Keywords
Phase noise, central limit theorem, radar, characteristic function
Abstract
The phase noise problem (or Rayleigh problem) occurs in all aspects of radar. It is an effect that a radar engineer or physicist always has to take into account as part of a design or in an attempt to characterize the physics of a problem such as reverberation. Normally, the mathematical difficulties of phase noise characterization are avoided by assuming the phase noise probability distribution function (PDF) is uniformly distributed, and the Central Limit Theorem (CLT) is invoked to argue that the superposition of relatively few random components obey the CLT and hence the superposition can be treated as a normal distribution. By formalizing the characterization of phase noise for an individual random variable, the summation of identically distributed random variables is the product of multiple characteristic functions (CF). The product of the CFs for phase noise has a CF that can be analyzed to understand the limitations CLT when applied to phase noise.
Recommended Citation
Gray, John E. and Addison, Stephen R.
(2023)
"The Rayleigh Problem (Random Flights) is Everywhere Redux,"
Journal of the Arkansas Academy of Science: Vol. 77, Article 2.
https://doi.org/10.54119/jaas.2023.7701
Available at:
https://scholarworks.uark.edu/jaas/vol77/iss1/2
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