On the capacity penalty due to input-bandwidth restrictions with an application to rate-limited binary signaling

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 to its capacity with the optimum signals of similar average power. For band-limited channels of bandwidth B, however, the constant-envelope constraints does reduce the capacity, even if the signals themselves are allowed arbitrarily rapid alternations (transitions). Here, using a recently introduced technique, it is shown 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 restrictions can be met, for example, by restricting the average rate of transitions ρ of the binary input signal. It is shown that in this case, ε⩽0.573 ρ/B, which is a result used to upper-bound the capacity for binary signaling under an average-transition-rate constraint