Moments of Complex Gaussian Ratios

We study the moments of general complex Gaussian ratios (CGRs), whose numerator and denominator are correlated and have arbitrary mean. In particular, we calculate the mean of these ratios in a closed form and prove that the mean-square and higher order absolute moments are unbounded in general. Then, we show that the earlier results generalize existing results in the literature and apply the mean of general CGR in a novel problem of antenna impedance estimation at single-antenna receivers.