The distribution functions of certain random geometric series concerning intersymbol interference

The author presents some numerical methods for the calculation of the distribution functions of certain random geometric series. The semicontraction mapping approach of A. Huzii and H. Sugiyama (Electron. Commun. Jap.., vol.53-A, p.21-30, 1970) is generalized to give a convergent solution for most cases of interest. Also, initial approximations are discussed based on the moments of the distribution. In particular, the normal approximation seems a useful candidate since it is easy to construct. An alternative technique is outlined based on the Fourier transforms of the density functions. This approach seems to be particularly useful when accurate results are required