Outage Probability Analysis of Uplink Cell-Free Massive MIMO Network With and Without Pilot Contamination

Shashank Shekhar*, Muralikrishnan Srinivasan, Sheetal Kalyani, Mohamed Slim Alouini

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper derives approximate outage probability (OP) expressions for uplink cell-free massive multiple-input-multiple-output (CF-mMIMO) systems with and without pilot contamination. The system's access points (APs) are considered to have imperfect channel state information (CSI). The signal-to-interference-plus-noise ratio (SINR) of the CF-mMIMO system is approximated via a Log-normal distribution using a two-step moment matching method. OP and ergodic rate expressions are derived with the help of the approximated Log-normal distribution. For the no-pilot contamination scenario, an exact expression is first derived using conditional expectations in terms of a multi-fold integral. Then, a novel dimension reduction method is used to approximate it by the sum of single-variable integrations. Both the approximations derived for the CF-mMIMO systems are also useful for single-cell collocated massive MIMO (mMIMO) systems and lead to closed-form expression. The derived expressions closely match the simulated numerical values for OP and ergodic rate.

Original languageEnglish (US)
Pages (from-to)168-184
Number of pages17
JournalIEEE Open Journal of the Communications Society
StatePublished - 2024


  • Cell-free massive MIMO
  • outage probability
  • univariate dimension reduction

ASJC Scopus subject areas

  • Computer Networks and Communications


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