An Upper Bound on the Performance of Pulse Modulation Systems

A lower bound is found on the mean square error achievable by any nonlinear pulse modulation system without memory. This bound differs by 6 dB from the limit given by Shannon theorems, at high signal-to-noise ratios. The bound is obtained by finding the signal locus which minimizes a simple lower bound on mean square error, for a given average signal energy and without bandwidth constraints. For the locus that we have found, an upper bound on error shows that the degradation with respect to Shannon´s limit is within 8 to 9 dB. The locus, however, does not seem of practical interest.