The analysis of digital communication systems by moment space methods

An approach utilizing moment space geometry for bounding generalized moments of random variables is developed. Upper and lower error bounds for the linear pulse amplitude modulation system with bounded intersymbol interference and additive Gaussian noise are derived. These depend upon the absolute moment, the second moment, and an exponential moment of the intersymbol interference random variable. The exponential moment bounds are found to form a family of upper and a family of lower bounds, each family parameterized by an arbitrary real valued number, which permits a trade off between computational complexity and the tightness of the consequent bounds. As an application of the approach to the analysis of nonlinear systems, upper and lower error bounds for a coherent phase-shift-keyed system comprised of a cascade of an arbitrary number of bandpass hard limiters are derived.