On the detection and classification of quadrature digital modulations in broad-band noise

Optimal and suboptimal decision rules for the detection of constant-envelope quadrature digital modulations in broadband noise are derived and analyzed. The effect of various stochastic models for the carrier phase is examined in detail, while no epoch or frequency uncertainty is assumed. The delay-and-multiply type of detector is considered. A new binary/quadrature phase shift keying (BPSK/QPSK) classifier is compared to the more traditional ad hoc techniques of a square-law classifier and a phase-based classifier (weighting on the phase histogram). The new classifier is derived by approximating the likelihood-ratio functionals of phase-modulated digital signals in white Gaussian noise, hence is named the quasi-log-likelihood ratio (qLLR) rule. It is shown analytically that its performance is significantly better than that of intuitively designed phase-based rules or the conventional square-law classifier