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On the Scaled Eigenvalue Distributions of Complex Wishart Matrices

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Abstract

The eigenvalue distributions of complex Wishart matrices are critical research issues in random matrix theory (RMT). The scaled eigenvalue (SE) distributions of complex Wishart matrices with finite dimensions are deduced in this paper. The probability density function (PDF) and cumulative distribution function (CDF) of the SE are formulated in the closed-form and coefficient-based expressions. Moreover, the derivative of SE PDF is provided in an exact formulation utilizing the same coefficient vectors. The numerical results verify that the newly proposed SE distributions fit the empirical distributions very well and the dimensions of Wishart matrix can be identified by the derivative of SE PDF.

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Notes

  1. The coefficient matrices/vectors are used in the distributions.

  2. The dimension of \(\mathbf {W}\) is limited to \(M=2\).

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Authors and Affiliations

  1. School of Information Science and Engineering, Shandong University, Jinan, China

    Wensheng Zhang, Hailiang Xiong & Deqiang Wang

  2. School of Microelectronics, Shandong University, Jinan, China

    Di Chen

Authors
  1. Wensheng Zhang
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  2. Hailiang Xiong
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  3. Deqiang Wang
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  4. Di Chen
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Corresponding author

Correspondence to Hailiang Xiong.

Additional information

This work is supported in part by the National Natural Science Foundation of China (Grant No. 61371110, 61401253, 61471222), the Key R&D Program of Shandong Province (Grant No. 2016GGX101014).

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Zhang, W., Xiong, H., Wang, D. et al. On the Scaled Eigenvalue Distributions of Complex Wishart Matrices. Wireless Pers Commun 95, 4257–4267 (2017). https://doi.org/10.1007/s11277-017-4078-6

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  • DOI: https://doi.org/10.1007/s11277-017-4078-6

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