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Daniel Gaetano Riviello1, Giusi Alfano2, Roberto Garello2

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This summary is machine-generated.

This study analyzes quadratic forms using random matrix theory for wireless communications. It provides key formulas for performance analysis in spectrum sensing and multi-antenna systems.

Keywords:
6Gcognitive radiosmulti-antennaquadratic formsrandom matrix theoryspectrum sensing

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Area of Science:

  • Multivariate Statistics
  • Random Matrix Theory
  • Wireless Communications

Background:

  • Quadratic forms with random kernel matrices are essential in diverse fields like signal processing and wireless communications.
  • Statistical characterization of these forms is vital for design and performance analysis.

Purpose of the Study:

  • To characterize quadratic forms with unitarily invariant and non-unitarily invariant random kernel matrices.
  • To derive closed-form expressions for performance analysis in wireless systems.

Main Methods:

  • Exploiting advancements in spectral characterization from polynomial ensembles.
  • Analyzing quadratic forms in unit-norm vectors with random kernel matrices.
  • Utilizing simulations for a spectrum sensing application scenario.

Main Results:

  • Provided closed-form expressions for the moment generating function of quadratic forms.
  • Offered approximate but numerically accurate results for non-unitarily invariant kernel matrices.
  • Enabled analytical performance analysis for spectrum sensing schemes.

Conclusions:

  • The derived expressions facilitate analytical performance assessment of spectrum sensing.
  • This work aids in the rate analysis of multi-antenna systems.
  • Random matrix theory offers powerful tools for characterizing complex statistical models.