch system using optimal rate and power adaptation. Since channel inversion is the least complex scheme to implement, there is a tradeoff between complexity and capacity for the various adaptation methods and diversity-combining techniques.

Original languageEnglish (US)
Pages (from-to)1165-1181
Number of pages17
JournalIEEE Transactions on Vehicular Technology
Issue number4
StatePublished - 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Automotive Engineering
  • Aerospace Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics


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