Statistical Analysis of Phase-Only Correlation Functions between Real Signals with Stochastic Phase-Spectrum Differences

Shunsuke YAMAKI  Masahide ABE  Masayuki KAWAMATA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.5   pp.1097-1108
Publication Date: 2017/05/01
Online ISSN: 1745-1337
Type of Manuscript: PAPER
Category: Digital Signal Processing
Keyword: 
phase-only correlation functions,  real signals,  odd-symmetry,  characteristic functions,  trigonometric moments,  

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Summary: 
This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have odd-symmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions considering the odd-symmetry of the phase-spectrum differences. As a result, the expectation and variance of the POC functions can be expressed by characteristic functions or trigonometric moments of the phase-spectrum differences. Furthermore, it is shown that the peak value of the POC function monotonically decreases and the sidelobe values monotonically increase as the variance of the phase-spectrum differences increases.