Does the central limit theorem always apply to phase noise? Some implications for radar problems

John E. Gray; Stephen R. Addison

doi:10.1117/12.2262136

1 May 2017 Does the central limit theorem always apply to phase noise? Some implications for radar problems

John E. Gray, Stephen R. Addison

Proceedings Volume 10188, Radar Sensor Technology XXI; 101880O (2017) https://doi.org/10.1117/12.2262136
Event: SPIE Defense + Security, 2017, Anaheim, CA, United States

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 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 (see Gray and Alouani) 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. We mirror Kolmogorov's original proof as discussed in Papoulis to show the CLT can break down for receivers that gather limited amounts of data as well as the circumstances under which it can fail for certain phase noise distributions. We then discuss the consequences of this for matched filter design as well the implications for some physics problems.

Conference Presentation

Citation Download Citation

John E. Gray and Stephen R. Addison "Does the central limit theorem always apply to phase noise? Some implications for radar problems", Proc. SPIE 10188, Radar Sensor Technology XXI, 101880O (1 May 2017); https://doi.org/10.1117/12.2262136

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available