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.