  This paper proposes a novel approach to the statistical characterization of
non-central complex Gaussian quadratic forms (CGQFs). Its key strategy is the
generation of an auxiliary random variable (RV) that converges in distribution
to the original CGQF. Since the mean squared error between both is given in a
simple closed-form formulation, the auxiliary RV can be particularized to
achieve the required accuracy. The technique is valid for both definite and
indefinite CGQFs and yields simple expressions of the probability density
function (PDF) and the cumulative distribution function (CDF) that involve only
elementary functions. This overcomes a major limitation of previous approaches,
in which the complexity of the resulting PDF and CDF prevents from using them
for subsequent calculations. To illustrate this end, the proposed method is
applied to maximal ratio combining systems over correlated Rician channels, for
which the outage probability and the average bit error rate are derived.
