On The Positive Definiteness of Polarity Coincidence Correlation Coefficient Matrix
F. Haddadi, M.M. Nayebi, M.R. Aref · IEEE Signal Processing Letters · 2008
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.