Two small-SNR classification rules for CPM

The authors address the problem of constructing continuous phase modulation (CPM) classifiers by the likelihood approach. They start from the likelihood functions (LFs) of CPM signals in additive white Gaussian noise, and, based on a small signal-to-noise ratio (SNR) approximate LF, they derive easily implementable classifiers. Two log-LF-based classifiers are proposed. One of them, e(h₁, h₂), is equivalent to an energy comparator; the other, c(h₁, h₂), has a novel form. It is shown that the c(h₁, h ₂) rule performs much better than the e(h ₁,h₂) rule for short observation time., However, the e(h₁, h₂) rule may outperform the c(h₁,h₂) rule for adequately long observation time, since a performance upper bound exists for the c(h₁,h₂) rule, while the performance of the e(h₁, h ₂) rule can be improved by increasing observation time without limits