1 On The Positive Definiteness of Polarity Coincidence Correlation Coefficient Matrix
Farzan Haddadi, Student Member, M. M. Nayebi, Senior Member, M. R. Aref · 2012
Abstract — Polarity coincidence correlator (PCC), when used to estimate the covariance matrix on an element-byelement 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. Index Terms — Polarity coincidence correlator, elementwise covariance estimate, positive semi-definite.