Binary orthogonal signaling over the Gaussian channel with unknown phase/fading: new results and interpretations

The problem of binary orthogonal signaling over a Gaussian noise channel with unknown phase/fading is considered. By viewing the problem in a rotated coordinate system, the orthogonal signal structure is considered as the combination of an antipodal signal set and a pilot tone for channel measurement. For data detection the optimum matched-filter envelope-detector is shown to be identical to a novel detector-estimator receiver in which the detector performs partially coherent detection, using an absolute coherent reference generated by the estimator from the channel measurement provided by the pilot-tone component of the orthogonal signal structure. This detector-estimator interpretation shows that it is incorrect to refer to the optimum receiver as a noncoherent receiver. It also leads to the development of new approaches for analyzing the error probability of the receiver. An exponential Chernoff upper bound is obtained for the Rician channel