Statistical Analysis of Phase-Only Correlation Functions with Phase-Spectrum Differences Following Wrapped Distributions

Shunsuke YAMAKI  Masahide ABE  Masayuki KAWAMATA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.10   pp.1790-1798
Publication Date: 2016/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.1790
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
phase-only correlation functions,  wrapped distributions,  directional statistics,  circular probability distributions,  

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Summary: 
This paper proposes statistical analysis of phase-only correlation functions with phase-spectrum differences following wrapped distributions. We first assume phase-spectrum differences between two signals to be random variables following a linear distribution. Next, based on directional statistics, we convert the linear distribution into a wrapped distribution by wrapping the linear distribution around the circumference of the unit circle. Finally, we derive general expressions of the expectation and variance of the POC functions with phase-spectrum differences following wrapped distributions. We obtain exactly the same expressions between a linear distribution and its corresponding wrapped distribution.