Capacity analysis of asymmetric multi-antenna relay systems using free probability theory

Lucinda Hadley, Zhijin Qin, Zhiguo Ding

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


Random matrix theory (RMT) has been used to derive the asymptotic capacity of multiple-input-multiple-output (MIMO) channels by approximating the asymptotic eigenvalue distributions (AEDs) of the associated channel matrices. A novel methodology is introduced which enables the computation of the asymptotic capacity for a generalised system in which two relays cooperate to facilitate communication between two remote devices. It is computationally demanding to calculate this capacity using RMT when nodes are equipped with large-scale antenna arrays, and impossible in the case where asymmetry exists between channels within the system. This is because deriving the capacity across the combined channels from the relays to the receiver involves polynomials in large and non-commutative random matrix variables. This paper uses free probability theory (FPT) as an efficient alternative tool for analysis in these circumstances. The method described can be applied with no additional complexity for arbitrarily large antenna arrays. The minimum SNR required to achieve a given asymptotic capacity is computed and the simulation results verify the accuracy of the FPT approach.

Original languageBritish English
Title of host publication2019 IEEE 89th Vehicular Technology Conference, VTC Spring 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728112176
StatePublished - Apr 2019
Event89th IEEE Vehicular Technology Conference, VTC Spring 2019 - Kuala Lumpur, Malaysia
Duration: 28 Apr 20191 May 2019

Publication series

NameIEEE Vehicular Technology Conference
ISSN (Print)1550-2252


Conference89th IEEE Vehicular Technology Conference, VTC Spring 2019
CityKuala Lumpur


  • Capacity
  • Co-operative relay
  • Eigenvalue distribution
  • Massive mimo
  • Operator-valued free probability theory
  • Random matrix theory


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