Comments on "A Comparison of Several Types of Modulation"

In the above-named work it is argued that Weaver [ibid., vol. CS-I0. pp. 91l-101, March 1962] uses the criterion of error probability to compare several PCM modulation- demodulation schemes. His curves of error probability vs. signal-to-noise ratio for maximum likelihood detection of PCM-AM and discriminator detection of PCM-FM differ markedly from other published results. In both cases, the differences result from computing the error probability from an approximated Gaussian distribution at the detector output. Most Gaussian approximatious are valid in a region centered about the mean and are not valid for the tails of the distribution. Error probabilities are obtained by integrating over a region in the tail of the distribution. Small deviations in the tails of a distribution can result in large differences in error probability. Hence, the tails of the approximating distribution must closely approach the tails of the true distribution for a valid approximation. That this is not the case is illustrated by the divergence between Weaver's results and other published results based on the exact distribution.