On the difference of two sums of independent generalized gamma random variables with applications to error performance analysis and outage probability evaluation

The difference D of two sums of independent generalized gamma random variables is considered. The cumulative distribution function F_D(x) of D could be obtained directly from its PDF. Of particular interest to us is the value of F_D (0) which could be used to derive the error probability and outage probability of a communication system. In the error probability analysis for a variety of communication systems, the probability of error is given by P[D ≤ 0], where D is the decision variable which is a Hermitian quadratic form in complex-valued Gaussian random variables. As another application, we consider a cellular mobile radio system in which the desired and interfering signals are received over independent slowly-varying generalized gamma fading paths and the desired signal is independent of the interfering signals. The outage probability is defined as the probability that the carrier-to-interference power ratio falls below a predetermined threshold. The received desired or interfering signals need not be identically distributed and are not limited to be Rayleigh, Ricean, or Nakagami distributed; rather, each is allowed to be generalized gamma distributed.