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The performance of two types of digital phase-and amplitude-modulated systems is investigated for the high signal-to-noise ratio region. Approximate expressions for the probability of error and channel capacity of the more optimum of these two systems are compared with corresponding expressions for probability of error and channel capacity for a digital phase-modulated system. It is shown that the phase- and amplitude-modulated systems show a definite power advantage over the phase-only system when the information content per transmitted symbol must be greater than 3 bits. From a channel capacity standpoint, the phase- and amplitude-modulated systems make more efficient use of the channel for signal-to-noise ratios greater than 11 db. The more optimum of the two phase and amplitude systems has only a 3-db advantage over the less optimum and is considerably more difficult to instrument.
Hancock et al. (Thu,) studied this question.