Applications of stochastic ordering to wireless communications

Cihan Tepedelenlioglu, Adithya Rajan, Yuan Zhang

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


Stochastic orders are binary relations defined on probability distributions which capture intuitive notions like being larger or being more variable. This paper introduces stochastic ordering of instantaneous SNRs of fading channels as a tool to compare the performance of communication systems over different channels. Stochastic orders unify existing performance metrics such as ergodic capacity, and metrics based on error rate functions for commonly used modulation schemes through their relation with convex and completely monotonic (c.m.) functions. Toward this goal, performance metrics such as instantaneous error rates of M-QAM and M-PSK modulations are shown to be c.m. functions of the instantaneous SNR, while metrics such as the instantaneous capacity are seen to have a completely monotonic derivative (c.m.d.). It is shown that the frequently used parametric fading distributions for modeling line of sight (LoS) exhibit a monotonicity in the LoS parameter with respect to the stochastic Laplace transform order. Using stochastic orders, average performance of systems involving multiple random variables are compared over different channels, even when closed form expressions for such averages are not tractable. These include diversity combining schemes, relay networks, and signal detection over fading channels with non-Gaussian additive noise, which are investigated herein. Simulations are also provided to corroborate our results.

Original languageEnglish (US)
Article number6042309
Pages (from-to)4249-4257
Number of pages9
JournalIEEE Transactions on Wireless Communications
Issue number12
StatePublished - Dec 2011


  • Error analysis
  • fading channels
  • performance analysis
  • stochastic order

ASJC Scopus subject areas

  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Applied Mathematics


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