Standard Condition Number Distributions of Finite Wishart Matrices for Cognitive Radio Networks

Wensheng Zhang, Jiajia Wang, Jian Sun, Cheng-Xiang Wang, Xiaohu Ge

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


The standard condition number (SCN) in random matrix theory (RMT) has widely been employed in cognitive radio networks (CRNs). The paper studies the SCN distributions of central and complex Wishart matrices with finite dimensions. The exact and closed-form expressions of SCN distributions are first proposed in sum of multiple polynomials. The proposed formulations provide an efficient way to determine probability density function (PDF) and cumulative distribution function (CDF) of the SCN in finite RMT (FRMT). In particular, the specific SCN distributions of triple Wishart matrix are initially presented. The theoretical and precise sensing thresholds for cooperative spectrum sensing (CSS) systems in CRNs are calculated using the proposed SCN distributions. Numerical results indicate that the proposed theoretical SCN distributions match the empirical SCN distributions very well. Furthermore, the exact SCN-based CSS systems are able to obtain higher sensing performance than the asymptotic SCN-based schemes because precise sensing thresholds can be determined.

Original languageEnglish
Pages (from-to)4630-4634
Number of pages15
JournalIEEE Transactions on Vehicular Technology
Issue number5
Early online date29 Nov 2017
Publication statusPublished - May 2018


  • Cascading style sheets
  • Cognitive radio
  • cognitive radio networks
  • Eigenvalues and eigenfunctions
  • Probability density function
  • random matrix theory
  • Sensor systems
  • spectrum sensing
  • Standard condition number
  • Standards
  • Wishart matrix

ASJC Scopus subject areas

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


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