It is well known that in cases of unlimited channel bandwidth and unconstrained signal spectrum, a constant-envelope constraint on the signal does not reduce the capacity of an additive Gaussian channel, as compared with the capacity with the optimum signals of similar average power. For band-limited channels of bandwidth B, however, the constant-envelope constraint does reduce the capacity, even if the signals themselves are allowed arbitrarily rapid alternations (transitions). Here, using a recently introduced technique [1], we show that the capacity is further drastically reduced if, in addition to the channel limitation, the constant-envelope signal is itself restricted to a small fractional out-of-band power ε. Ideal lowpass and bandpass channel filters are considered, and upper bounds on the capacity are derived. The out-of-band power restriction can be met, for example, by restricting the average rate of transitions p of a binary input signal. It is shown that in this case, ε≤0.573p/B, which is a result used to upper bound the capacity for binary signaling under an average-transition-rate constraint. © 1990 IEEE
