Title :
On The Positive Definiteness of Polarity Coincidence Correlation Coefficient Matrix
Author :
Haddadi, F. ; Nayebi, M.M. ; Aref, M.R.
Author_Institution :
Sharif Univ. of Technol., Tehran
fDate :
6/30/1905 12:00:00 AM
Abstract :
Polarity coincidence correlator (PCC), when used to estimate the covariance matrix on an element-by-element basis, may not yield a positive semi-definite (PSD) estimate. Devlin et al. (Devlin, 1975) claimed that element-wise PCC is not guaranteed to be PSD in dimensions p > 3 for real signals. However, no justification or proof was available on this issue. In this letter, it is proved that for real signals with p les 3 and for complex signals with p les 2, a PSD estimate is guaranteed. Counterexamples are presented for higher dimensions which yield invalid covariance estimates.
Keywords :
correlation methods; covariance matrices; PSD estimate; covariance matrix; polarity coincidence correlation coefficient matrix; positive definiteness; positive semi-definite estimate; Computational complexity; Correlators; Covariance matrix; Radio astronomy; Random variables; Robustness; Strips; Yield estimation; Element-wise covariance estimate; polarity coincidence correlator; positive semi-definite;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2007.911193
