On The Positive Definiteness of Polarity Coincidence Correlation Coefficient Matrix

Details On The Positive Definiteness of Polarity Coincidence Correlation Coefficient Matrix On The Positive Definiteness of Polarity Coincidence Correlation Coefficient Matrix

2009-01-29

arxiv.org/abs/0901.4648v1

Computer Science

Information Theory

IEEE Signal Processing Letters, Volume 15, pp. 73-76, 2008

Scientific paper

10.1109/LSP.2007.911193

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. [1], 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<=3 and for complex signals with p<=2, a PSD estimate is guaranteed. Counterexamples are presented for higher dimensions which yield invalid covariance estimates.

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