Envelope-based classification schemes for continuous-phase binary frequency-shift-keyed modulations

Proposes two envelope-based schemes for classifying the index pattern of the full-response continuous-phase binary frequency-shift-keyed signal in broadband Gaussian noise. Both single-h and multi-h modulations are considered. When the set of index patterns is given and finite, one soft-decision scheme, referred to as the sum-of-squared-envelopes (SOSE) scheme, is proposed. This scheme combines successive squared envelopes over N symbols, and compares the combined statistic to thresholds for M-ary classification. By appropriately adjusting the thresholds, the SOSE scheme is able to classify a variety of candidate modulation sets. The classification performance is analyzed in terms of the probability of incorrectly classifying the received signal. It is shown that the SOSE scheme is adequate for M-ary classification of a large index set. When the set of index patterns is not finite, a classifier, which operates on the SOSE test statistic, is proposed to provide an approximate maximum-likelihood estimate of the index pattern. A Gaussian approximation analysis are developed to characterize its estimation performance. Numerical results show that this index estimator is asymptotically unbiased and consistent