Generalized quadratic receivers for orthogonal signals over the Gaussian channel with unknown phase/fading

The orthogonal signal structure has been shown to be the superposition of an antipodal signal set and an unmodulated (pilot tone) component which can be used for channel measurement. Starting from this point of view, the quadratic receiver for orthogonal signals over the Gaussian channel with unknown phase/fading has been shown to be equivalent to a detector-estimator receiver. The estimator makes an optimum estimate of the unknown complex channel gain based on the channel measurement provided by the unmodulated component of the received signal. This channel estimate then forms a (partially) coherent reference for the detector in detecting the data carried by the antipodal signaling component of the received signal. This paper exploits this detector-estimator structure of the quadratic receiver, and generalizes it to a receiver in which the estimator makes an estimate of the channel gain in each signaling interval based on the totality of signals received over all the signaling intervals or a subset of these intervals. The generalized quadratic receiver is just as simple to implement as the conventional quadratic receiver, and theoretical and simulation results show that it can achieve substantial performance gains over the conventional receiver. A theory is presented to show that the generalized quadratic receiver is an implementable approximation to the optimum symbol-by-symbol receiver for uncoded orthogonal signals over the Gaussian channel with unknown phase/fading. The theory shows that the structure provides a unified and systematic approach to the design of coherent symbol-by-symbol receivers, and shows that the conventional carrier-loop-type receivers are ad hoc