Channel Hardening of IRS-Aided Multi-Antenna Systems: How Should IRSs Scale?

Ali Bereyhi, Saba Asaad, Chongjun Ouyang, Ralf R. Muller, Rafael F. Schaefer, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


It is widely believed that large IRS-aided MIMO settings maintain the fundamental features of massive MIMO systems. This work gives a rigorous proof that confirms this belief. We show that using a large passive IRS, the end-to-end MIMO channel between the transmitter and the receiver always hardens, even if the IRS elements are strongly correlated. For fading direct and reflection links between the transmitter and the receiver, our derivations demonstrate that for a large number of reflecting elements on the IRS, the capacity of the end-to-end channel is accurately approximated by a real-valued Gaussian random variable whose variance goes to zero as the number of IRS elements grows unboundedly large. The order of this drop depends on how the physical dimensions of the IRS grow. We derive this order explicitly. Numerical experiments show that the closed-form approximation very closely matches the histogram of the capacity term, even in practical scenarios. As a sample application of the results, we characterize the dimensional trade-off between the transmitter and the IRS. The result is intuitive: For a target performance, the larger the IRS is, the fewer transmit antennas are required.

Original languageEnglish (US)
Pages (from-to)2321-2335
Number of pages15
JournalIEEE Journal on Selected Areas in Communications
Issue number8
StatePublished - Aug 1 2023

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


  • Reconfigurable intelligent surface
  • asymptotic channel hardening
  • ergodic capacity
  • large-system analysis
  • outage probability


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