Modem constellation identification: a performance comparison of two methods

Two algorithms are described for determining the signal constellation quadrature amplitude modulation in use on a (QAM) modulator, one based on Radon transform ideas and the other based on histogramming received signal radius information. The detection performances of the two specific algorithms are compared as a function of the signal-to-disturbance power ratio and the number of samples available. Generally speaking, it is shown that, when the carrier frequency is known with reasonable accuracy, the Radon transform method performs much better than the specific radius- or magnitude-only method tested, in the sense that for the same signal-to-disturbance ratio the former can reliably determine the constellation size and orientation with about one-tenth of the data samples required by the latter. It should be noted, however, that neither of the two algorithms has been optimized, nor have the comparisons taken into account other issues such as the details of particular applications, the relative computational requirements, and the added complexity needed by the Radon transform method to deal with uncertainties in the carrier frequency